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Vol.47 No.2
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2023

Review: MSJ Awards 2022
Research on Spintronic Functions of Non-Metallic Materials and Its Modulation by External Fields
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M. Shiraishi…28

Measurement Technique, High-frequency Devices, Magnetic Imaging
Improvement of GHz Range Electromagnetic Properties of Ferrite Thin Film Magnetic Core Integrated RF
Inductor

T. Nakano, S. Miyazaki, Y. Ozaki, K. Koike, and D. Inokuchi…38

Power Magnetics

Reluctance Network Model of IPM Motor Representing Dynamic Hysteresis Characteristics for High-Accuracy
Iron Loss Calculation Considering Carrier Harmonics
Y. Hane, and K. Nakamura…42

H. Yano, and K. Sugahara…52

Magnetic Moment Method with the Idea of Magnetic Surface Charge Method

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47

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Electronic Journal: http://www.jstage.jst.go.jp/browse/msjmag

2

2023

INDEX

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INDEX

Journal of the Magnetics Society of Japan
Vol. 47, No. 2
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

CONTENTS
Review: MSJ Awards 2022
Research on Spintronic Functions of Non-Metallic Materials and Its Modulation by External Fields………………………………………………………………………………………………………… M. Shiraishi

28

Measurement Technique, High-frequency Devices, Magnetic Imaging
Improvement of GHz Range Electromagnetic Properties of Ferrite Thin Film Magnetic Core Integrated
RF Inductor……………………………………………… T. Nakano, S. Miyazaki, Y. Ozaki, K. Koike, and D. Inokuchi

38

Power Magnetics
Reluctance Network Model of IPM Motor Representing Dynamic Hysteresis Characteristics forHigh-Accuracy Iron Loss Calculation Considering Carrier Harmonics……………………………………………………………………………………… Y. Hane, and K. Nakamura

42

Magnetic Moment Method with the Idea of Magnetic Surface Charge Method………………………………………………………………………………………… H. Yano, and K. Sugahara

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52letters to nature
Copyright ©2023 by the Magnetics Society of Japan.

This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/
45many times without any apparent degradation. After neat cleaning 10 –10 Q that depends on the deposition rate and thickness of theusing acetone, the LSMO was introduced into the evaporation Co electrode; such resistance is also consistent with a dominant
J. Magn.
47, 28-37
chamberwith aSoc.
baseJpn.,pressureof 5 £(2023)
1027 torr, where the OSE pinhole-free organic spacer. Devices with d , 100 nm,<Review>
however,film (Alq3) was thermally evaporated. Without breaking the vac- showed a linear I–V response and lack of both conductivity detected
uum, we then depositedandeelectroluminescence,
Resa ethinar(3–6ch nm)
oncobaltspin(Co)
trofilm
nifollowed
c functmagnetic
ions oresonancef n o n -m
tallic materileading
als us to believe
by an aluminium (Al) contact, using a shadow mask. The obtained that these devices have an ‘ill-defined’ layer of up to 100 nm thata n d it s m o d u la t io n b y e x t e r n a l f ie ld s
active device area was about 2 £ 3 mm2. We have fabricated several may contain pinholes and Co inclusions. These findings suggest thatspin-valve devices with various OSE thicknesses d, between 130 to the OSE spacers in the spin-valve devices fabricated with
250 nm. The OSE thickness was measured by an in situ thickness d . 100 nm may be composed of two sublayers: one sublayer
monitor and independently confirmed outside the chamber M.
by Shiraishi
with a thickness d 0 of the order of 100 nm immediately below thescanning electron microscopy and thickness profilometry, Co electrode that contains Co inclusions owing to the interdiffuDepartment of Electronic Science and Engineendring, Kyoto University,
Kyoto-Daigaku-Katsura, Nishikyo-ku, Kyoto 615-8510, Japan.

Current (µA)

shown in Fig. 1c. In the rigid band approximation—that is, without which carrier transport is dominated by carrier drift.
taking intoNon-metallic
account the relaxation
andsuchpolarizationenergy associ- semiconductors
The magnetoresistanceof the fabricatedwas measured
materials,
as inorganic/organicand topologicalquantumdevices
materials
are now
ated with charge injection—the highest occupied molecular orbital in a closed-cycle refrigerator from 11 to 300 K by sending acollecting significant attention in modern spintronics. The progress of the research field using the materials is quite(HOMO) of Alq3 lies about 0.9 eV below the Fermi levels, E F, of the current through the two interfaces, while varying an external
rapid andwhereas
tremendous
amountsof significant
been magnetic
published.
In Hthisreview
article,someloops
important
FM electrodes,
the lowest
unoccupied
molecularstudies
orbital havein-planefield,(Fig.
1a). Thehysteresisof themilestone
works
areintroduced
toenhancefurther
accelerationoftheresearchfields.
(LUMO) lies about 2.00 eV above E F (refs 14, 15). At low applied magnetization versus H for the FM electrodes were measured bybias voltages V, holes are injected from the anode into the HOMO
level ofby tunnellingthrough the bottom
potential
Kethe
y OSE
wordmainlys: Organic
semiconductors,
graphene,
inorganic semiconductors, silicon, topological insulator, Weyl
barrier.
In addition, Weyl
the similar
work function
value f ofthemanipulation,twoferromagnet,
semimetal,
spin injection,
spin
gating effectelectrodes (Fig. 1c) leads to a symmetric current–voltage I–V
response (Fig. 1d). For fabricated devices with d . 100 nm we
found that the I–V characteristic
waswith a weak
1. Introd
uctinonlinearon
temperature dependence (Fig. 1d), indicative of carrier injection
by tunnelling.
devices withsimilar
OSE thickness, in which
Since Control
the discovery
of giant
magnetoresistanceeffect,ITO replacedtheLSMObottomelectrode,the field of spintronics has been showed
rapidlyelectroluminesexpanding. As
cencetheand alsofirst-generationa conductivity detectedmagnetic resonanceat g < 2materialinspintronics,(see Supplementary Information), indicating carrier injection into
ferromagnetic and nonmagnetic metals have been and is
the OSE. In addition, at low V we measured a typical resistance ofstill now playing the central role. Meanwhile, inorganic
semiconductors have been collecting significant attention
as the second-generation material in spintronics since
the advent of diluted ferromagnetic semiconductor andbaspin transport
in semiconductors. In the 21st century,Vnovel materials systems
such as organic molecules,ihetero-interfaces, atomicallyVacuum
flat materials
200 nm and
Co/Al rising stars
topological FM
quantummaterials
arebecoming
2
Alq3
Co/Al
of materials
Attractivenessof nonOrganic in spintronics.
LSMO
Alq3
O
Fig. 1 Two-terminal magnetoresistance in a
metallic materials
inspintronics
is,forexample,M
LS
Substrate
FM1
Co/Alq3/LaSrMnO spin valve (ref. 2)). Notable is anpotentialfor
spin
modulation
byexternal
fieldssuchasSubstrate
observation of negative magnetoresistance.
an electricfield,
longspin
coherence
and
so
on.
In
this
H
in spintronics usingdc review article, significant milestones
magnetoresistance in an electric local two-terminal
Vacuum levelsuch non-metallic materials 6 including the author’s
method strongly hampers precise detection of spinachievements
for the MSJ Award 2022 are introduced,
Ip = 5.7 eVtransport signals, and sufficient elimination of spin3
φLSMOalbeit= 4.8 eVnot
all of theφConotable
294 K= 4.9 eV studies cannot be introduced
LUMO
tunneling in molecules was not realized. Furthermore,
0250 K
because the field is rapidly expanding, and tremendous
200 K
long-term problems were missing of the Hanle-type spin
2.8
eV
EF
EF
110 K
–3
amounts of works have been
implemented.
11 K
precession and non-local four-terminal spin transport in
–6

HOMO

2. Spintronic function of m–0.6
olecu–0.3
lar m
ials0.6
0.0ate0r.3

most of works using molecules, where both achievements

providesteadfast evidenceof OSE
successful
spin a,transport,
Figure2 The magneto-transport
response of thespin-valve devices.
GMR loop of(3.5 nm)devicemeasuredat 11 K. Thea LSMO(100 nm)/Alq
albeita trialto nm)/Co
explainthespin-valve
missing
was
unsuccessfully
3 (130
Attractivenessof molecularmaterials
in spintronics
Figure 1 The
structure and transport
properties of thefabricated organic
spin-valve is blue implemented(red) curve denotes GMR
measurements
made
while
increasing (decreasing)H. The3). Theproblemalso
indicates
the difficulty
its
small
spin-orbit
interaction(SOI)
attributed
to its anti-parallel (AP) and parallel (P) configurations of the FM magnetization orientations aredevices. a, Schematic representation of a typical device that consists of two FM electrodes
in estimating precise spin lifetime in molecules, and mostlightness,allowsexpectingFM2) and an which
OSE spacer.
Spin-polarized
electricalgood
currentspin
I flowscoherence.
from FM1(FM1 andshown in the insets at low and high H, respectively. The electrical resistance of the deviceof the works utilized a method of gap-dependence of spin
(LSMO),Thus,
through molecular
the OSE spacer materials(Alq3), to FM2 (Co)when a positive
bias Vattention
is applied. Anin is higher when the magnetization directions in FM1 and FM2 films are parallel to each
attracted
muchsignals
insteadtheofHanle
However, to note isin-planethe
magnetic
field,
H,
is
swept
to
switchthemagnetization
directions
of
the
two
FM
other.
b, The GMRvalue of aofseries
LSMO/Alqmethod.
st
3/Co devices with different d. The line fit
beginning of 21 century. In the advent of thethat
thepoints
gap-dependence-likecan equation
be obtained
the data
was obtained using the spinresults
diffusion model,(1), withelectrodes separately. b, Scanning electron micrograph of a functional organic spin-valve 1) throughresearch field, magnetoresistance in sexithienyl (T6)
adjustable
as explained in the
text. All devicesSince
were fabricatedconsisting of a 60-monolayer-thick
LSMO film, a 160-nm-thick Alq3 spacer, a 3.5-nm- threeeven
inparameters,
spin-dependent
tunneling.
moston theof2)and Alq3 were reported by using a conventional electric
thick Co electrode and a 35-nm-thick Al electrode. c, Schematic band diagram of the OSE samemolecular
LSMO film. c, Magnetic
hysteresisare
loops measured
using MOKE formaterials,
the LSMO
materials
low-conductive
method,of whichmagnetoresistanceand spin
Co film transport
deposited on Alq
asdevice two-terminalin the rigid band approximation
showing
the Fermi levels
and the work functions of(in electrode(H c1 < 30 Oe), of
3 under the same conditions
identification
mechanisms,
i.e., spin
is shown
1. Meanwhile,
as widelylevels
recognized
the twoAlq3)
FM electrodes,
LSMOinandFig.
Co, respectively,
and the HOMO–LUMO
of Alq3. that for the Co electrode in the actual spin-valve devices (H c2 < 150 Oe). These coercive
injection into molecules or spin-dependent tunneling via
d, I–V response
ofpresent,
the organic spin-valve
device with d ¼ 200 nm
atsuperpositionof at several
anisotropic fields are seen in a when the resistance switches from parallel to the anti-parallel
molecules,
difficult if spin transport in moleculartemperatures.
configuration,and viceisversa.
LSMO

Alq3

Co

Voltage (V)materials would be successfully realized. Thus, the822

Corresponding author: M. Shiraishi(e-mail: shiraishi.masashi.4w@kyoto-u.ac.jp).

28

NATURE | VOL 427 | 26 FEBRUARY 2004 | www.nature.com/nature©2004 Nature PublishingGroupresearch topics of the field with sufficient
centralreliability is an interesting and unique physical featureof spin-dependent tunneling via molecules, where exotic

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

INDEX

PHYSICAL REVIEW B 76, 214414 2007 ZHENYAO TANG et al.

0

gap

Py

Pd

(b)

SLG

SiO2 subAlq3-Co (v(vCo = 29%) 5
C60-CoNATURE(vCo = 18%)(v
MATERIALS DOI: 10.1038/NMAT3634

00
5 10 15 20 25
a
4
LETTERS Electric field [10 V/m](c)

1

SLG #1
SLG #2

θ =0

(d)
5 µV

dI(H)/dH (a.u.)

Al

(e)

5µ V

V (µV)

4

10

(b)

(a)

H

dI(H)/dH (a.u.)8(a)Intensity

15

MR ratio (C60-Co) [%]T = 4.2 K 20

12

PHYSICZHENYAO TANG et al.

(b)

(a)

MR ratio (Alq3-Co) [%]Co intersults due
iameters
ometers
particles
ter case,rom that
the MR.
sly beentemperanfluence
ase with
nanoparotal sur-

INDEX

G

D

1000

-1

2D

1500

2000

0

2500

3000

-40
-20
0
20
40
-40
-20
-1
with themicrowave
excitation
power
P0 (mT)
as 20s
Raman
H-H(mT)shift (cm )H-H
isconsistentwiththeprediction
of
the
spi
NATURE | Vol 448 | 2 August 2007
FIG.
4. (Color
online)on spinsample.
pumping andspintransport in sample
2. (
FIG.
1.
(Coloronline)(a) Atransport
schematic imageof theSLG
spin Results
pumping
The
CVD-grown
SLG
Y
Fe
O
film;
the
spin
pumping
intensity
F
i
g
.
4
(a)
Spin
deviceusing
single-layer
3512, and (c) 180 under the
microwave powerof 200 mW. where(d)–(f) Electibe (a)
0 , (b) 90single-layer
Fig.
4 (Left)
Spintransportaredevice
usinggraphene(SLG),
and
the
Al/Py
and
the
Pd
electrodes
separately
evaporated
on
the
SLG.
The
angle
of
the
externalFig.
2
Tunnelmagnetoresistanceinmolecule-Co
,
(e)
90
,
and
(f)
180
under
the
microwave
power
of
200
mW.
Electrom
to
be
(d)
0
FIG. 5. Color online A comparison of applied bias-voltage
numberofexcitedmagnons,or
microwave
graphene(SLG),
where theNiFe(Py)spinspin
sourcePd
PEDOT:PSS
solutiondynamical
injection.
However,theandsignalweakareand noisy.
The
red solid(b)Ramanspectraof theSLG
just after
The
black
and
red
solidwas
lines
from
sam
sourceandPd
spin
current
detector
aretheequipped
separately
andandataexternalmlobserved
To investigate
dependenceof thesignal
on3-Cothe electrodesepaand theantiparallela negativeone.
Insynthesis.
Fig.
3c
gate
voltageV
nanocomposite
systems(ref.
5)).
Eq. (2).
g the ferromagnetic
dependenceof MRtheratioin C60-Co
andAlq
Ref. 32
nano-value
Althoughthecan
shape
of
reson
spinRamancurrent
detectorareequipped
separately
andansymmetric
peaks
of
the
G
and
2D
bands
from
SLG
be
seen.
The
D
band
can
be hardly seOOOOrationat
77
K,
we
preparedandmeasureddevices
2
and
3,
in
which
dependenceofthegraphene
resistanceisplotted.
The
typicalshapeforlained ascomposites measured at 4.2 K.
film
is appliedcomplicatedto2 substrate
the presence
appliedtolayers
ferromagnetic
resonanceof ofthe(Right)
The
upper
pa
(a black
defectof sample
1 exciteis lessthat of sample(c)spectrathetoPy.
Pyowing
onexcitethe SiO
external
magnetic
field
isFMR
enhancement
magnetoresistance
ratio
was
discoveredgraphene strips of
2 mmwide were used. On eachdevicea sequenceofsinglegrapheneisthanobserved,
witha 2.slightly
shifted√ neutrality
magnetic
exponent
g γ ofh h̄[4πMγlinewidth+ (4πM) γcommonly+4ω
] be seen, foundS
S
resonances,
as
for
this
mate
substrate
(a
red
solid
line,
sample1).
Anincrease
the
can
which
is
attributed
toas4-7)ferromagnetic, whereh loweris the microwave
withthemonotonicallyincreasingO 1spacings
andpointferromagnetic
atferromagnetic
Vg 5 19S V, wheretheresistivity
reachesaPy.
maximumof] 3.2
kV
resonanceof thefrom
(b)
upper
8πα [(4πM) γ The+4ω
resonance
spectrumthePy
andthepanelpanel shows(see Fig. contacts2), until
era of graphene
spintronics.
the abovee5 2nnamely,spin
pumping into
theS SLG.
ect is almagnetic
field, set
to 0.16mTisat a microwave
power ofthevoltagesignalexhibitsapredominantlysym
Y 3Felsewhereis estima
different
widthswere
deposited.
We willgive
details(manu(ref.
1).
A
comparison
between
Fig.
3c
and
Fig.
3b
shows
that
there
curves
for
C
-Co


=
18%

and
for
Alq
-Co


60 were someCo
3GwithCoshows theO ferromagnetic
resonancethe
200 mW. As spectrum
discussed above, fromthe broadening
W in theAlthoughthere
contributions facing
a 5O 12forthe
sameg
force
fromsignal
the Pd.
The
external
magnetic
field
is ofattributed
appliedat theq =0.
ponents,
O spinscript in preparation). We summarize the spin signals asGfollows:theresonance
field,
asexpected
for atovoltage
only electromotive
aOsmallOdecreaseof theat theDiracpoint. with
Py/SLG
comparedthat in thePyfilm waswhere th=remaining29%
 measured
atresistance
4.2 K. was
Coulomb
energyEV;Cd3forof1 the
Co
8)
↑↓
Py
and
the
lower
panel
shows
a
concomitant
17,20,
seriousproblems
inmolecular
spintronics
spacing
350
nm,
the
31
V;
for
550
nm,
35
mm,
spinthepumping
into theSLG andgr in the Py/SLG. layer was
Next,
we
present
room-temperature
Hanle-type
spin
precession
quality is
R ratio isinconducting
polymer
17−2 electromotive force appea
field spins
is consistent
withaccumulation
the field wherethepeakcalculated
to be
1.6which× of1019 the, andjs was that
calculated
thethusresult
the ISHEsipumpedspin
ina theSLG,
isfor
estimated-Tnanoparticles
in theAlq
was mea
21 V;offor 1.5mm,
21 V;
for 23-Co
mm, 22V;
forsolving
3 mm, 8 V;fromand for 
5problems
mm,curves
5 V.
electromotive
force
from
the Pd.
The
external
magnetic
experiments.
Forinduce
this purpose,wefirst appliedmagnetic
field
inmthelack
seriousdevotiontheseWe
dependenceof the
el
Co:
to be
7.7 ×measured
10−9 J m−2 . Here,thehalf ofthe generated js cany thangenerationofthe
a purespin
current
in
the
SLG
(see
the
The
theoreticalfittingvoltage
was a
This
shows
that thespin signals
start
to go downat spacings
beyond fory allowszdirectiontoprepareelectrodesinaparallelor
antiparallel
magtoimpedes
be
3.29
meV,
which
is
largerthevalueestimated
evidenceofsuccessful
spininjectionandtransport
in
SLG
by
spin
pumping.
contributetotheelectromotive
force
in
the
Pd
electrodehere agai
The resonancefield
is the substrate
field is applied
at q =0.out-of-plane
further progress of the
field, andat present, Supplemental
13
angle
betweenin spins
our device
geometry,since aθpure
spinandcurrent).thisThefield
propagatingareabsorbed
Material
V448 | 2 August 2007 netization
NATURE
ISHE
thediffuses
AHE signals
2 mm, indicating a spin
relaxationof about| Vol
2 mm.
ISHE
sigi
direction.
Then
was removed
anda magnetic
NATURE
MATE
meV.
Thislengthis possibly
theresultof chargCspintronics
LETTERSx
60-Co EC = 2.55
4
isotropically.
The
generated
js decays
bythe
spinindiffusionin
consistent
with
the
field
where
the
peak
of
reversed.
magneticfield
H
asdefined
the
inset
of F
using
molecules
exceptforgrapheneis)isconverted
in
the
Pd
wire,
where
a
pure
spin
current(J
Spin transport at room temperature is shown in Fig. 3a for device field B in the z direction was scanned. The datad by using the following equs jshown
are
in
Fig.
4.
SLG, anddecays
to
j
exp(−
)
when
spins
diffusestoPdss
the estim
λ29%(,6
 beingthanshowing
inElectronsing
effectsin Alqshrinking.
3-Co
Co =
θwire.
dependenceofvoltage=
4.
The magnitudeof thespinsignalV) is larger
comparable
tothosethatto a charge
current with(Jc )force
the inverse
Halleffectelectromotive
whichisdirectionanevidenceofFurthermore,theelectromotive
force−2(Htakingthe FMRspin) V̄isISHE−H
unfortunately
Novelapproaches
with
a
c the
are injectedadue
spintoappears,
polarization
inspinthe upby VelectricAu
in agreAHE
2 as182 + aH +14
cecompo(a)(b)
relaxation in the
Pd
wirePdinto accountcan(Hbewritten−H
FMR ) +
reported
observed
at
77
K
for
a
3-mm-spacing
device.
Figure
3b
shows
the
gate
-Co


=
18%
.
While
the
increase
of
the
MR
ratio
C
and
an
electromotiveforce
isgenerated
atthe(ISHE)
contact
3.
They
precessaround
the
B
field
with
a
Larmorfrequency
in
Fig.
2c,
where
P
is
the
absorbed
microwwθ λ tanh(din/2λ SLG) 2e abs byelectrode sepa- reliable
the antiparallela negative
one. In Fig.are
3c thestillgate voltage
Vg
60 value andCo
successful spin injection
andtransport
spin
1.0
and
reproducible
evidencestrongly
V
=
(
)j
in
the
simplest
model.
Here,
is
the
vo
tive
force,
V
ISHE
s
typ
n
AHE ◦ Yafet
d σ +d σh̄Experimeof
ofin
theCnon-local
signalin attributed
paralleland antiparallel
0w,
The
ISHE
effectofThethe(,2)
withisgthe
thereciprocal
effective LandéfactormσBeffect,
Bohr
λPdspin, Hallandsignal
are disappears
thelength of the Pd
andpara3, in which8voltage
dependenceof thegrapheneisbe
plotted.
for vwire.
L 5 gmBB/",
Pdand
Pd the-Cocanto shape
the Cou V dependence
14VV̄, dISHEat wireθ =facing
90
and
thfi
is attribu
AuThe typical
60resistanceexternal
magnetic
pumping(ref. 15)).
awaitedtohelp
the
field
from
stagnation.
θ SL
Py spin(900 direction).
nm), the spin diffusion
length (9staticnm),19 theconfigurations.
Inlayers
agreementwiththesevere
principleof theshifted
non-local
techincos
theand the Jc is described as Jc ∼ Js × σ (σ reversed
isthetheeiceLangea sequence oflomb
26,28
singlegrapheneisobserved,withaslightly
neutrality
0.5
byandfurther
increasing
θ, which
isthealssuchtrends areblockadein theCo nanoparticles,
thickness (5 nm),the conductivityof the Pd, respectively,magnetic
field
whereSLG,
wh
it V
shows
that
the parallel
configuration always yields
the direction
point atof 3.2 kV aNote that the signPof Jc is changed by varying
a 5O 1a2 positivebe ◦ca.
g 5 19 V, where the resistivity reaches a maximum
6and dSLG and σ SLG are the thickness (assumed◦ 20).toHere,ningofspacings
the andnot nique,is compa
symmetry
of
the
ISHE
(ref.
the
spin
d 3G
and
180
,
and
1084
at
0
provided
great
impactin
broadresearchfields.
Quite
seen
for
eitherAlq-Coorrubrene-Co
systems.
If
the
G
18
0.3
nm)
and
conductivity
of
the
SLG
(measured
to
be
ca.
3
0.0
force atestimated
H and Fig. 3b shows that there is of spin (σ ), namely, the sign of the electromotive
elsewhere (manu- (a)(ref. 1). A comparison between Fig. 3c2, the3.10 × 106 S/munder
the zero gate
voltageapplication;
fitting
parameters.
H seeis An
spincurrent
attheinterface
directspin exacohaof theCoulomb
blockade were dominantmass whenof electrons
holes
in
SLG
V
als as follows: forinfluence
Y3Fe5O12in the the small
Pdwire effective
becomesj opposite,
theinjected
pure spinandcurrent
is
13
Co
only
a smalldecrease
Co spin signal at the Dirac point.
Co of the
4the Supplemental Material ). The spin-Hall angle in a Py/Pdlonger
12
s
SiO
and
VAth
Fig.
3(a),
and
V
ressedas 1 mm,MR-VNext,
15
ISHE
θ φ
2
¬0.5
zationprecession
axis.
The
angle
of
the
mag
junction,
θ
,
has
been
reported
to
be
0.01,
which
allowsMm,
35 V; forsuccessfully
generatedandpropagated
in
the
SLG
and
σ
is
SHE
we forpresent
precession
the samespin
trendsshould enables quite fast charge motion withcurve
the room-temperature
C60-Co system,Hanle-type
highmobility and φ −7 which di
3 4 the electromotive
1 2 Vestimate
us to theoreticallyforce
the Pd V, transport
6.67
×in10
respecb
4
and for 5 mm, 5 V.be expectedwithrespect
to theand
film
plane
is
obtainedfFigure1(c)experiments.
thisAlq
purpose,we first10applieda magnetic field in the reversed
6 by a static external
forFortheσ magnetic field.
as 2.37
× 10−5showsV ifatoms
no spin relaxation
thelightnessof SLG consistingofaxisonly
carbonallows2wire
In sum
3-Co and rubrene-Co systems. There¬1.0
AHE
tooccurred
the inelectromotive
spacings beyond
SLG.
In contrast,
the experimentallyobserved
electromotive
y direction to prepare the electrodes in a parallel or antiparallel mag- the FMR spectra of the Py with and without
the
SLG/Pd.
The fieldoftheresonance
H
(Fig.
2d)
using
spin
injec
FMR
fore,
it
is
natural
to
think
that
the
anomalousbias-voltage
−5
5
good
coherence,
bothofareV, appropriate
0
Figure3(b) showst
forcewhich
was 1.16 × 10
and thisweak.
discrepancy
is ascribed
2 removed
In-plane and La =magnetic
at roomm.
10
240 µmnetization direction. Then this fieldGraphenewaslinewidth
ofspinthe spectrum
from thesamplewith
the
SLG/Pd045135t
Gilbertequationas shown
inelectromotiveFig.
2ein90(ref.
20)
during spintransport
0to dissipation of spin coherence ofnanocomposites
resultsofz MRin Cwastheforcthθ (°) current
Fig. 3a for devicedependence
60-Co
physicalnatureforthespin
transport.
Since
2007,
the
field
field B in the
directionscanned.
The data are shownin Fig.from
4. is larger
than thatwithout
SLG/Pd,which
attributed
the SLGis(thedecay ofjtos ), which can be described as an
M(t)
spin
coh
–6
the magnetization-precession
axiselectromotive
is almost
Y Fe5O12y states. The variabilitydesample. The
100
nm up direction
Linearby the of
mparable to thatC60 Electrons
180/ Co interface
in different
240
260 into
280
are injectedwith a spin polarizationin the100 L = observed
modulationof α dueto 3successful
spinpumpinggraphene
spintronics
rapidlywhere
0 yields
SiO
becauseofexpanded,
the thesmall0.5demagnetizationfield
Out-of-plane
H (mT)
Exp.
2
nearlyproportionaltothe im140401-4
3b shows the gatematrix–12
contact
3.
They
precessaround
the
B
field
with
a
Larmorfrequency
1 µm
SLG/Pd.
materials
suggests
that
the
OSC/FM
interface
has
difx
135
11,12)
byrealizationofroom
temperaturespintransport
on
and
thus
the
effectofspin
precession
aroundthatthedensityofthegel andlimit.
antiparallel¬0.1(,2) and
0.0 mB the0.1
vL 5
gmBB/", withg thedepending
effective Landé
2(a)–2(c) show the FMRb signals
as a function of 0.4
interfacestatesonfactor
OSC
species.
TheBohrpara- Figures90
16
1.0 organic–18 non-local
Fig.
5the(Left)
Devicestructureofspin
convertor.
Organic
polymer,Ithefour-terminal
method(Fig.
3),Thespin
lifetime10%
, b tech-ferent
e non-local
proportionally
increases
wiP
layer
on
V
is
negligible.
Ifthevoltages
ISHE
Voltage
(V)
θ,
where
FMR
of
the
Py
occursin
every
condition.
b– which+have
significant
influenceon the anisotropy/isotropy
200
3000.3–300–200–100 13,14)0
45 3(c)0.5 100s yields
a positivemagnetic moments,
V
Also,
as
inupperFig.
Exp. shown
Exp. weσ,andsoforth,
and
now
spin
by
the
ISHE,
would
expect
E

j
×σ
,
1
2
3
4
to
be theelectromotive
force
of
the
Pd
wire
is
shown
in
Figs.
2(d)–2(f),
ISHE
s
(mT)
a
B
equippedonferrimagnetic
insulator,
Y
FeO(YIG).
(Right)
The
pa
3
5
12
Calc.
y
(b)
Alare
LinearMR,
believed to be due Figure
to the1 |CSpin–charge
2O3 18the microwavb
60 / Co interface.
wouldresultin40 toV̄ISHE linearly
where
the electromotive
force
observedwhenθ isbut
set
conversion in organic
material.
a, Schematic∝ 45|js 90×withσ135|/P∝ cosφ24.0
relaxation
physics
of isnot
only
SLG
also
7.3%,
20
0bilayer
180 abs0045◦◦◦ and toferromagnetic
resonance
spectrum
from
the
YIG
thethe
lower
panel
shows
was
small.
Inwi
fa
θAHE
Co
(°)
P (mW)
and180, iswhereasno wassignal andwas observedat θ =
90detail.
. are again
befilm.
0graphene
experimental
data
fully
consistentFe
O
The
PEDOT:PSS
film
illustrations
ofthe
PEDOT:PSS/Y
3
5
12
12
o govern
SiO
investigatedunderstoodinGraphene
2
by
the
ISHE
and
AHE
a
Since
this
findingisinaccordancewiththeangulardependence
Figure2|
Observationof
spin–charge
current
conversion
in
PEDOT:PSS.
a,
Field
(H)
dependence
of
the
FMR
signaldI
Wegrapheneemphasize
againthat Y3 fields
spin-coatedonto a Y3 Fe
H and M(t)denotethealsoexternal
Fe5 O12whereis anthinelectromotive
force
from notable
the organic
polymer.
Again,spintronics
the magnetic
3 film.
4
1 52O12alue also
It
is
quite
that
n-doped Si
23.9
which
indicates
that
th
for
the PEDOT:PSS/YFe
O ISHEfilm
at 20 mW
microwave
excitation.
I is the17,
microwave
absorption
intensity. The
externa
6
∼
J
×
σ
),
of
the
electromotive
force
due
to
the
(J
V. CONCLUSION
c signalss
appearin the,film
js plane.
andTheσ backgroundvoltage
magnetic field and dynamical magnetization, respectively. EISHE
voltage due to themicrowave irradiation
is subtracted
from thePEDOT:PSS
V spectra. b, Microwavof Co
observed
electromotive
exploredavenue
van
der
Waals
andanthethe
electromotive
force
peaks
appearare consistent(ref.
[18]). forc
the resonanceobserved electromotive
force
istowards
ascribed. Thetofilledthe
circles ISHE
are the experimental data. The solid line shows the linear fit tomagnitude ofthe electric
voltageV
clearly
shows
that
the
observed
volt
denotetheelectric
field
due
to
the
spin–charge
conversion,
the
flow
0
= V into/P , where
PSLG
is theandabsorbed
microwave
intensity atdue
FMR forthe
PEDOT:PSS/YFeθ dependenceof V̄
mainlytoelectric
spintransporplain the
Pd,
which
is
due
to
spin
pumpingthethe
We have examined various properties of C60-Co nano- of theheterostructure
spintronics,
wherebilayer
of
SLG
and
23.8
experimental
data. The solid curve
is a function proportional
to cosθ. We
The inset
shows the definitionofthe out-of-planec
PEDOT:PSS
layer.
found
that
the
organ
direction
of
the
spin
current
andthespin-polarization
vectorofthespincontrol
experiments
wereachievementof
spintransportofadynamicallygeneratedpuremagnetic
measured for the PEDOT:PSS/Y Fe O fi
magnetization
φ. d, θ dependence of the ferromagnetic
resonancefieldHcomposites.
Magnetization,
electricalconduction,
and
MR
–6
transition
metal
dichalcogenides(TMDs)
iscollecting
Spin
up
1
experimental
data. The
solid curveis thenumerical
solutionthe Landau–Lifshitz–Gilbertequation. e, θ dependenceointhePEDOT:PSS
filmandis Py/SLG/Cu
vanishinglysmcurrent, respectively. b, Current–voltage characteristics
for thePEDOT:PSS
Pd)
sampl
current at room
temperature.
Here,
note
that
there
is ofnonic insumeasurements
reveal that spin-polarized carriers tunnel be- spinbroad
Fe O
obtained from the Landau–Lifshitz–Gilbertequationwith the measured values of H . The
PEDOT:PSS/Y
attentionin view
offilmproximity
effectofSOI.
–12
from both
samples (see thshowing
thatthetheorganic
magnetoresistancfilm, where the blue and red circles are theexperimental
data
spurious
effectwiththemeasured
observed
symmetryand only
the ISHE
1 µm
23.7magnetic
The MR ex- L is thetween Co0 nanoparticles throughC60xmolecules.
We
that the magnitude
is induced
perpendiculartothe
σ , oranomalous
H. Figure3c shows
the voltage
Notableexperimental
methods
applicabletospin
resultin foundthe control
experithe symmetry.
For
example,
Hall
for
the
observedvoltage(SupplementaryInfoalong theand y directions, respectively.possesses
distance
betweenthespectra for the PEDOT:PSS/Y Fe O film measured at various increases with decreasing the thick–18
CoI nanohibits strong
temperature dependence,
which is commonly effectsymmetry
of
the
ISHE
inthe
thi
(AHE)
signalcanbeincludedasaspurioussignal,
which
This
is
becausethicker
PEDOT:P
microwave
frequencies
f
.
As
shown
in
Fig.
3c,
the
magnitudeoftransport
measurementsformolecularmaterials
are
the
only
potential,
alternative
originofvoltageprobes.
Spin
down
100
200
300
–300
–200
–100
0
signals generated
near theintercV̄of=theV /P ISHEis almostindependentof H AHE, which does
is evidence that
23.6
transportofISHE,the pure
spin
observed–1in FM/OSCs/FM junctions.
impededetectionbut
4
By (mT) While the temperature maydynamical
200
300
–300
–200
–100
0signals,
for100thethespintheinjection.
Asignals
pioneeringwork
wascarriedwith the prediction
ofinthetheISHEP
observed voltage
cannotbespin-pumping-induced
attributed
to theNernstb 24.0 of FM/OSCs/FM junctions is typically attributed not show such an externalof thepure
spincurrent(mT)field
By effect
magnetic
becausethe ISHE
voltage
is genereffect; theNernstpredictsdependenceV̄= V /P of∝ Hthe, because
composdependence
Supplementary Information). The large
conductivity
film
isthermoelectriceffect,outby force.
using
CVD-grown
graphene,room
a thickness
that isincluding
determined btheanisotropy
electric
voltage due to the
Nernsteffecta
at FMRis where
proportional
20
temperature.
electromotiveThe
following
investigations
also
supportd disappearance of magnetization in FM or spin scatter- cnorganic
toFthethe
PEDOT:PSS
layer.
The
d dep
to
|∇T
×H
|
=
|∇T
|H
and
the
magnitudeofthetemperaturereflects
the high degree of polymer alignment
in thespin
planeof the in-independent
effects,
inducedmicrow
ig. 3 Graphene spin valve(left)
temperaturetransport
SLG
wasmicrowave
demonstrated
in by tothe
gradient|∇T | is proportional
to the absorbed
intensity approximated
be V
∝ (1/
Spin
up and observed nonseries ofing in 23.9
OSCs,
its mechanismhasnotbeen understood.
We
P at
FMR. These
resultsPEDOT:PSS/Y
demonstrate that electromagnetic
and
λ
is
the
spin
diffusion
length
in
1
film
that
is
commonly
foundinconjugatedpolymerthinfilms.
We
Fe
O
film.
However,wefoun
3 source
5 12
local magnetoresistance at room temperature (right),
a10lateral spin thermoelectric
device artefacts
withareseparatedspin
and (1)). The experimentallyirrelevant
140401-2 equation
4.2 K to the observed voltage.
ces, such
have provided sufficient materials
fortheoreticiansspin-wave
to imple-resonance (FMR) in the
inducedferromagneticYeffectsareunlikely
the
cause
of
de
Fe
Indeed,the5 Oobserved
microwave
frequency
dependence ofto
thebearound
15–45%
whend theis decreas
3
1215). A subsequent
where 0 the non-local four-terminal measurement
detector electrodes(see Fig. 4)
electric voltage shown in Fig. 3c is consistent with the prediction of see Methods). From this, we can e
O3 , Alq3
ment quantitative
analyses oftheandtemperatureof
Most
importantly,
the detectedvoltageret
film
measureddependence
the d.c. electric-potential
difference
between0
thespin
pumping
and
ISHE.
The
d.c.
componentofaspin
current
inthe
PEDOT:PSS
layer
to
be
of
technique was introduced (ref. 11)).
achievement ofgenerated
dynamical
spin77
injection
intomoleculeKby the spinis proportionalz component
assume thewith
diffusionthe
coefficientrubrene,MR in 23.8
FM/OSCs/FM junctions,andelectrodes
one can on
discuss
the unreversing
H.to theThis
is consistentexpeinthe Authe PEDOT:PSS
layer that was generated
by pumping
ofas
the magnetization
damping
D = 8 × 10 cm s
: j current∝ [M̂ × ∂ M̂] ∝transportf , where the order–1
wasachieved
polaronspin
in ofthermoelectricbutexcludesH-independent
exciting
FMR.
For
clarity
we
refer
to
this
voltagealready
at
this
point
the
estimatedspin
relaxation
time
and
M
is
the
saturation
value
of
the
magnetization
M.
M̂
=
M/M
ctronics.
derlying physics of the spin-dependenttransport
in
OSCs.
–10
Spin down16) by is the solidof themagnetization precession
trajectory . consistentreports oof graphene
spintronics
strongly
helpsthat thisintroducing
a verticalspin with previous
conjugatedpolymer
23.7
Seebeck
effect,fromto thesig
as VISHE. However,wenomenclature
wasbyanglenowithagnetiza-Coemphasize
nanocomTheEstablishment
observed
temperaturedependencein C60The errorHere, decreases
increasingf , because
the coneangle contributingof organic semiconductors.
Figure 1 | Spin transport
in aserious
four-terminal
spin
valve device.
a, molecular
Scanning
circumventing
stagnation
precession
decreases withincreasing
fdetection, or H ,signal
large,inbecausea more accurate
devicefor dynamical
spin injection
and–20It is based
found
that
the voltage
is insensitive
tode
means
adoptedas aofforegone
conclusion.
on amagnetization
careful andat highly
positescannotbe theexplained
only
by
the
Coulomb
blockadeshowing that j ∝ f  is insensitive to f . Using the Landau–Lifshitz– voltage measurements on PEDOT
electronmicrographofa four-terminal
single-layer
graphene
spin valve.
17)
spintronics.
“Discovery”
ofsingle-layer
graphene
(SLG)
26,28
thicknesses
was
found
to
be
expe
Gilbertequation,thef semiconductor
dependenceof V
is expressed
as
.
As
in
spintronics,
itcondensed
matters
field
strength,Hdetailed
experimental
analysis
that
tests
this
hypothesis
and
forms
,
showing
that
H
-depe


FMR
istics areanda theresultsof thiseffectin
Co nanoparticles,
Cobaltelectrodes(Co) are evaporated acrosssingle-layer
graphene
strip study
23.6
samples of Y Fe O prepared in di∝ (4πM γ ) + (4πf ), where γ = 1.78 × 10 T s
V̄9,10)–30FMR
100
200
300
–300
–200
–100
0spin
exhibiting
exoticandintriguing
topologicalphysics
surface.
b,
The
non-local
valvegeometry.
A
currentIisprepared
on
a
SiO
the
heart
of
the
present
paper.
Under
conditions,thespineffects,
that
is,
the
Nernsteffect,arealfiscorroborated
that
dynamical
spin
injectioncanbeaslightlydifferent
FMR
resonanceisthegyromagnetic
ratio
and
4πM
=
0.175
T
is
the
saturation2
he MR-V
shed light on factors with theBy following
features: a large
–100
–50
0
50
100
magnetizationBof(mT)the Y Fe O film. As shown in Fig. 3d, the This is a well-known problem with
injected from electrode 3 through the
Al2O(mT)
into grapheneandis current into the PEDOT:PSS
3 barrierpumping
injectsapure
spin
layer.
observedvoltagesignal.
To
investigatethey If
experimentallymeasuredfdependenceofV̄
identical
samples
of
the
same
PE
is
well
reproducedc
20 at contact 4. The voltage difference is measured between contacts 2
extracted
variations in the magnitude of thusing
calculation.
the spin current j can be convertedFigure
the detectedvoltage,
into2a| charge
current
jcthisthrough
Spin transport
at 4.2and
77 K. a, Non-local
spin valve signal
for we measured the ele
214414-6 and 1. The non-local resistance is Rnon-local 5 (V1 2 V2)/I.s c, Illustration ofspin injection
and spin diffusion forthe
electrodes
havingparallelmagnetizations.layer,
device4.2 K.current
The sweep624
directionsgiveof the magnetic
field are indicated
PEDOT:PSS/YISHE
in thePEDOT:PSS
this1 atspin
shouldusing
a coplan
MATERIALS| VOL 12 | JULY
3 Fe5 O12 film NATURE
10
4.2 K
Injection of up spins by contact 3 results
in anaccumulation
spin-up between(red orgreen
arrows).
magnetic configurations
the electrodes
are Publishers Limited.fAll rights© 2013 Macmillan
rise toa d.c.
electricofvoltage
thetwogold The
electrodes(see the ofmicrowave
frequency
canreserved
be controlof theof JapanVol.47,No.2,
29electrons underneath contact 3, with aJournal
corresponding
deficitMagneticsof spin-down Society
illustrated
for both sweep
directions.
The2023
widths of the electrodes are 330 nm
1a).
For decays
the measurements,
PEDOT:PSS/Y
thefield HFMR as shownwas
3 Fe(for
5 O2),
12 film
0 Owing to spin relaxation Fig.
electrons.
the spindensity
on a scale given by the(forelectrode 1), 90 nm
140 nm(for 3),to
250varynm (for4), resonanceand the77 K
the spin relaxation length. The dotsplacedshow theatelectric
voltage measured
electrode spacings
330anmfor the gaps between
electrodes
2,f2 and HFMR is given by
the centre
of a TEby
relation
betweencavitywere
withresonance
011 microwave√1 andcontacts 1 and 2 in the ideal case of 100%spin selectivity.
A positiveand 3, andthe
3 and
4. The graphene
width was 1.4 mm.
electrodefrequencyof f =
9.45 non-local
GHz, in whichmicrowave
magnetic
f =Inset,(γ /2π)Hspacing–10
FMR (HFMR + 4πMs ). Figure 3b
resistance is measured. (We note that a larger positive signal can be obtained
configuration. b, A two-terminal local spin valve signal (measured between
field was applied along the y direction. An external static magnetic for the PEDOT:PSS/Y3 Fe5 O12 film measur
FMR

FMR

◦

◦

◦

◦

↑↓
r

2 2

◦

s

s

2

s

2

2

2

2

2

dI/dH (a.u.)

SO3H

SO3H

SO3H

SO3H

SO3H

2

SO3H

◦

SHE Pd

Pd

Pd

Pd Pd

V (102 nV)

5

12

ISHE

Rlocal (kΩ)

Rnon-local (Ω)

3

ISHE

ISHE

abs

3

abs

Spin density

FMR

3

5

3

12

3

5

5

12

12

FMR

ISHE

FMR

ISHE

abs

FMR

FMR

20

ISHE

Rnon-local (Ω)

abs

14

s

s

t

−7

z

s

20

FMR

s

ISHE

s

ISHE

2 −1/2

2

s

3

5

12

ISHE

Rnon-local (Ω)

5

FMR

abs

Rlocal (kΩ)
Spin density

φ (°)

HFMR (T)ISHE

P = 40 mW
VISHE/VISHE

Rnon-local (Ω)

Current (A cm¬2)¬¬θ = 0V ISHE/V ISHESLG SLG

23

11

−1 −1

3

5

12

2 −1

200 mW. As discussed above,
the broadeningof W in the
opposite
directions
external
field
wascausedthesamegenerated
experiments
by byusingthetheothersample(sample 2,
field was caused
electromotive
external
magnetic
field
isin
applied
atthe
q4(b)
=0.
The magnetic
resonance
O forceO from the Pd. theOO[24]).
resonance
field,
asexpected
for
aof
ISHE
Py/SLG
comparedwiththatin thePyfilm wasattributed
tovoltage
¼
0.5
V
[red
line
Figs.
4(c)],[24]).
At V GThewhere
the gapand
length wasmeasured tothe
be 780 nm), whose
17,20
bydifferences
in
the
spin
wave
resonancesduetoslightly
spinthepumping
into the SLG and
g in the Py/SLG. layer was
quality is not as good as that of sample 1 (the conductivity
Fermi
in
conducting
polymerfield spins
is consistent
withaccumulation
the field where
peak
force
appears,which
isdominantly
an S/m underobserved.
s due topumped
slightly
INDEXm , electromotive
andj was that
calculated
calculated
to be
1.6which× of
10 theinduceFermi
spin
in SLG
thetheSLG,
thethusresult
theISHE
signalswere
wasmeasured
topoint,
be 6.40× 10
the zero
gate
level
in
was
tuned
below
the
Dirac
where
different
sampleposition
at
θ
¼
0°
and
θ
¼
180°.
H
H
We
dependenceof theelectric
voltageontoshow
the
holes
to be
7.7 ×measured
10 J m . Here,thehalf ofthe generated j can
voltage
Figures4(a)–4(f)the result,allowsgenerationof a pure spininthe(see theThefitting
was application).
performed
in orderseparatetheandevidenceof successful
spincurrent
injection
andSLG
transport
in SLGbyspin
pumping.
contributeto the electromotive
force
intheoretical
thePddiscusselectrodeNext,
weelectricalof theYIG/SLG
here again plane
the response
obviousand
ISHE signals
and theinversion of the13
out-of-planeangleθbetweenthesubstratethestatic1.0
V
H ¼ 180°.
was
tuned
to
holes
acted
as
a
dominant
carrier.
WhenV
our device
since a purespinandcurrent
aregeometry,absorbed
Supplemental Material ). The propagatingin spins
ISHE
thediffuses
AHE signals
inGtheelectromotive
ISHE
signals
canobserved
be seen as theexternal magnetic force
field was
NATURE
MATERIALS
LETTERS
under
gate
voltage
It
was
shown
that
spin
by spinin
diffusion
in application.
isotropically. The
generated
j decaysreversed.
However,thesignals
were comparatively
weakandmagneticfield
H
asdefined
the
inset
of
Fig.
2c.
The
field
angle
crosse
14
in
the
Pd
wire,
where
a
pure
spin
current(J)
isconverteds j decays to j exp(− ) when
V = VISHElevel+by using
the following
equation,f the YIG/SLG
spins diffuses
to Pd
SLG,
and
(H
) +
the estimatedspinFermi
coherence lengthwas−H
ca. 460
nm, which
1.0
V [blueθwire.
line
in theeffect
Figs.
and
4(c)],
thedependenceofthe 4(b)electric
voltage
=
V
/P
is
shown
from
spin
Hall
to a charge current (JFurthermore,
electromotive
force−2(Htakingthe spin) V̄isISHE
−H
Au
ISHE
abs
c ) due to the inverse
inagreementwiththesamplequalities
and
also
with
aH +spinb, relaxation
where Vmechanism
theelectromo-the
VAHEcan(Hbe−Hwritten) +ISHE is in
14(a)spin(b) is generated
relaxation in thePd
wire
into accountas + reported
SLG, i.e., the Elliothown that
(ISHE)
and an electromotive
force
at
the
Pd
in
Fig.
2c,
where
P
is
the
absorbed
microwave
intensity
at
FMR.
accom
crossedn theof Diracpoint,
thecarrierwaschanged
V
=
( abs
)jand
intivethe simplest
model.
Here, is Yafet
thetypevoltagedue tothe
AHE, H
force,
VAHE
type.
These
observations
also corroboratethat isour anresult◦wire. The ISHE is the reciprocal effect
the
spin
Hall
effect,
,
d
,
and
σ
are
the
length
of
the
Pd
wire
facingw,
λ
The V̄ISHE signal disappears
atstatic
θ = 90thesignthespinvoltageis spinistransport
is attributed
to dynamical
injectionboththeexternal
magnetic
field
forofthe
FMR,
HinandFMR
Py(900 direction).
nm), the spin The
diffusion
length
(9 nm), theelectrons.
changein andthecarriertype
wasin the SLGs.
The spin coherence
lengththe CVD-grown
and the Jc is describedfrom
as Jc ∼ holesJs × σ (σ toisthethespinreversedbyandfurther
increasing
θ , whichisthealso
consistent
with
the
magn
thickness (5 nm),the conductivityof the Pd, respectively,magnetic
field
whereSLG,
FMR
occurs,
and
it
is
107.7
mT
which was estimated by using the dynamical method,theNote that the signPof Jc is changed by varying
and σdirection
are the thickness (assumed
be ◦ca.
and d◦ 20).toHere,◦ σreported
is comparable
to theatpreviously
value b(1.1areµm)
symmetry
of
the
ISHE
(ref.
the
spin
polarizationofthegate v
and
180
,
and
1084.5
mT
90
.
,
a,
and
at
0
accompaniedbyswitchingofthevoltagesignalsign
for
0.3 nm) and conductivityof spin (σ ), namely, the sign of the electromotive
force atof the SLG (measured to be ca. estimated by using an electrical method. In contrast, theunder
the zero gate
voltageapplication;
seeis An3.10 × 10 S/m
fitting
parameters.
of
the
in
injectedspincurrent
attheinterface
directedalong
themagneticurren
spin example
coherence
lengthofthefitting
SLG in is
this shownstudy is mucheO
the Pd wire becomesjboth
opposite,θwhen¼
the0°
pure
spin current
is¼). The180°
spin-Hall angle
in a Py/PdtheSupplemental
Material−5andθ
directions
ofthelongerthanthatinp-Si (ca.external
130 nm)in ourprevious
study,
s
H
H
and
V
are
estimated
to
be
1.16
×
10
Fig.
3(a),
and
V
ISHE
AHE
zationTheof themagnetization
In F
junction,θprecession
, has
to be
0.01,angle
which φallowssuccessfully generated and propagated in
the SLG
andbeenσ reported
isaxis.
which
directly indicates theprecession
advantage of graphene for spin
−7
us to theoretically estimate the electromotive
force
the Pd V, transport.
and
6.67
×in10
respectively.
The
contribution
from theaxis
withrespect
to
the
film
plane
is
obtainedfromtheθ
dependence
magnetic
field[Figs.
4(b)
and
4(c),
respectively].
Thus,areversed by a static external
magnetic
field.
Figure1(c)showsexternσwire as 2.37 × 10 V if no spin relaxation occurred in the
In summary,
we successfully
demonstrated
the electromotiveforce
was revealed
to thebedynamical
very
SLG.
In contrast,
the experimentallyobserved
the FMR spectra of the Py with and without
the
SLG/Pd.
The fieldAHEofthe
resonance
HFMRtoelectromotive(Fig.
2d) usingthe
Landau–Lifshitz–
spin injection,
resultingin generation of spin current in SLG
circlegate
voltagecanbetoswitch
the
sign
of
the
chargeweak.
Figure
3(b)
shows
the
microwave
power
dependence
V, and thisdiscrepancy
is ascribedforce
was 1.16
× 10usedatroom
temperature,whichenables
generation
of
a
pure
spin
= 240 µm
linewidth of the spectrum from the sample
withthe
SLG/PdGilbertequation
as
shown
in
Fig.
2e
(ref.
20).
Figure
2e
shows
that
the reto dissipation of spin coherence during spin transport inthat isatfreethe
from Pdelectricalmismatch. The
ofcan theelectromotivecurrent
force
forconductancethe Py/SLG/Pd
is larger than that
the SLG/Pd,
which
attributed), whichSOI.
be described as an
the SLGis(thedecay of jto
M(t)without
spin coherence
length of
CVD-grown
SLG
was 1.36 µm,
current
generatedthroughthemagnetization-precession
axis
isalmostparallel
to
H,
θ
≈
φ,
and
t
Y
Fe
O
,
is
sample.
The
electromotive
force
at
the
Pd
wire,
V
LinearISHE
the modulation of α due to successful spin pumping into the
because
of
the
small
demagnetization
field
in
the
Y
Fe
O
layer,
Exp.
3
5
12
nearlyproportionaltothemicrowave
power,
which
indicates
currenfor twoIn Fig. 5(a),the thegate
voltageprecession
dependence ofV SymPEDOT:PSS
SLG/Pd.
andspineffectH in thethat the density ofaroundthe generated
spin current in the SLG
0.1
Fig. 5 (a)Deviceshow
structureof organic
convertor.
Figures2(a)–2(c)the FMRsignals
asthusa functionof of spin
16
Fig.
5the(Left)
Devicespin
convertor.
Organic
polymer,
PEDOT:PSS,
is filledpower.15
H proportionallydirections
θH ¼with
0°the(black
appliedmicrowave
layer
on Vfield
isnegligible. If theincreases
voltagesignals
were generated
ISHE onOrganic
polymer,isorganicequippedV)θ , where
FMR
ofexternal
thePEDOT:PSS,
Pystructure
occursmagnetic
inof
every
condition.
The
Also,
as shown3(c),the electromotive
σpanelby intheISHE,
we would
expect
EThe
Fig.
js ×σ
, and
with js ∝Pabsforce
thisincreases
ferrimagnetic
Fe isOinsulator,(YIG).
(b)
The
upper
electromotive
force
ofcircles)
the Pd Y
wire
shown
Figs.
2(d)–2(f),ISHEinupper
equippedon insulator,
ferrimagnetic
Y(Right)shows
theUsing
3Fe
5O12 (YIG).
¼
180°
(red
filledcircles)isshown.
andθ
H
linearly
withthemicrowave
power,
althoughthevoltage due
σ
panel
shows
the
ferromagnetic
resonance
spectrum
wherematerial.
the electromotive
force is observed
whenresult
θ is set
would
in to
V̄ISHE ∝ |js × |/Pabs ∝ cosφ ≈ cosθ (ref. 20). The
version in organica, Schematic◦◦◦ and toferromagnetic
resonance
spectrum
from
the
YIG
the
lower
panel
shows
a
concomitant
the
AHE
was
small.
In
fact,
the
ratio
of
the
signal
be
0
and
180
,
whereasnosignalwasobserved
at
θ
=
90
.
from
the
YIG
and
the
lower
panel
shows
a
concomitantmeasurements
thedetermined
fromfullythe
I D -Vwith
experimental
data are again
consistent
this expectation. intensities
film resistancewas
SS/Y3 Fe5 O12 film. The PEDOT:PSS
Gat 200
by
the
ISHE
and
AHE
mW was estimated to be
Since
this
findingisinaccordancewiththeangulardependence
electromotive
force
from
the
organic
polymer.
Again,|
We emphasizethat Y, 3 fields
denote the externalFe
is antheinsulator.
Nevertheless,electromotive
force
from
the organic
polymer.
Again, again
the Vmagnetic
whereferromagnetic
2 film. H and M(t)
5 O12
and
the
detected
voltage
we
extracted
17,Symwhich indicatesthat the ISHE thesignal charge
is dominant in the
∼
J
×
σ
),
of
the
electromotive
force
due
to
the
ISHE
(J
the
magnetic
fieldswheretheferromagnetic
resonancecsvoltagesignals
appearinthe
PEDOT:PSS/YFe
O
Thissignal was
al magnetization, respectively. EISHE , js and σ
35that12thefilm.
observed electromotive
observed
andthe electromotive
force peaks
appearare consistent(ref. [18]). force andthe resonanceobserved
electromotiveforce
is ascribedto theISHE
peaks
appearareandtheelectromotive
force
currentI
generatedinthe
YIG/SLGsystem.
Contributions
clearly
shows
that
the
observed
electric
voltageisinducedinthe several
e to the spin–charge conversion, theflowmainly due to spin transport in the SLG. Furthermore,of thePd, whichis dueconsistent(ref.
18)).to spin pumping into the SLG and the

SO3H

SO3H

SO3H

SO3H

SO3H

SO3H

Ga 5

19

−9

−2

s

c

dI/dH (a.u.)a0wθSHE λPd tanh(dPd /2λPd ) 2edSLG σSLG +dPd σPd
h̄
Pd
Pd

ISHE

Pd

5

s

s

s

s

↑↓
r

−2

DOI: 10.1038/NMAT3634

FMR

FMR

1.0

s

SLG

6

V (102 nV)

12

cos θ

4

5

21

θ

15

¬0.5

SHE

H

V

φ

VISHE

−5

2

0

s

12

240

260
H (mT)

M

¬1.0

0

3

20

0.0

−5

280

45

90

135

180

θ (°)

d

e

0.5

180

140401-4

3

5

12

1.0

0.5

0.4

φ (°)

HFMR (T)135b

P = 40 mW
VISHE/VISHE

5

13

2

Experiment19¬¬θ = 0VISHE/VISHE

SLG

2

FMR
182
2

0.5

6

2

d
λ

0.3

Exp.

40

0

P (mW)

45

90 135
θ (°)

φ =θ

45

Exp.
Calc.

Linear

20

0

90

180

0

45

90 135θ (°)

180

Figure 2 Observation of spin–charge current conversion in PEDOT:PSS. a, Field (H) dependence of the FMR signal dI/dH and the electromotive force V
for the PEDOT:PSS/Y3 Fe5 O12 film at 20 mW microwave excitation. I is the microwave absorption intensity. The external magnetic field was applied along
the film plane. The background voltage due to the microwave irradiation is subtracted from the V spectra. b, Microwave power P dependence of themagnitude of the electric voltage VISHE . The filled circles are the experimental data. The solid line shows the linear fit to the data. c, Out-of-plane field-angle
θ dependence of V̄ISHE = VISHE /Pabs , where Pabs is the absorbed microwave intensity at FMR for the PEDOT:PSS/Y3 Fe5 O12 film. The filled circles are theexperimental data. The solid curve is a function proportional to cosθ . The inset shows the definition of the out-of-plane angle of the external field θ and themagnetization φ. d, θ dependence of the ferromagnetic resonance field HFMR measured for the PEDOT:PSS/Y3 Fe5 O12 film. The filled circles represent thepotential approach for
injecting
spins
into
molecules.
The
experimental
data. The
solid curveis thenumerical solutionof the Landau–Lifshitz–Gilbert equation. e, θ dependence of the magnetization angle φ for thethe Landau–Lifshitz–Gilbertequation with the measured values of HFMR . The dashed line shows θ = φ.
PEDOT:PSS/Ybased
3 Fe5 O12 film
other notable achievement
onobtained
the from
dynamical
spin

PEDOT:PSS
found
that the organic
magnetoresistanceand the spin-polarizationof the spin
control
experiments
were carriedout by using Py/SLG (noachievement ofvector
spin transportof a dynamicallygeneratedlayer.
pure Wefilmandis Py/SLG/Cu
vanishingly
small,where
less nothan
rent–voltagespincharacteristics
for thePEDOT:PSSHere, inPd)samples,signal0.1%,
was observed
current at room
temperature.
notethe
thatPEDOT:PSS
there is no). Thefromboth(see the Supplemental
showing
theFIG.
organic
magnetoresistanceis notd circles are theexperimental
data
4. (d)(a)
I Dsamples− V G measurement
at T responsible¼ 250Material
K. In 13theredspurious
effect withthemeasured
observed symmetry
and onlythat
the ISHE
inthe
molecular
spintronics
isthe
We
that istheholes;magnitude
ofthe
the blueelectric
voltage,the
VISHE
is induced
perpendiculartothe
σ , orH. Figure 3c shows
voltage,the observed
resultin foundthetypecontrol
experiments,
in addition
tocarrierthe techniquesymmetry.
For
example,anomalous
Hall
area,
the
carrier
in
area,
type
is
for
the
observedvoltage(Supplementary
Information).
Therefore,, respectively.possesses
Lpumpingis the distance
betweenspectra for the PEDOT:PSS/Y3 Fe5 O12 film measured at various increases with decreasing the thickness d of the PEDOT:PSS layer.
demonstration
ofcan
spin
aforementioned,a electrons.
symmetry
of
the
ISHE
in
this
study,
corroborates
thesuccessful
effect(AHE) signal
beconversion.
included
as aAssignal,
which
This
is
becausethicker
PEDOT:PSS
films
tend
to
short-circuit
microwave
frequencies
f spurious
. As
shown
in
Fig.
3c,
the
magnitudeofGeneratedvoltage
under
the
FMR
and
applicationofthe only potential, alternative origin of the VISHE signals, except
signals generated
near theinterface.
This inresultconsistentV̄of=theV /Pofis almostindependentof HFMRAHE, which does
is evidence
characteristic
naturemolecularmaterials
in the thatabstransportofISHE,thespincurrent
theisSLG
conversion
may
impede detection
ISHE
signals,
but
¼
0.5
V
(red
lines)
V3GFeand¼5 O
1.0
V (bluegate
voltage
V G pure
forpeople
thethePEDOT:PSS/Y
with
the prediction
ofinthetheISHE
inducedby theandspin pumping
the observed voltage signals
cannotbespin-pumping-induced
attributed to the
Nernst12
spintronics
is
its
weak
SOI.
Hence,
had
beenofforthepure
spincurrent
to inthechargelayercurrent
room
not show such an external
magnetic
becausethe ISHE
voltage
is generated
an magnetic
interfacialwith H ateffect; theNernst effectfield
predictsdependence
V̄ISHE = VISHE /Pabsof∝ Hthe, because
FMRlines)the
directionoftheexternalfield
θ
H ¼ 0°
ation). The large
conductivity
anisotropy
film
isthermoelectriceffect,-dependent
a thickness
that isincluding
determined by theHspin
diffusion length ofandtheelectric voltage
due to the
Nernsteffecta
at FMRis in
proportional
believingthatspinchargeconversion
is impossible
temperature.
electromotive
force.
The
following
investigations
also
support
¼
180°
(c).
(b)
and
θ
the
layer.microwave
The d dependenceof VISHE for d >into |∇T ×Hof
= |∇T |HFMR
and the magnitude of thetemperature
λ is theH PEDOT:PSS
FMR | theof polymer alignment in the plane-independent
effects,
inducedby theabsorption
molecules because gradient
its SOI
too weaktoabsorbed
realize
the intensity|∇T |isis proportional
to themicrowave

approximated to be20 VISHE ∝ (1/d)tanh(d/λ)tanh(d/2λ), where

FIG. 5ence omagne(red fithe pr(solid(dasheP at
FMR. Thesedemonstratethat electromagnetic
andfilm.
λ is thespin diffusionwelengthin the PEDOT:PSS
layer (see alsoound in conjugatedpolymerthinfilms.
We
PEDOT:PSS/Y
However,
foundthat thermoelectric
3 Fe5 O12
conversion.
The achievement
by results
Andoet al. overturned
thermoelectric artefacts are irrelevant to the observed voltage.
140401-2 equation (1)). The experimentally observed increase of V is18)
pin-wave resonance(FMR) inunderstanding
theIndeed,
Y3 Fethe5 O
effectsareunlikelythe 15–45%
causewhen
ofd thedetectedsignal.
observed
dependence
is decreased
from 80 tovoltage
40 nm (for details,. The
key oftothebearoundthe conventional
Fig. 5)frequency
12(seemicrowave
166102-3
electric voltage shown in Fig. 3c is consistent with the prediction of see Methods). From this, we can estimate the spin diffusion length
Most
importantly,
thedetected
voltagereverses
its
sign
when
d.c. electric-potential
difference
betweenfor the successful
spinconversioninmoleculesisthe spin pumping and ISHE. The d.c. component of a spin current in the PEDOT:PSS layer to be of the order of λ = 22–31 nm. If wegenerated by thebyspinpumping
is proportionalthez component
assume thewith
diffusionthe
coefficientin the PEDOT:PSS
to be ofsufficientspinwasaccumulation
spin
pumping
reversing
H.to fromThis
is consistentexpected
ISHE layer
symmetry,e PEDOT:PSS
layer thatgeneratedbytheof the magnetization damping : j ∝ [M̂ × ∂ M̂] ∝ f , where the order of D = 8 × 10 cm s (Supplementary Information),
YIGvoltage
as thesubstrate
a ofsolutionbut excludes
H -independent
thermoelectriceffects,such
as is thewe refer to thisalready
at= thisspin relaxation time becomesτ = 5–11
andPEDOT:PSS,
M is the saturationvalue
the magnetization
M. the estimatedµs, whichM̂M/Mofpoint
6 (a) Gate
voltagedependenceof the times
source-drain is the solid angleof the magnetization
precession trajectoryF.ig.consistent
with previous
reports
on long spin relaxation
inprocessed
spin
convertor.
Althoughtheconversion
Seebeck
effect,fromto thesignal.
Furthermore,
mphasize that this nomenclature
wasby nowith increasing
The error
in our estimateof λ is relatively weHere, decreases
f , because
the coneangle contributingof organic semiconductors.
electric
current
in
SLG.
(b)
Gate
voltagedependence
of
FIG.
5.
V
(a)
and
spin-charge
conversion
current(b)
dependSym
efficiency
was onindeed
small,
thesufficient
precession
decreaseswithincreasingf , or H ,signal
large, because
a more accurateof λ froma fit offound
that
thespinvoltageis insensitive
todetermination
theexternal
magneticgone conclusion.
It is basedamagnetization
carefulandshowing that j ∝ f  is insensitive to f . Using the Landau–Lifshitz–
voltage measurements
onin
PEDOT:PSS
films withmany
different whenelectromotive
forces
SLG
under
spin
pumping
accumulation
into thepolymerallowsdetectionof charge
250
Intests
thethisredforthewasdirectionof theexternal
ence
the
gate
voltage
V Gas, showing
thicknesses
found
be experimentallychallenging
becauseGilbertequation,
the f dependenceofV
is expressedfieldstrength,
HFMR
nalysisK.that
hypothesis
and
forms
that
Hto-dependent
thermoelectric
 on
carrieris Ohole(+0.5
V, theredrunssolidline) andof Y Fe∝(4πM γ ) spin
+ (4πf Hall), effectwhere γ =1.78 × 10 T sthe samples
preparedin different
deposition
exhibitedV̄flow generated by the
inverse(ISHE).
paper.
Under
FMR
conditions,thespineffects,
that
is,
the
Nernsteffect,arealso
irrelevant
to180°
theslightlydifferent
FMR
resonance
fieldsandshapes(see
Methods).
isthegyromagnetic
ratio
and
4πM
=
0.175
T
is
the
saturation¼
0°(blackfilledcircles)andθ
¼
the carrierThis
typeis
magneticfield
Hθelectron
(+1.0
V,
the
blue
solid
line).
(c)Gate
voltageH
H
work opened magnetizationa new frontier
conversionof the Y FeofO spin
film. As
shown in Fig. 3d, the This is a well-known problem with Y Fe O that led to nominallyspin current physics,
into thewhere
PEDOT:PSS
layer.
If
observedvoltagesignal.
To
investigatetheH
dependence
dependenceof theforces exhibiting
in SLG ofwhen
FMR thickness
experimentallymeasuredf dependence ofmaterials
V̄
identical samplesof theelectromotive
same PEDOT:PSS
is well reproduced
heavy
elements
andtopological(redfilledcircles).
Lines
show
the
fitting
that
takes
into
account
andapplicationofvariations
inthemagnitudeofthevoltagesignaloftheorderof theusing
thiscalculation.
thedetected
voltage,wemeasuredtheelectric
voltageforconverted intoachargecurrentjthroughthedirectionoftheexternal
magnetic
fieldisreversed.
cpivotal roles. The same concept was applied forV
1.0 played
V (bluethepresenceofelectron-holepuddlesnear thepoint
Gatevoltageof Dirac
generated
electric
PEDOT:PSS/Y
T:PSS
this
spin current
shouldgive
using
a coplanarwhere
19-21)the
NATURE
MATERIALS|dependence
VOL 12 | JULY 2013 |waveguide,
www.nature.com/naturematerials
G ¼layer,
3 Fe5 O12(d)film, where there
substantiating
spin 624
conversion
in SLG© 2013 Macmillan
Publishers
Limited.fAllbyrightsreservedcurrent
the
ISHE.
The
saturationof
thecurrent
tage
between
the
two
gold
electrodes(seethemicrowave
frequency
canbecontrolled.
This
enabledus
strongregardingthe andmechanisms.
The using a simple one-carrier-type model
0° debate(solidc field H θwaslines)
the fitting
H ¼
under
highergate
voltagesiscompelling
evidence
thatements, the PEDOT:PSS/Y
to
vary
the
resonance
field
H
Fe
O
film
was
as
shown
in
Fig.
3a.
Here,
the
sample structure
the same, SLG/YIG bilayer, in the
3 was
5 12
FMR
(dashedlines).
the
ISHE,
not
the
Rashba-Edelsteineffect,governs
TE011 microwave
relation
betweenf and HFMR is given by the Kittel formula: thewitha resonancestudies.cavity
Mendezet al.
claimed that the
spin conversion√
spin conversion (ref. 21)).
was thegovernedby the magnetic
Rashba-EdelsteineffectGHz, in whichmicrowave
f = (γ/2π)dueHto
FMR (HFMR + 4πMs ). Figure 3b shows the V signals
inversion
symmetrybreakingalong thetohe y direction.
An external
staticmagnetic
forperpendicular
the PEDOT:PSS/Y
with applying
an its3 Fe5 Oof
12 film
laggedthe measured
other spintronics
fields and. Meanwhile,group field
the SLG
plane direction
ng the film plane
as166102-3
shown
in Fig. 1a.20)All
in-planeour
magneticH
perpendiculartothedirectionacrossattractiveness has not been explored yet. Hence, muchreported
that the ISHE governs the theconversion
physics
ormed at room
temperature.
electrodes
and a serious
microwave
a frequency of f = 6.5 GHz,
effort withis awaited.
by demonstrating ambipolar and gate-modulated spin
microwave absorption and the d.c.
elec- showing again that the observed electric voltage changes sign onconversion (see Fig. 6) 21). The conclusive work was
3. Spintronic function of topological quantum materials
reversing the magnetic
field direction from H to −H in this system.
ignals for the PEDOT:PSS/Y3 Fe5 O12 film,
implemented by Raes et al. 14), where spin relaxation inThe
voltagesignal,which
is asymmetric to H, disappears when the Hage spectrum,avoltagesignalappearsat
SLG is isotropic resulting in no Rashba field is created in
A topological quantum material (TQM) is a novel
directionisparalleltothedirection across the electrodes, consistentof the
=
260
mT,
indicatingthattheelectricMR
SLG instead of its inversion symmetry breaking along
material phase in 21st century. Since the discovery
20
the symmetryofthematerial
ISHE inducedby, tremendous
the spin pumpinge PEDOT:PSS
concomitantthelayerperpendicular
to withthe theplane withdirection,
which
effort has, been
newphase 22-24)
the detected electric
voltage
VISHE thebecausethe ISHE, EISHE
js ×
σ , predicts
theofelectric
voltageincreases
unequivocallynegatedclaim by Mendez
et al.
made toexplorea wide thatvarietynovel andabundant
abs

ISHE

14

s

s

t

−7

z

s

2 −1

s

20

FMR

s

ISHE

s

ISHE

2 −1/2

2

23

11

−1 −1

3

5

12

s

3

5

12

3

5

12

ISHE

In summary, progress of molecular spintronics is still| JULY 2013 | www.nature.com/naturematerials

physics appearing in topological insulators (TIs),
623© 2013 Macmillan Publishers Limited. All rights reserved

30

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

INDEXno Letters

topological superconductors (TSCs), Weyl semimetals
and Weyl ferromagnets for creating novel electric and(a)spintronics devices by utilizing their fast carrier
mobilities due to the linear band structures. Contrary totopologically trivial materials, TQMs exhibit great
potential to show exotic and intriguing physicalproperties. TIs possess spin-polarized Dirac fermion
bands resulting in the quantum spin Hall effect andpersistent spin current that are resilient to defects 25),
and TSCs can be a material platform for realizing faulttolerant quantum computing utilizing Majorana
fermions that can exist in TSC states 26). A Weyl
semimetal is a considerably new family of TQMs 27),
where nondegenerate linear conduction and valencebands touch each other at the Weylpoint
by breaking
Figure2. Electricaldetection of the spin polarization in the surface state of Bi1.5Sb0.5Te1.7S
either spatial or time reversalresistancesymmetries,
yielding(b)K in BSTS device A at bias currents of (a) +100 μA and (b)R2, measured at 4.2
gapless Weyl fermions. In addition,aWeylsemimetalisd) R2 vs H curves for device B made with a 23 nm-thick BSTS ﬂake, measured at 4.2 K for
known to be an ideal material platform of the appearance
2 to contact 1 in (c), and from contact 2 to contact 3 in (d).
of the Adler-Bell-Jackiw (ABJ) anomaly of Weyl fermions
28), which is due to the breaking of chiral symmetry in
Moreover,theThereversal of the rectangular hysteresis feature is
TI, in our dmassless Weyl fermions under quantum
fluctuation.
ABJ anomaly was experimentallyalso
corroborated
in TaAs,
total condu
observed
when the current−voltage scheme is changed as
the fingerprintofthe
NbAs, TaP and WTe2 29-32) and isshown
becausethe
Figure 2c andSuch dependence
a behavior indicates
thatsignal.
the (a) R2 vs H cur
Figure 3. inTemperatureand d.
currentof the spin
Weyl nature. A Weyl ferromagnet and anti-ferromagnet
thanuppera factodirection ofthe
spin ofpolarization
reverseswiththeatcurrent
C (67 nmthick)
I = +50 μA. The
an
Temperaturedependence
ΔV2 in device33) andare also a novel family of TQMs,
where Co2MnGa
that,
which
is a naturalconsequence, of device
K,direction,
respectively.
(c)andI dependenceof themagnitude ofofthethe
spinspinsignal, ΔV2note
respectively,
Mn3Sn 34) are representative materials,
transport r
a number of spin-related effects, suchas giant anomalous
momentumlocking in the surface state. In this respect, it is, giant spin-Hall
andHall 35,36) and Nernst effects 35)important
increasing
to notestate
thatofthe
sign of the spin-dependent signal isre 2. Electricaldetection of the spin polarization in the surface
Bi(c)1.5Sb0.5Te1.7Se1.3. (a, b) Magnetic-ﬁeld (H) dependences of th
inverse spin-Hall effects 37) in Co2MnGa and the
Figure3b]consistent
with ofthe
helicity
topologicalat spin
4.2 KHallin BSTSat bias(a) left-handed+100 μA and (b)−100 ofμA;thethe thicknessof the BSTS
ﬂake wastance R2, measured
magnetic
effect ( device
a novelAfamilyof currents
Hall effects)
4
BSTS
shou
forindevice
made
with
a 23 nm-thick
BSTS
ﬂake,
measured
4.2 K
for I =
−100 μA.
The charge wecurrent wasappliedfrosurfacestate Becauseof BSTS
aboveat theDiracpoint.
Furthermore,
2 vs H curves38)
Mn3Sn,Bhasbeen
discoveredand detected.
of
the
bulk
contact 1 intremendous(c), and fromcontact
2 tohavecontact3in(d).
amountsof works
been
implemented,
it
have also measured R2 vs H for the case when H is parallel tois difficult to cover and follow thethe
wholeresearch topics
reduction icurrent.
As shown in Figure S4 of the Supporting
for
TQMs,
the
authorintroduces
his
own
and
relatedMoreover, the reversal of the rectangularInformation,hysteresis featureis
TI,hysteresis
in our devices
fraction inof theconductan
to te
the rectangular
is nottheobserved
this surfaceusefulworks regarding spin polarization detection in thistotal conductanceis expected to be not reduced
sig
for elucida
observed when
the current−voltage scheme
is changedasgeometry,
which strongly
supports
our conclusion.
chapter.
becausethe
totalresistance
of
our
BSTS
ﬂakes
chang
spin
polarizwn in Figure As
2c andd.
Suchabehavior
indicatesthattheaforementioned, topologically-protected
In passing, surface
because the dip features marked by thick arrows
thanattributeda factor of to
1.3 thebetween
4.2 and 300 K.passing,Also, it thisction of thespinspin
polarizationwiththecurrent
polarization
in TIs isreverses
an intriguing
research
in Figure 2aobject
and b areanisotropic
inspintronics,
andmucheffortwas
paid
for
detecting
the
note
that,
whereastheentering
into
thesurface-d
betweensa
ction, which is a natural consequenceof the spin-(AMR) of the Py electrode, one can bemagnetoresistance15
spin polarization. Two possible pathways to the goal; aΔotransport
regimeoccursat50−100
K in the
BSTS,
shape
mentum locking
inthesurfacestate.
In
this
respect,
it
is
F
i
g
.
7
(a)
Magnetoresistance
due
to
the
topologicallyconﬁdent
thattherectangular
hysteresis
feature
is
not
due
to
potentiometric method and a spin pumping method. The
increasing
decreasinginhysteresis
temperature
belowan5
is sharp
protected
surfacewith
spin polarization
BiSbTeSe at 4.2even
ortant to notetheto signthedetection
spin-dependent
signalfirstthatstudy
claimofthe
the surface
spin
theofAMR
eﬀect
of is
the Pyelectrode.
This
rectangularK.
(b)
Magnetoresistancein
BiSbTeSe
whenthe
Figure3b].
Therefore,
thedisappearance
of
the
spinw
stronger,sistent withpolarization
the left-handed
helicitybybehaviorofthetopological
was implemented
using
Bi2Se
3, a threewas
reproduced
in several
BSTS
devices.
Therefore,
it of
directionofthechargeflow
wasreversed.
Polarity
4
39)
BSTS should be due to a mechanism other result,than thethedo, wherethepoint.
potentiometricmethod was
TI theace state of dimensional
BSTS above
Dirac
Furthermore,
we the thatis reasonable
to conclude
the charge-current-induced
magnetoresistancewas opposite to thatspinin (a). (c)utilized. However, strong debate arose about what the
of
the
bulk
transport.
In
thisregard,apossible
orig
when
the
e also measured
R vs H for the case when
H is parallelto Missing
magnetoresistancein BiSe
at 4.2 K,inwhich24−26
polarization
at theTI/ferromagnet
interfaceauthors 2detected, because the Fermi
level of Biis
2Sedetected
3 is
but itreductionin thespinFermi
polarizationof Py,
signifies
the positionof thelevel is crucial
for charge-curr
current. As
shown
Figureband
S4 andofthethelocatedin the in
conduction
topologicalstate magnetoresistanceterms
of Supportinga peculiarfeature.
usefuldetection
to test otherferromagnets
or to insert
aThetunnelindepof the surface
spin polarizationinrmation, theis buried
rectangular
notTemperatureobservedin thisinto thehysteresis
topologicallyistrivial
bulk
state. Thus,
aand successful
Current
Dependencesofthe toSpin
topologicalinsulator
(ref.
41)).
for
elucidating
thekeyfactorprohibitthedetectio
showninthatsupports
the authors
spin polarization
metry, whichquestion
strongly
our detectedconclusion.
Signals.
The
temperaturedependenceofthemagnitudeoftheattributed not to the topological state but to the Rashba
polarization
room temperaturein astheessentiallypresent danda bulk at insulative
Bi2Sespin3)n passing, because
the dip features marked
thick
spintoby
signalwasarrows
in thedevices
A and inC. theTheTIobservability
R2(suchvsstate. The similar debate also arosethe claim
ofalsothe investigatedpassing,
diﬀerenceof
the AMg
Bi1.5Sb0.5Te1.7Se0.3) is quite important. Indeed, the equations
Figure 2a roomand temperatureb are attributed
the measured
anisotropic
detection of tothetopologicalsurfaceat 300 K in device A at I = +100 μA is shown
H curve
Sb0.5Te
Semostpossibleauthors’group introduced
Bi
1.5
1.7
0.3 as alikely
betweensamples
A
and
C
is
due
to
a
diﬀ
in
the
FM/
netoresistancethe such
Py electrode,one 3a.
can Thebe candidate
To avoid
confusion,
identificationofstate(AMR)
in Bi2Se3. ofin Figurerectangularbehavior
has of the when a Py
TI andhysteresis
detection
the shape
ofreported
the Pysuccessful
electrode;remember,the polarityof the hysteresis
spin signals,feature
which comesfromtheﬁdent that therectangular
is
not
due
to thesurfacespin signal
polarization
up tobeingca. 150observed.
K (Fig. 7) 41). The
disappeared,
whereasAMR
iskept
4. Magnetoresistanceinis Bisharp-baseddevice. Rthe
H curvesof a 72 anisotropy
nm-thickand smooth,shapemagneticalignments of the surfaceFigure
spin currentof a TI and
2Se
2 vs
ΔV2 =B
spin signal
is3detectable only from
Bi1.5Sb0.5Te1.7Se0.3 andAMR eﬀect spin
of
the
Py
electrode.
This
rectangular
hysteresis
40)
In
deviceC,neithertherectangular
hysteresis
nor
the
AMR
, andatcontrol
detector ferromagnet, is quite significant−100 μA, and
300 K forI =is+100
μA in
and
I =a −100μA,
respectively.
stronger,
which
leads
steep
magnetizationchan
Se3 to
even
at
4 K,
which
is
no (c)
signalobserved
Bi2(d)
avior was reproduced
BSTS
Therefore,
experimentsin
to several
support aclaim devices.
isindispensable.
Thus,it at 300result,signalwasobserved
K
[the
inset
of
Figure
3b];
in
fact,
the AMR
whosespinorigin
compelling evidence
that signal
the detectedsignalisis resistanceeasonable tocomparison
concludeofthat
thein charge-current-induced
results
a bulk non-insulative
TI (suchspin
27
the temperatureof thethemagnitudeof BSTS,the spinwhere
expectation.
Whenasdependence
we use thevalue
kF magnetization≈
0.1 Å−1 forη is perpendiculaAs ηa ciwhen
direction
rization is detected at the TI/ferromagnet
interfacein C [main panel of Figure 3b] indicatessignals, ΔV,
indevicecurrent
from2
charge-current direction is diminished.
resistanceis calculated to be 0.05−0.5%. Such a small η is reasonably
ms of a peculiar magnetoresistance feature.
that ΔV2 decreases monotonicallywith increasing
temperatureis theeledeThe dependenceof ΔV
2 on current I e inBS
deviceemperature and Current Dependences
of
the
Spin
understoodasaresultoftheconductancemismatchproblem
JournaloftheMagnetics
SocietyofJapan
Vol.47,
No.2,
2023
31
and vanishes at around 150
K. Although
the3c.
bulkOneconduction
the relatio
width
shown
in Figurecan see that istheforbothnals. The temperature dependence ofbetween
themagnitudeoftheusually
becomesdominant
at
300
K
even
in
a
bulk-insulating
in
eq
1,
our
the metallic Py essentiallyelectrode andrelatively
highlinear.theFrom
the spin-charge
coupled9 hysteresis
signal was also investigated in devices A and C. The R2 vsequationsand Hawthorn, magnetor
resistance TI channel, whichleadsgiven
to by
a Burkovsmall magneto-

INDEX

ascribed to the topologically-protected surface helicalspin state. To note is that the similar comparison was
carried out in the spin pumping approach 42).
Topological nature in TQMs allows the other intriguing
physics in Weyl materials. TaAs is the first material as a
Weyl material 43), and a Weyl material collects significant
attention because of its band-crossing points that giverise to plenty of unique physical properties, such as the
Fermi arc surface states, the chiral anomaly coming fromthe Nielsen-Ninomiya theorem 44) and monopole-like
Berry curvature 45). In addition, a prominent class of
Weyl semimetals is Weyl magnetic materials such as
ferromagnetic Co2MnGa and antiferromagnetic Mn3Sn.
These two materials are playing pivotal roles incondensed-matter physics because of the recent
discoveries of the gigantic anomalous Hall effect (AHE)
46,47), the magnetic spin Hall effect (a novel family of Hall
effects) 48), and spin caloritronics phenomena such as thelarge anomalous Nernst effect 49,50). Additionally,magnetic Heusler alloys have emerged as promisingmaterials in the field of spintronics due to their either
half-metallic or semimetallic nature, which would lead toa high spin polarization 51,52), as has been reported in Cobased full Heusler compounds 53,54). Co2MnGa is a
representative Weyl ferromagnet as aforementioned, andsizable spin Hall effect (SHE) and ISHE can be expected
due to its topological nature like in the case of AHE.
Indeed,coexistenceof theINgiant
ISHE andthe SHEGIANT SPIN
HALL ANGLE
THE HEUSLER
ALLOY
… was
corroborated by using the electric non-local four-terminal(a)method 55) and more importantly, it was observed that
Onsager’s reciprocity does not hold for the system unlike
for conventional metallic ferromagnets (see Fig. 8) 56).
Furthermore, two orders of magnitude enhancement ofmagnetoresistance attributed to the anomalous Nernst
effect in single Co2MnGa wire was also reported 57).
Not only Weyl ferromagnets and antiferromagnets, but
a Weyl semimetal also enable significant spintronic
effects. Among a number of Weyl semimetals, the Td-type
WTe2 58) possesses abundant spintronic nature, where
the Weyl points appear at the crossing of the obliqueconduction and valence bands due to the broken
inversion symmetry and nonsaturating giant positive
magnetoresistancea HEUSLER
manifestation
GIANT SPIN HALL ANGLE INisTHE
ALLOY … of the type-II Weyl
PHYSICAL REVIEW B 10
character 59,60). As aforementioned, fictitious magnetic
the magnetization of F 1, where it is worth(a)(b) at each Weyl point,monopoles
can appear
which
giveswas found to be negati
AMR
of Co2 MnGa
reported [46].
rise to in-plane spin polarization at the surfaceofthe
For the ISHE measurement setup, theRISHE can be expressedspin as [37,45]
Weyl semimetal 61,62). In fact, the in-planexIs 
polarization along the b-axis (Sy, parallel to the WTe
2
R
θSH
,
ISHE =Ic
WD
plane) is ascribed to the Weyl node, which was
where Is  is the spatial average of the abso
electrically detected 63). Meanwhile, the Salongy polarization
the z direction, WD is the width of the dx is the shunting factor that takes into accou
disappears
at
very
low
temperature(<
15
K)
due to lattice(c)generated charge current is being shunted by
By applying
a one-dimensional spin diffusio
expansion, which has been hampering spin
informationtransparent interfaces and considering tD 
propagation and extraction at higher thetemperature
thickness of the detector electrode an
diffusion length,
RISHE can be written as
available for all-electric spin devices. Importantly,
angle
θSH xWN 1 − αF2 2αF RF2 R
resolved photoemission spectroscopy (ARPES)R
revealed
2W
ISHE =
tF(2RF + RN )2 − Rother possible spin polarizations along the c-axis (Sz,for a two-wire LSV using F 2 as the detector
perpendicularPHYSICAL
to the plane)in addition
to thosealong theREVIEW
B 103, L041114(2021)
3W
R
ISHE
b-axis in WTe2 64). A pioneering work utilizingthe Sz 2 θSH xWN 1 − αM=polarizationofWTe
2 is detection of anomalous
the magnetization of F 1, where it is worth noting that the spintM
. The authors 2αF RF RM RN e−L/2λtorqueST-FMR(seeFig.
9) 65,66)
MnGa
was foundto benegative,as previously
AMR
of Co2in×(2RF +
RN )(2RM + RN ) − (2RM −introduced
andreported[46]. a potentiometric approach to create
Fig.
8the
Measuring
setupsfor the ISHE(a) theandtheSHEresistance(b) in Co2proved
MnGa, a Weyl ferromagn
For
ISHESzmeasurement
setup,
ISHE
polarization,
andexperimentally
detectthefora three-wire
LSV using M as detector,
canexpressed
asISHE[37,45]
RSpinNATUREPHYSICS
DOI: 10.1038/NPHYS3933
ISHE resistances
polarizationis thequite
to reciprocity
thermalthatthebe S
to theand
SHE,resilient
where
Onsageris broken (ref. [5z dueARTICLES
width of the N wire, λN is the spin diffusi
α
and
α
are
the
spin
polarizations of th
F
M

x
I
(a)
(b)
WTe /Py, I || a-axis
a
Pt/Py
b
s
electrodes
RISHE =θSH,(1)and the middle wire M material,
30
Ic
W10D
RN , RF , and RM are, respectively, the spin res

(b)

2

20

F 1 (considered to be the same as F 2), and(c)

VS (µV)VS (µV)5
spinin current
where 10Is  is the spatial average of the absorbed
Ref. [43]. For Eq. (3) it was considered tha
M was andlocated at the middle of the gap distan
00along the z direction, WD is the width of the detector wire,
F 1 and F 2 electrodes.
−10−5x is theshunting factor that takes into accountthat partInofthethecase when a FM material is us−20
electrode,R
can be written in terms ofgeneratedchargeSsin(2current
wire.
−10 by the copperφ − 2φ )cos(φ −isφ ) being shunted
φ − φ ) ISHE
Ssin(2φ − 2φ )cos(−30(NL4T) resistance 
By applying a one-dimensional spin diffusion modelnonlocal-four-terminal
[47]
for
−
be measured by connecting the VNL4T
ter
40
40
− t
is
transparent interfaces and considering tD  λD , where
VSHE
in
Fig.
1(b)
and
sweeping the externa
D
20
20
in
a
directionparalleltotheferromagnetice
the thicknessof the detector electrode and λD is its spin
FIG. 2. (a) Schematics of the ISHE setup for a ferromagnetic
A typical NL4T signal is shown in the in00
diffusion
length,R
canbewrittenasdetector. In this kind ofISHE
sample both FM electrodes are made ofwhere two different voltage levels are mea
SHE setup, thethe−20same material, either Co2 MnGa or Py. Forthe −20
on whether the relative configuration of the2
2 polarity.
−L/λN
current source and Asin(2voltmeterareexchanged,
preservingtheAsin(22φ )cos(φ − φ )theφ −ferromagnetic
electrodes is parallel or− 2φxW)cos(Nφ − φ ) 1 − αF 2αF RF RN e−40−40
2W of theθφSH
φ − 2φ )(b) Schematics
detector. In + Bsin(2= ISHE setup for a nonmagnetic(2)between these two voltages, no
RISHE2−90−−2L/λNdifference
this −90case Py wasused forFM electrodes,
butRonethem(2RF +
RN2ise0not
0
90tF
180
270
90
180
270
N ) ofinjection
current, defineRNL4T , which is00VA (µV)0

VA (µV)

0

0

0

0

0

0

φ (°)The SHE setup is obtained by exchanging
used in this measurement.

current
sourcewith using
the voltmeter
preserving
the polarity.
cττ
for athe(c)two-wireLSV
F 2 whileas thedetectorandBB(c) Nonlocal resistance of the ISHE setup and of its reciprocal (direct)3W
SHE setup for Co2 MnGa, measuredI as a function of in-plane
R
ISHEmagnetic field H at room temperature. The bottom panel
external
 curve 2forCo2 MnGa electrodeσ v(bc)F 1. (d) Equivshows a typical AMR
θSH xWISHE− SHE
αM resistances measured for Pt and Py
alent nonlocal
N 1andat=room temperature.
The bottom panel shows the
AMR curve forτB ≠ 0atMof Py in both cases.
is allowed
electrode F 1 madeφ (°)

of the amount of spin current being absorbed
wire. Then, Eqs. (2) and (3) are simplified toIθSH xWN 1 − αD2
RISHE =RtD
2αDwhere the only unknown spin transport parapolarization of the detector electrode αD . I
mine αD , RNL4T was measured in two-wire

2αF RF RM RN e−L/2λNb
×−L/λFigure 2 | Angulardependenceof ST-FMR
signals.
a, Symmetricand
ST-FMR −resonancecomponents
for a Pt(6nm) control
N nm)/Py (6Fig. 9(2R
Anomalous
spin-orbit
torque(SOT)
appearingin)(2R+torque
Rantisymmetric)−(2R
RL041114-3
F + Rspin-orbit
N angle.
N
N )RN
sample asFig.
a function
in-plane magnetic-field
TheM
microwave
frequency
is 9 GHzM
andthe applied
microwave
is 0 dBm.
The2parameterφ
9 ofAnomalous(SOT)
appearing
ineTdpower
-type
WTe
. (a) SOTin Pt/Py an
accounts for any
misalignment
betweenthe sample
and the magnet.
b, Symmetricandantisymmetric
ST-FMR resonancecomponents
forin
a
T
-type
WTe
.
(a)
SOT
in
Pt/Py
and
(b)
SOT
d
2
(3)
Fig. 8
8 Measuring
andthetheSHE
WTe (b)(5.5 nm)/Py(6Conm) device(device 1) as a functionof in-planeferromagnet.
magnetic-field angle, with current(c)applied parallel to thea-axis. The microwave
Fig.
Measuringsetups
setupsfor
forthetheISHEISHE(a)(a)
and
SHE
in
MnGa,
a
Weyl
2
frequency is 9 GHz and the applied microwave power is 5 dBm. The error bars in a and b represent the estimated standard deviations from theWTe
2/Py, where the electric current flows along the a(b) in Co2MnGa, a Weyl ferromagnet. (c) Spin least-squares
procedure used to determine V and V . c, Illustration that a magnetization-independent, linear-in-current out-of-plane S–O torque isforafitting
three-wireLSV
M /Pyasbilayer.
detector, where WN is theallowedby symmetry
for current appliedalong theusing
a-axis of a WTe
NATUREPHYSICS
DOI: 10.1038/NPHYS3933
axis.
(c)
Schematic
imagesof [55]).
structural symmetrySpinresistances
due
to
the
ISHE
and
the
SHE,
where
Onsagerreciprocity
is broken(ref.
ARTICLES
resistances due to the ISHE and the SHE, wherewidth of the N wire, λN isbilayer
thewithspin
diffusion length of Cu,
sample plane. In a simple heavy-metal/ferromagnet
no component is very different from cos(φ) sin(2φ) (Fig. 2b bottom
(ref.
65)).
breaking
inWTe
2torquepanel).
The
variationsin the absolute values of signal amplitudes
brokenlateralsymmetries,
thecurrent-induced
amplitudes
Onsagerreciprocity
isbroken(ref.
55)).
α are the spin polarizations of theferromagnetic
αtoFIthe||and
(a)
(b)
(due
spin HallMeffect, the Rashba–Edelstein effect, or the reflect the broken symmetries of the WTe surface: the absence of
WTe
a
Pt/Py
b
a-axis
2 /Py,
Oerstedfield) have a cos
φ dependence. The AMR
in Permalloy
mirror symmetry
in the ac plane (corresponding
electrodes
andthemiddlewireMmaterial,
respectively,
and to φ → 180 − φ,has an angular dependence that scales as cos φ, which enters since m̂ is a pseudovector) and the absence of two-fold rotational
30
10
V R
symmetry
about the c-axis (φofasNdR/dφof these two contributions→the180 +N,φ). This result indicates the, RF∝, sin(2φ).
and RTheM productare, respectively,
the spinresistancesthen yields the same angular dependence for the symmetric and existence of a source of out-of-plane torque not previously observed
20
antisymmetric
ST-FMR components:
V the
in anyS–O torqueexperiment.defined= S cos
φ sin 2φasandF
1(considered
to
be
same
F
2),
and
M
wires,
5
The unusual angular dependence we measure for the antiV = A cos(φ) sin(2φ). Our Pt/Py control samples are well10
in Ref.
For
it wasconsideredthat
thesignal
middlewireapplied along the a-axis
ST-FMR
with current
described
by this[43].
behaviour(Fig. Eq.
2a; the (3)parameter
φ accounts
for symmetric
Journal of the Magnetics Societyof Japan2023
32
any misalignment
between the Vol.47,
sample and theNo.2,
electromagnet,
and can be fitted well by the simple addition of a term proportional toM wasdistance L between the00sin(2φ):is typically<5 ).located at the middle of the gap
For our WTe /Permalloy samples with current along the a-axis,
F 1 andcomponent
F 2 electrodes.
V (φ) = A cos(φ) sin(2φ) + B sin(2φ)
the symmetricof the ST-FMR signal also has this form
(3)
−10
−5
(Fig. 2b top panel). The non-zero symmetric component indicatesthecasein whena FMbilayer,material
is Auseda detector
that S–O In
torquesare present
the WTe /Permalloy
and B areas
constants
independent of the field angle (seesince where−20
the symmetric component corresponds to an in-plane torque and the solid line in Fig. 2b bottom panel). To quantitatively translate
be written in terms of the conventional
electrode,R Oerstedcan−10cannotfield. However, the more the measured angular dependence of V and V to torques, we
φ − beSsin(2
2φ generated)cos(φ − φby) anISHE
Ssin(2φ − 2φ )cos(φ − φ )
0

2

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◦

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[27]

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c2

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c2

5

2

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84

2

17

16

n-Si

10 µm

Ic1

80

NiFe

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c2

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contact

2

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3

e

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e 80

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Universityof Delaware,
Newark,DelawareFurthermore,
19716, USA. Cambridge
NanoTechInc.,
Massachusetts
02139, USA.
32.6
nng,current
wasthe same(1 mA)
the result
shown
inCambridge,
Figure 2g
also
unequivocallycontact
32.6
z voltages current
296
e samecurrent
densitythe 2 andeliminates
the possiblerespectively.
fringe-field-induced
in
ments
using
theforWTe
Pt channels,
TheHallinjection
was set to be 1 mA for both devices and the measuring295
0.00temperature was 5 K.
Nature Publishing Group
Nature©2007weak
PublishingGroup
A electrode. Whilst
voltagethehysteresis, since no hysteresis was observed in the©2007
PMA/PtTJ
Nature Publishing Group
©2007
emitter
Pt channel device, where thechannel device. We also emphasize that the interface eﬀects
contact
resis is about 2 µV, the voltagethat can appear in FM/semiconductor spin devices under theonof the hysteresis due tothe anomalous Hall eﬀect (AHE)of thetheconPMA electrode. The coercive
32.4by32.4force and saturationde smaller than the spin voltage
same measuring setup[28–31] are also eliminated–0.05
oe2 300
K. b) Furthermore,
Schematicit imageof the measuring
setup ofspin
from a WTe2 spin device. Spin accumulationn-Sitrol experiments
because the interface
eﬀectsdo extraction
not enablespin device.
900 µmcollector
explaining
the polarity
the hysteresis
tage hysteresis
is successfully
reatedand potentiometricallydetected.
c)change
Spin ofvoltage
hysteresis
at 5 K. Alignments of spins created in the WTe2 andz by the reversalof the charge momentum, which is discussed in detail below
device even when the electrichown
Temperature
evolution of spin voltage hysteresis observed from the WTe2 spin device. Red
ionof the correspondingly.
Si spin transport device. ad), Schematic
band
–0.10
32.2
NiFe

Second collector curre

e

NiFe

20

80
e

84

[28–31]n-Sicollector

900 µmc1
Adv. Electron. Mater. 2022, 2200647

20

Cu

80

Ic2

NiFe
contactBasecontact

2

2
[27]

2

Magnetic moment (10–3 e.m.u.)

420

Second collector current, Ic2 (pA)

3

Ic1
80

Cu

Al

1

e

Vc1

d

2

10-µmthick2
FZ-Si

Second collector current, Ic2 (pA)[27]

[28–31]

CoFe

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2

n-Si

10 µm

2

2

2

2

2

Al

5

2

c1

Second collector current, Ic2 (pA)

Al2O3

14

14

80

16

20

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Second collector current, Ic2 (pA)

2

c2

d

2

Second collector current, Ic2 (pA)

2

84

80

16

c2

2

2

e

Magnetic moment (10–3 e.m.u.)

c2

c1

Cu

c1

c2

2

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3–9

c2

c2

e

16

Magnetic moment (10–3 e.m.u.)

LETTERSec2

20Magnetic moment (10–3 e.m.u.)

15,16

1,2

c1

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CoFe

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c1

2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202200647 by Kyoto University, Wiley Online Library on [19/10/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

14

20

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2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202200647 by Kyoto University, Wiley Online Library on [19/10/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

c1

e

c1

Al2O3

c2

20

Al

c2

Second collector current, Ic2 (pA)eMagnetic moment (10–3 e.m.u.)

LETTERS

16

Second collector current, Ic2 (pA)

First collector current, Ic1 (nA)

15,16

c1

Second collecto

Second collector current, Ic2 (pA)

First collector curreFirst collector
First collector current, Ic1 (nA)

Emitter current, I

Emitter current, Ie (mA)

Emitter cu

Emitter current, Ie (mA)18

c1

2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202200647 by Kyoto University, Wiley Online Library on [19/10/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

16

80

c2

2199160x, 0, Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202200647 by Kyoto University, Wiley Online Library on [19/10/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

c1

e

Downloaded from https://onlinelibrary.wiley.com/doi/10.1002/aelm.202200647 by Kyoto University, Wiley Online Library on [19/10/2022]. See the Terms and Conditions (https://onlinelibrary.wiley.com/terms-and-conditions) on Wiley Online Library for rules of use; OA articles are governed by the applicable Creative Commons License

SOT1.5in WTe2/Py, wherewww.advancedsciencenews.com
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LETTERS
NATURE
Emitter
voltage| Vol(V) 447 | 17 May 2007
andtransport
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Figure2b shows
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current
16
hot-electron
filtering
throughferromagnetic
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Emitter voltage(V) thin electrons,
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the
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by Ic1, andIspin, Igenerated
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to
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surement andcontrol
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In
Fig.
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contactfor
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temperature
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for the electrons to exceed
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spin
injectionand current
spin
detection.
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it is
not
on
magnetoIn Fig.
3a,in-planemagnetic
hysteresis
data ofM
16
voltagethecurrent,Si
drift
region.
means
that
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the
one
and
shown
in themicrographdis-shown.
I . b, First
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n-Si
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There
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those
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Coseveral
Fe /FZ-Si
Schottkybarrierheight,and wire-bonded
is typicalforsuchour
c2the
c1
FZ-Si
are
severaldesignaspects metal
thatbaseprovide
ourdevicewithtransport
a throughresistance,
the hot-electron
spin
injectionandspindetection
and FZ-Si
85 K areshown.
Measurements begin with f
undopedSihas
variesThereby manyordersofmagnitude.
The
insensitivity
transistor-type
structures.
AfterverticalHall
voltage
in
the
FZ-Si
no
effecton
I.
The
underlying
backplayed
in
Fig.
1b.
c2
clean
spin-transfer
currentI.
(1)
An
undopeddevicelayer
voltageacrosstheSi
drift
region.
This
also
means
that
any
generateddevices
like
the
one
wire-bonded
and
shown
in th
alignedmagnetizationsc2
allowing
effective
injection
anddetectionatcryogenic
and
room
Fe
Schottkybarandenableelectrons
injectedbythehigherSi/Niof I to FZ-Si resistance
impliesthat
I all-electric
is also insensitive
magne10 mm FZ-Si,
someof-typetheseelectrons
travelballisticallythroughtheFigure to2.
a)Temperature
evolutionofthehysteresis
due
to
the
anomalous
Hall
eﬀect
(AHE)
of
the
PMA
electrode.
The
coercive
fo
Fig.
10
(a)
Opticalmicroscopic
view
of
an
spin
device
using
T
WTe
,
a
Weyl
& Douwe J. Monsma2 temperatures
d
2
clean
spin-transfer
currentI.
(1)
An
undopedFZ-Si
devicelayeralignedmagnetizations
byrampingtoourmagnetavoids
impedancemismatchissuesandprevents
interferencefromc2
rier toovercome
the Cu/n-Si
Schottky(4)
anisotropy. (2) Because
spin insensitivity
filteringis caused bybulk
scattoresistanceinthe FZ-Si.
In fact,atin
thetemperature
we useformea-barrier.
Ni
Feon/CuIfilm
andintounderlying
the 2an-Si shows
collector,
resultingin a played
current
groundtothethetoresistanceandvoltage
of
the
FZ-Si
isShapeFiguretheinjector
tunneljunctioncurrent–voltage
charHallvoltage
the
FZ-Si
has
no
effect.
ThebackinFig.
1b.
ischosenbecauseits
extremely
low
impurity
density
results
in
wide
When
the
magnetic
fielS
magnetization
can
be
seen
up
to
300
K.
b)
Schematic
image
of
the
measuring
setup
of
spin
extraction
from
a
WTe
spin
device.
c2
2
www.advelectronicmat.deoftheferromagnetic
films
allows
us
to
apply
a
perpendicularmagtering in the ferromagnetic films, they are easy
to reproduce,as
there
www.advelectronicmat.desurements
here
(85
K),
the
FZ-Si
is
completely
frozen
out
and
its
n-Si
(Iimpurity) detected at the
In contact results
to the substrate.
This signal rises
aboveischosenbecauseits
extremelylowdensity
in
wide
When
the
magnetic
field
is
swept
through
zero
and
10
µm
parasitic
effects.
The
clean
collector
currentshows
independent(b)semimetal.
(b)
setup
the
Sfieldspin
detection
createdinoftheWTebeneaththeresistance
PMA
iselectricallycreatedandpotentiometricallydetected.
voltagehysteresis
at 5theAlignmentsofspins create
that
thetopotential
isresistivity
screenedbytheThistwobarriersoneithernetic
for spin
precession
measurements,
withoutorientingis no interface
sensitivity
thespinMeasuring
filtering(as
there is,example,zSchottky
2. (c)
acteristics,
illustrating
expected
nonlinearis for
.10
Vfor
cm.
means
that
therepolarizationareno thermallyorgroundtotheinsensitivity
toandvoltagetheFZ-Si
is theourdetection
limit
atthe
an emitter
voltage
21.2Vc) Spin2a
Figureshows
the Iinjector
tunneljunction
cur
Schottky
depletion
regionsandaof approximately
linearconduction
band.
This
e–V
e K.relationship.
Niswitches
to80Fe20polarization
is maintained
through
theThisundopedSi layer.
Therefore,
h of electrons are transportinmagnetic
magnetizations
outelectronsofplane.
magnetic
tunneljunctions). (3)
device,likeaSchottky
spin-valve
depletion
regionsandlinearconduction
band. This
the Ni
Fe20 ofswitches
to
align
with
the field
andt
impurity
generated
electrons,
and the only freepresent
are a(Fig.
2c). are
those
in
the
PMA
electrodeshown correspondingly.
d) Temperature
evolution
spin voltage
hysteresis
observedfrom theWTeandelectricalcontrol
of
spin
thus
con80measurement
theelectrons
travellingin fabrication
the FZ-Si
conduction
band
Figure2b hysteresis
shows
the
ofthe
injected
current
herence in spintronic devicestransistor,
this device
the andelectronthat
analogueof sourcethephotonpolarizationthat
the precession,
potential
isofandscreenedbythetwoSchottkybarriers
onupward
eitherillustrating
expected
nonlinearI
prevents
wells
and
long
spin
dwell
times.
(2)The
deviceisside,a ishigh-impedance
current
.of
As
Ispin
ispolarized
drivenOur
procedures,
described
in potential
thesection,areare
antiparallel,
resultintheinjectedelectrons.
InMethods
Fig.
3a,in-planemagnetic
dataof Isimultaneousat V 5acteristics,
21.8
Vsweeping.
Temperaturedependence
magnetoresistance
the
WTe
spin
device.
TheS
spin
polarization
2z(blue)
closedsquaresareexperimental
data
in
the
(downward)
Whilesuperposition
of
the
AMR
can
be
seen
at
many orders of magnitudebyfirms
experiment
prevents
potential
and transistor
long
spin
dwell
times.
(2) Thedeviceofaareantiparallel,
resultinginareduction
in
I
drift
in
conduction
bandofsilicon.
I analyser, and Ispin
by I , coherent
I inisoptics.
virtually independentofthe
Vare, theappliedsimilartothoseofwellsthe
spin-valve, and85
resultinshown.
an array
of
c2
There
severaldesignaspects
thatprovideourdevice
with
a
and
K
are
Measurements
begin
with
fully
saturatedandgenerated
not
by
an
ohmic
source,butbyhot-electron
injection.
side,
and
that
the
electrons
travelling
in
the
FZ-Si
conduction
band
I
–V
,
demonstratingathreshold
in
I
at
V
5
20.8
V.
This
repreFigure
2b
shows
the
simultaneous
measurementoals , semiconductors could
There areare various
intrinsic device
aspectsthatallow
a cleanspinsalient
hysteresis
attributed
tosuccessful
spindetection
by
the
PMA
can
be
observed.
The
range
of
the
hysteresis
isconsistentwit
ismeasuredat85
K
toeliminate
Schottkyleakagecurrents.
(3)
c1
e
c1
e
As
the
magnetic
fieldpa
voltage across the Si drift region. This also means
anyisgenerated
likeundoped
the
one
shown
in themagnetizations
micrographdis-byclean thatspin-transfer
current Idevices. (1) atAn
FZ-Si
deviceandlayeralignedto our magneticfield
maximum.
measured85
K wire-bondedtoeliminate
Schottkyleakagecurrents.
(3)e)
Veramping
VMagnified
Ic1viewo far, spin transport has only
magnetic
field
passesthroughtheatCoFef)16Astransport
signal1ain Iillustrates, and tothat structural
make itimmuneto fringe
fieldis (4)attributed
symmetrybreakingalong
theb-axisinBlack
WTe
andisfield
resilienttothermal84K.
Figuretheoperatingprinciple
andschematicband
c1 As the2magnetic
AHE
of
the
PMA.
solid
bars
show
the
scale
of
20
µV.
of
the
spin
voltagehysteresis
observed
300
voltage
in
the
FZ-Si
has
no
effecton
I.
The
underlying
backplayed
in
Fig.
1b.
is
chosenbecauseits
extremely
low
impurity
density
results
inwide
Figure1. a)Hall
Opticalmicroscopic
image
of
an
all-electric
spindevice
made
of
WTe
.
The
inner
two
electrodesconsistofferromagnets
with
PMA,
and
When
the
is
swept
throughzero
andchanges
sign,
first
are
generated
not
by
an
ohmic
source,butbyhot-electron
injection.
These
devices
operateoverawide
temperature
range,
without
I–V,
demonstratingathreshold
in
I
at
V
5
2
sents
the
0.8
eV
potential
energyneededfortheelectrons
toexceedmiconductors orin comIc2
induced magnetoresistance and Hall effects. (1) The exponential spin
Copper
(Cu)
is
used
below
the
Ni
Fe
to
providealowbarrierc1ec1emagnetizations
again
80
20
the
outer
two
electrodesconsistofnonmagnetic
Pt.
The
PMA
is
realized
bya[Pt/Co]multilayer,
where
the
thicknesses
of
Pt
and
Co
are
4.1
and
1.0
nm,
groundtotheinsensitivity
toresistanceandvoltage
of
the
FZ-Si
is
Figure2ashows
theinjector
tunneljunctioncurrent–voltage
charCopper(Cu)
is used
below
the
Nithe
FePt20toprovidea low
Schottky
depletion
and a linear
conduction
band.
This
magnetizations
align
and
themeasuring
higher temcoexperiment
using
only
The with
amplitudeof theinjectedelectric current wasagain
set to be
50 µA,and theFeelectrodes.
switches
to align
the fieldbarrier
andthe magnetizations
ors, excluding a wide range diagram
selective meanof
free pathdependence
in theSpin
ferromagnetic
films
createregions
80Ni
ourdevice.
injection
detection
is
based
on
the
respectively,that
and thenumber
10. An external
magnetic
field is inappliedtoand
the WTeacteristics,
plane.
b)factSchematic
imageof the
Tthe
-type
WTe
.
These
devices
operateovera widetemperature
range,
withoutsents
0.8
eV potential
energyisfor
neededeappreciablechangeIperpendicular,(4)
despitethat
resistivity
thestacking
potentialis isscreenedby
two Schottky
barriersoneitherCoin84awhich
Fe16is/FZ-Si
barrierheight,is typicalsuchtofor–V
relationship.
illustrating
expected
nonlinearIof
fluctuation(ref.
[67]).
th indirect bandgaps.
Most
prevents
potential
wells
and the
long
spin
dwell
times.
(2)The
devicevery
large
spin polarizations.
In theprinciple,
thiscan approach
100%,
are
resulting
reductionin
I of Schottky
approximately
2%.
Neitherhysteresis
norantiparallel,
AMR
canthebe seen,compelling
evidence
thatthethe hysteresis
ofand
the spinvoltages
ascribed
thethesuccec) Raman spectrum from the WTe . The identified Raman modes are denoted inc2
the figure. d) Magnetoresistance eﬀect of the WTe. Large positiveandthe electrons
travellingin theconduction
band
which (in addition
to itsside,
Figure2bshows
thesimultaneous
measurement
injectedfieldcurrent
isFZ-Simeasured
ata manifestation
85
K to eliminate
Schottkyleakagecurrents.
(3)
attenuationofminority-spin
hotelectronsinferromagnetic
thin
Asthe
theof
magnetic
passesthroughthe Co Fe switching
field,
theCo Fe /FZ-Si Schottky barrier height, andmagnetoresistanceunderthatthe applicationof an external
magnetic
field
along
the
c-axisisofa type-IIWeylsemimetallic
nature.
e)TembappreciablechangeinI,
despite
fact
that
the
resistivityofthedetection
of
the
S
spin
polarization
via
spin
accumulation.
The
inset
shows
the
measuring
setup.
g)Comparisonofresultsfor
spin
ex
undopedSivariesby
manyordersofmagnitude.
The
insensitivity
metal
base
transistor-type
structures.
Afterverticaltransport
throughc2
84 16
has long
been
predicted
aare generated
not by anresistanceohmic source,byhot-electron
I the
–Vthe
, demonstratinga thresholdin I atzV
5 20.8 V. This
repreperature dependenceof the two-terminalof WTe . Abutmonotonic
decreasetheresistance
supports
type-IIrolof
spintransport
Copper(Cu)in15,16
isinjection.
used
below
Ni
Fe Weylto semimetallic
provideanaturelow ofbarriermagnetizations
again
align
and
the
highercollector
currentis(b)
ato exceed The
bstructures.
nics with enhanced(c)
WTelifetime. The results
shown in(c–e) inobtainedfrom athewide
spin device
shown in (a).
films,
asspin-valve
transistors. thatIn ourdevice,thespin-valve
ments
using
themagneWTe
Pt channels,
The injectionbcurrent
wassettransistor-type
to be 1 mA for bothdevices and themeasuring
tem
(4)
These
devices
operateover
temperature
range,
withoutsents
eVapotential
energyneededforthe2 and
electrons(a)(b)
a
undopedSivariesby
manyordersofmagnitude.
insensitivity
base
vertical
Iwere
to
FZ-Si
resistance
implies
I CotheisFe0.8
also
insensitiveto
10 suchmm respectively.
FZ-Si,
someof thesemetalelectrons
travelballisticallythroughAfterthe–orbit scattering and latticeappreciable of
c2 in
0.15
changeI , despite the fact that the resistivity of
thec2/FZ-Si 33.0
Schottkybarrier height, and is typical for33.0
0.15
magnetoresistance(MR) of the WTeitself,a spurious
signalcurrent
isdetection
notainjected into the
PMA electrodeinhavethe “crossed”
10-µms promise, a demonstrationb Itransistors
usedforinjection
and
each
only
a
single
of
I
to
FZ-Si
resistance
implies
that
is
also
insensitivetomagneundopedSi
variesby
manyordersofmagnitude.
The
insensitivity
10mm
FZ-Si,
some
of
these
electrons
travelballistmetal
basetransistor-type
structures.
Afterverticaltransport
through
33.0
c2
c2
toresistanceinthe
FZ-Si.
In
fact,
at
the
temperature
we
use
for
meaNi80
Fe20/Cu film and into the n-Si collector, NiFe
resulting in a current
0.15
duebecause
to the fringe field in the PMA electrode, and the interfageometry and the AHE signal is negligibly small in the b-axis
remained elusive,thickof
Iclarified
resistance
impliesthat
I all-electriciscarefulalsoandinsensitivetomagne10 mm
FZ-Si,
someof-typetheseelectrons
travelballisticallythecial eﬀects
asin FM/semiconductor.
oriented
WTe
Thus,
device.
These
results
unequivocallynegate2.
a)spinTemperature
evolutionofthehysteresisdue
tothethroughanomalous
Halluseeﬀect(AHE)of the 2d
PMAelectrode.
The
coerciveforce
andsaturation
netoresistive
devices;these
0 (a) Optical
microscopic
view
of
an
spin
deviceusing
Tall-electric
WTe
,and
athe
Weyl
ferromagnetic
base
layer,
wedefinetheseas‘hot-electron
spin
d(see
2at
toresistanceinthe
FZ-Si.
In
fact,
temperature
we
meaNi0.10
Fethe
/Cu
film
and
into
the
n-Siabove
collector,
resu
FtoiFZ-Si
gwere.surements
0FZ-Si.
(a)
Opticalmicroscopicofanhysteresis.
Furthermore,
the polarization
also
Figure3a).
Hence,
theresults
shownin
Figurearecontact
80
20voltage
here(85K),Figure
the
FZ-Si
is
frozenits
toresistancein1
theat thetemperatureuse
forcontribution
mea-view
Ni
Fe
/Cu
into
the n-Sicollector,
resultingin a(Icurrent) detected
atfor
the
In
contact
tosubstrate.
Thissignalrises
experiments
carriedout Into fact,
negatecontribution
thewepossibleofcompletely
theAHE
offilmthe and
PMA
electrodes
toout
0.10
0.10
ental impedance control
mismatch
FZ-Si
32.8can be seen up to 300 K. b) Schematic image of thec2
magnetization
measuringsetup
of spinextraction
from
a WTe
spin device.
Spinaccumulation2
32.8
surements
here
(85
K),
the
FZ-Si
is
completely
frozen
out
and
its
from
the
artifacts.
Figure2f
showsa
resultofasimilarmeasthehysteresis(see
Sections
S8
and
S9,
Supporting
Information(I)
detectedattheIn
contact
tothesubstrate.
Thissignal
rises
above
14
32.8
miconductor , and measure- transistors’. In step 1, a solid-state
tunneljunction
injects
unpolarto
themomentumk,resultingin aVlinear Thi
dep
compelling
evidencefor
successful
electricalS
spin
informasurements
here
(85
K),
the
FZ-Si
is
completely
frozen
out
and
its
(I
)
detectedattheIn
contact
thesubstrate.
zc2
resistivity
is
.10
V
cm.
This
means
that
there
are
no
thermallyor
metal.
setup
theSz thatspin
polarization
createdin the
the
WTe
our
limit
at anatemitter
voltageof approximately
beneaththeofiscreatedandpotentiometricallyhysteresis
5 K. Alignmentsof spins
created in the to
WTe
and
spin
deviceusing
Twhere-type
WTe,ora adetection
Weylsemimetal.
(b)dthere2PMA
2. (c) detected.
urement
using
only threenonmagnetic
Pt means
electrodes,
forno
estimation
magnitudeof theAHE
voltage
resistivity
is .10Vfor
cm. Thisarethermally
221.2
electronic (b)effects Measuring. Here weourelectricallydetection
limit
at an using
emitter
voltageof 0.05
approximately
21.2 detectionVc) Spin voltage
14
magnitudes
ofat
injectedelectricvoltage
current of(i.e.,
antionthecorrespondingly.
extraction
andthatoperation
ofare
anall-electric
spindevicemadedetection
maintained
throughthehysteresis
undopedSi layer.
Therefore,
no
like
those
observedfrom theanddeviceequipping
Pt channel
device).
we alsothat
results means
ized
hotelectrons
from
Alresistivity
emittertheferromagnetic
n transport
across10mmimpurity
32.6
generated
electrons,
theonly freethe
electronspresent
are In addition,
isinto
.10
V
cm.
This
there
no
thermally
or
(Fig.
2c).
those
in
the
PMA
electrodearenoteshownd)Temperature
evolutionof spinvoltagehysteresis
observed
from
the
WTe
device.
Red
our
limit
an
emitterappr
TJ
2 spin0.05
impurity
generated
electrons,
and
the
only
free
electronspresent
are
0.05
(Fig.
2c).
he
electronanalogueof thephotonpolarizationCoFe
a PMA
electrodewasobserved.
This
resultapparently
elimishownin
Figure
2d
also
bear
out
that
the
AMR
does
not
gen0.00byspin-dependentballistic
SWTe
spin
polarization
detection
Measuringthez closed
the injected
spin polarized setup
electrons. forof
In Fig.
3a,in-planemagnetic
data ofI and
at V the5 21.8Vsweeping.
eraturedependence
ofFemagnetoresistancethe
spindevice.
The
SzWTe
spin
polarization
field)canwithina low
excitation
regime. Figure 3aofup
to 300K,
detected
Szpresent
spin
detectionis quite
2hysteresis,(blue)
squaresareexperimental
intheupward(downward)
Whilesuperpositionof theAMR
be seenat eachtemperature,2hysteresis
emitterment in optics.
nates
the scenario
theof the WTe
erate resistancebecausethespin voltages
at data
the posgives rise to theCobase,forming
emittercurrent
I.
Spin-dependent
hotmagnetic
thin films
for bothimpurity
generated
electrons,
and
the
only
free
electrons
are
(Fig.
2c).
84that16MRinjectedeTherearetheseveraldesign aspects
that
provideourdevice
with
a
32.6
and
85
K
are
shown.
Measurements
begin
with
fully
saturated
and
base
32.6
polarized
Fig.
3a, in-planemagnetic
hysteresis
dataof
Ic2theat range
Ve 5ofof21.8
V
32.4
ous
aspects
thatallow supportinga clean spinevidence is thespin
itive andelectrons.
negative
higherattributed
magnetic fields
notrobust
identical inspin
the detection
signals.
Further
successful
sup- salienthysteresis
toaresuccessful
the
PMAIn
can
be observed.
The range
hysteresis
is consistentwiththe hysteresis
itis intrinsic
not baseddevice
onspinmagnetoparison
ofthedependences
the
pol
and
resilient
tofield
thermalfluctuationcompared
toofSythe
spin–0.05 bycontact
Temperaturedependenceofcreatedinbreaking
the
WTe
clean
spin-transfer
current
I . (1)
An undoped
FZ-Si
deviceThelayer
2. (c)alignedmagnetizations
bytherampingtoour magnetic
maximum.
in I , and
that
make
it immune
to fringe
fieldscattering
attenuatesminorityspinelectrons
(step
2),
so
that
injectedspin
polarized
electrons.
WTe
pressionof electron
the parabolic
oﬀset
voltages
ascribed
to the along
MR ofdevice.
remaining
artifactis
attributed
tofringejectionandto
spinstructuraldetection
In Fig.
3a,in-planemagnetic
data of0.00
ibutedsymmetrytheb-axisinBlack
WTe
andisfield
resilienttothermal0.00
2magnetic
AHE
ofthe
the
PMA.
solid
bars
show
the
scale
ofzero20andµV.changese) theMagnifiedviewof[17]theshown.
spin voltage
hysteresis
observed
at 300
K.extractionf) fully
A resultof a hysteresis
control
ismadechosenbecauseitstwoextremely
low
impurity
density
results
in FM
wide
There
aregapseveraldesignaspects
thatprovideourdevicewithatoof an all-electric
spindeviceWTedevice. The innerelectrodesconsistof ferromagnets
with
PMA,
and
When
the
is analyzed
swept
throughsign,
first
information
signals
on andthe electriccupolarization
ascribed
Weyland
85node.
K are
Measurements
begin
with
saturatedoresistanceand Halleffects.
(1)
Theof
exponential
spin
the
WTe
field
from
the
electrode,which
was systematically
in
the
spin
possessing
shortlength,wheredage
prevents
interference
from
–0.10
32.2
onmagnetic Pt. The PMA is realized
bya[Pt/Co]multilayer,
where
the
thicknesses
of
Pt
and
Co
are
4.1
and
1.0
nm,
spin
device.
TheS
spin
magnetoresistance
of
the
WTe
Schottky
depletion
andFigurea linear
conduction
band.
experimentusing thePt
Theamplitudeoftheinjected electric
currentwassetbehind
to
be 50
and
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switches
to align
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2This
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There
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andKTheshown.
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spin
voltagehysteresis
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aonly
CoNi
electrodewith in-plain
magneticurrent
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polarity
oftemperature
the field
hysteresis
nicely reversedIn
following
paragraphs,
wediscuss
physicsof µA,
the85
er is 10. An external
magnetic
field is applied perpendicular
to spin-transfer
the WTe plane. b) Schematiccurrent
image of T -type WTe.. (1) An undoped FZ-Si
clean
ISeThatdevicelayeralignedmagnetizations
rampingtoare
ourmagnetic
maximum.
ation
(ref.
[67]).
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times.
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thiscan approach100%,
c2deviceof approximately
2%.
are
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resultingin afringereduction
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porting
Information).
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study shedlight
on significanceof thenolarizations.
precession,thus
con32.4
32.4
Neitherhysteresis
nor
AMR
can
be
seen,
which
is
compelling
evidencethatthehysteresis
of
the
spin
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tothesuccessful
creationandThe
identified Ramanmodes
are denoted in the
figure.
d)shows
Magnetoresistanceeﬀectofotherthe WTe. Large positive–0.05 magnetizations
–0.05
n-Si
clean
spin-transfer
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Itheaccumulation.
(1)
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undopedsingle-crystal
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our magnet
rent
directionis switchedfrom positive
to negatall-electric
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bear
out thatthe observed
control field
experiments,
wheresimilaraleakagefield-induced
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voltage hysteresis,
whereisalongmeasured
ataamanifestation
85
K to spin
eliminate
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polarizationis possessing
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the c-axis
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detection
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S–200
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inset
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0
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100
150
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–200
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50
100 150 900
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minal
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ments
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channels,
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to
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K.
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-axis
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trons in ferromagneticthin
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collector
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32.2
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Fe
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.
32.2
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80
20
84andallows
16 thethe possible AHE-induced 33.0
of the PMA electrode, i.e.,
the PMA electrode is used in our study, whichsame
our device, thefrom
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5 21.8 V times.
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0 V,
showingathecurrent,
Iinandindicate
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prevents
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long
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(ref.
67)).
chargecurrent
direction.
direction
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current
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deviceallowsonly
artifactsof Si-based
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athot-electron
both sides of the by
PMA transistor.
electrode.
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wells
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results
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Si
(step
4),
due
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the same(1 mA)
Furthermore,
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(see
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3a).
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are
–0.15
isWTe
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S
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s
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a resulta cross-sectional
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Sections
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Information
84in
to
spin
injectionandspintransport
via
10Feelectrons
mm
Si.
(c)
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CoFe
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as
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spin
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and
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polarityofthehysteresisisnicelyreversed
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2200647(blue)
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data
in
the
upward(downward)
While
of
the
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be
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ton-Sisuccessful
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to (TJ)
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he salient‘secondcurrent’attributed
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0 See
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100
150 200–200 –150 –100 –50 0
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undopedfloat-zone
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the single-crystal
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the
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e)antiparallel,
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observed
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A resultof a control
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issolid
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than
when
are
but
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steps(1)–(5).
32.8
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296
contributionof spintranssides
of ofthesequential
Co electrode,
resultingin theyhysteric
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spin
dible
isexperiment
dependent
on therelativeofarepresentative
wire-bondedSi
spin-transport
device,showingthedevice296
using
only voltages
Pt electrodes.
amplitude
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was set tomeasurementbe
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the measuring
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Department
of seen,Electrical
ComputerEngineering,of Delaware,
Newark,Delaware
USA.
Cambridge
Cambridge,
Massachusetts
02139,
theUniversity
chargecurrent
direction.
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direction
Figure3b shows
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current
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The inset shows the measuring setup. g) Comparison of results for spin extraction measure-S spin is determined by the polarity of the vector product ofamplitudes, where the amplitude of the spin voltages is defined295
n injection and spinFor
transport
via 10mm non-doped
Si. (c)Magnetizationof theas the diﬀerence of the0.00
voltages at 0 mT in the downward andmomentumk andthe symmetrycurves
breaking
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severaldecades,
inorganic
semiconductors
play
one
the upward sweep of the external magnetic field (the spin voltage
Thus, when the direction of k is inverted, the polarity of the spinode (ref. [74]). of central roles in material
choiceinvoltage
spintronics.
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the upward sweeping
is reversed,
yielding
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the spin isunderhysteresis.
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proportional(see also Figure 3a). Hence, the results shown in voltages
Figure 2d
areare fortwo
pivotaltrendsinorganic
to the semiconductor
momentum k, resulting in a linear dependence on thecompelling evidence
successful
electrical
S spinininformamagnitudes of injected
electric current (i.e., an applied electriction extraction andoperation of an
all-electric
spindevice made–0.10
spintronics:(1)
dilutedmagnetic
semiconductors,
and
(2)
32.2
© 2022 The Authors. Advanced Electronic Materials published by Wiley-VCH GmbHant emitter voltage (V ), we measure the ‘first collector
2200647(4regime.
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Adv. Electron.
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2200647
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published by Wiley-VCH GmbH(3
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–0.15
oped
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for
–0.15
s show
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Magnifiedview of the spin voltage hysteresis observed at 300 K. f) A result of a control, A top-down
uentialtransport(1)–(5).
information
extraction signals on the electric current directions.
polarization
ascribed
to micrographtheWeyl node.[17]topic,
epoch-making
achievements,
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spin-transport device,
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TheSi amplitudeoftheinjected
set to –200
be 50 –150
µA, andthemeasuringtemperaturewas5
K. –50 0–150
50–200100
150
200–50 0
50 100 150 200
0 of50100
150 –100
200
–150
–100
50 –200
100 –150
150 –100
200 –50 0
s to the spin-injection
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the–200
hysteresis
is nicely
reversedwhen
thecurIn the following
we discuss physics behind of the –100
e

c2

c1

be
seen,
which
is compelling
evidencethat the hysteresis of the spin
voltages is ascribedto thesuccessful creation and68) anddetector
buriedNiFe layer.
realization
controlof ferromagnetismin InMnAs
rent direction is switched frompositiveto negative,
which In-planeis the magnetic field (Oe)all-electricspin deviceThe
operation.
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In-planemagnetic
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viaNanoTech
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first
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ferromagnetismin bothInFeAsmanifestationofspinpolarization
hysteresis
stemsThefromthe successful
extracannels,
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injection
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wasSsetto beinformation
1 mA fordevices andthe since
measuringthe
temperature
was 5 K. switching, as in TIs,[18,20,21]295
z spinfieldsconsistent with the behaviour seen in a. Arrows
Figure 3 |measurement
In-plane magneticconducted
field dependence
at 85K.
Secondcollectorinversion
Fig.showing
11symmetry(a)switching
Schematiction from WTe2,realization
but dueto thea,absencein WTean additional70)of
2. image of Si-based hot-electron.Velocalof dilutedwas
magnetic
semiconductor
at constantemitterbiasshowing
5 21.8
V indicate
and Vc1 50 spinV, showingacurrent,
indicate
magnetic field sweep direction.
emitterbias
VeIc2
5, Figure
21.8
V3bandVc1 5
V,a dependence
Ic2, at constantmagnetic
field sweep
direction.
by inverting the charge current,
current direction.
The directionof theshows
the0 electric
current
ofvoltagetransistor.
(b) Magnetoresistanceeffect due to spin
b,is
SQUID
magnetometermeasurements,,2%
spin-valve
voltagethe polarization
proportional
thein Figure2d,2%areMeanwhile,
unfortunately,thehaseffect.
notbeenbclear,Furthermore,
SQUID
magnetometermeasurements,
clear
spin-valve
effect.productSz results
amplitudes,
where
the
amplitude of the spin voltages is defined
spin isshown
determinedbythepolarityof thehysteresis.
vectorofauthor
to the axis
momentumk, resulting
ina diﬀerence
linear dependence
on theatinjection
ccessfulelectricalSz spininforma- breaking
andspintransport
via
10
mm non-doped Si.
as
the
of
the
voltages
0
mT
in
the
downward
andmomentumk andthesymmetryn(||theb-axis).
296
focusing
his workon theof material,andin this chapter,
296mademagnitudes
injectedelectricthe
current
an ofappliedelectricmagnetic field (the spin voltage
n of
an all-electric
deviceupward(i.e.,
sweep
the external
Thus,when the spin
directionof k is inverted,
the polarityof the spin
©2007 Nature
Publishing
Group
(c)
Magnetization
curvesofthe
CoFe
electrode (ref.
Nature©2007
PublishingGrouptheyielding
authorshedsoflightonly
onexcitation
spin
transportininorganic
withina low
Figure3a shows
the come detected
spin detection
is quiteunder theupwardsweeping
is set as the standard voltage. See
voltages S
isz reversed,
a reversalfield)thepolarityof thespin regime.
parisonof the dependencesof the hysteresisinorganic
polarity of the spin 74)).
mal fluctuation comparedto Sy spin
semiconductor,
especiallygroup-IV
information extraction signals on the electric current directions.
Weyl node.[17]semiconductors.
The polarity
nicelyreversedwhen
the curhs,Adv.
weElectron.
discussMater.
physics
2022
The Authors.
AdvancedElectronic
Materials published by Wiley-VCH GmbH
2200647(4 of of7) the hysteresis© is2022,behind
2200647 of thesemiconductors
are available to the Das-Datta type andrenttransport,
direction is switchedfrom positive
to negative, which is thetion. To bear out thatSpin
the observed
injection,
detectionand manipulation[18,20,21]
group IV inorganic semiconductors including graphene
manifestation of spin polarization switching, as in TIs,
ccessful Sz spin information extracinorganic
are keyscientificforin WTe .
but due to the absenceof localinversion issues
symmetry
onal measurementin
wasconducted semiconductor
2
aresuitable for the Sugahara-Tanaka type, sinceent direction. The applications
direction of the towards
Figure 3b
shows the electric
current dependenceof spin voltage
spin-basedtransistors.
In principle,
operation principles of both transistors are different.
amplitudes, where the amplitude of the spin voltages is definede polarity of the vector product of
two different types of spin transistors using inorganicas the diﬀerence of the voltages at 0 mT in the downward andmetry breaking axis n (|| the b-axis).
Group-IV semiconductors (diamond, Si and Ge) possess71) and (2)semiconductors
Das-Datta
theare:upward(1)sweepof the externaltype
magnetic field(the spin voltage
k is inverted, the polarityof the spinlattice inversion symmetry and carbon and Si are light72). In
undertypethe upward
sweeping
is set as
the Sugaharastandard voltage. Seea reversal of the polarityof the spin
addition,theSugahara-Tanaka
Figure 3 | In-plane magnetic field dependence at 85K. a, Second collector

showing switching fields consistent with the behaviour

elements, which is the underlying physics of possible long
Tanaka type spin transistor allows a new spin logic
spin coherence in the materials, such as graphene and Si,
©
2022
The
Authors.
AdvancedElectronic
Materials
publishedbyWiley-VCH
GmbH
2200647 (4system,of 7)
the Dery-Sham type spin logic 73). To note is thatand is the reason why these materials garner muchcompound inorganic semiconductors such as III-V

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

33

SD

y

∆R [mΩ]∆R [mΩ]

T

SD

INDEX

∆R [mΩ]∆R [mΩ]

2)(b) including
250 K
8 Knm
300
~ T=
200
Figure 3(a) shows SiO
the 2 magnetoresistance,theBecause the mismatch
spin ﬂow in problem.
the Si is aﬀected
The by thewhich is noted detector.
as a conductivity
0.0
25
N w
14,15) in a highly doped Si channel at room temperature (RT) using a-800 -400 100
400 200 K800
reporton thefirst demonstration
generatinga spincurrent
minor loop, observedSiwith
the 3T-MR method. At 20
an electric
spin
drift
eﬀect
causedspin-dependent
by ofanelectricﬁeld
in andthespin
Si,transport
subst.
introduction of Wea sufficiently
largeinterface
150 K
300 K
8
four-terminal lateral device with a spin injector and a detector consisting of an Fe/MgO tunnel barrier. Spin current was generated using a nonlocal
Applied
Field
[
Oe
]
the downstreamside experiences
eﬃcientspin
spinprecession
accumulation.
current of 1 mA, the magnitude of the magnetoresistance15
Fiand spinjunction
injection signals
were successfully detected at 300 K, thus proving spin injection with theresistance, suchtechnique,as a tunnel
andandaHanle-type
Schottkybarrier,
6
100 K
meas
10 where
Because ofthe
spin signals.
directionin twoferromagnetic
electrodes
measuredThemagnetic
m be
and 0.38
1.3 nsΩ.
by theHanle-typespin ﬁelds,
elimination
spurious
The spin
diffusion
length and its lifetime
at RT werewas
estimated
to be 0.6toFig. 2. Nonlocal MR curves at 8 (upper panel) and 300 (lower panel) K,
z
Fig.
(a)
Schematic
imageafour-terminal
n-typeSi
4 spin valve. (b) Non
Fig.
1. 12
Schematiccross-sectionalview ofofa Si-basedfour-terminaldegenerate
lateralhas been theoretically
proposedasapossiblesolution
to
this
by
th

m.
The
inset
shows
the
observedinasamplewithagap
lengthdof
1.75
precession,respectively.
#
2011
The
Japan
SocietyofApplied
Physics
5
is controlled by an external magnetic ﬁeld parallel to the Si the hysteresis and the minor loop appeared, are consistent
50 Kred and blue
gap length dependence of nonlocal magnetoresistanceR. Themen(a) The second issue Bisy the detection of the injected
device. Magnetic fields were applied along the long axis of 0the magnetic
2
problem.3–6)
x of the spin direction of the detector
channel, the alignment
the measurements,
showingthat theatmagnetoresistclosed
circles panel)indicate data atand
8 and 300
K, respectively.
The dottedlines aresmal(a) between
magnetoresistancethe Sispin valve
82.5KT=(the
upper
300
K
(the
lower
panel
8K
contacts(y-direction) for a innonlocalmagnetoresistancemeasurementand0
300 Kthegrad
and accumulated
spin.
Recently,
a four-terminal
nonlocal
electrodeandthe accumulated
spin beneaththe detector ance is ascribeda successful spin ztransport
in the Si spin fitting10 lines. 8 K
I = 1 mA
he International
Fe toy spin precession
V Technology Roadmap for Semiconz
along
the z-direction
fora four-terminal
Hanle-type
VNL
1
2.0
10
Al
-100 -50 0 50 100 -100 -50 0 50
clear
= 4 TheVpanelductorslists
Si-based
spintronics
as Si)
an(NL-MR
emerging
electrodethe propagating
spin
in thearecontrolled inset
toAl MOSFET
atVRT.
distanceof theferromagnetic
electrodes 0.1of spin
300 K resistances (ref. [79]).
of the lowershows
gap-length
dependence
detection techniquein a (=
lateralspin valve
geometry
Applied Field [ Oe ]A
Applied Field [ Oe ]xmeasurement. B x
This
1)
1.5
2
3
4
I
MgOµm2 and 3a spin
MgO
The firstyielding
importantconcerning
researchorarea.
[ µm ]
4be parallel
antiparallel,theissueresistancehysteresis. (b)1was 4.26
transportof 4.26 µm was realized. Figure 2 dshows
the results obtainedby theNL-MR
method) has semiconductor
beendemonstrated
asanelectricaldetection
Hanle curves observed
at different
temperatureschanof the
~
20
nm
Appl.
Phys.
Express
8,113004(2015)
1.0
spintronics
the injectionof spins
at (a) 8, 50, 100, 150,
2
gap length d ofbackground1.75 m. Hanle curves
A more quantitative
andisdetailed
discussion
will frombe reported Such~ 60µa µlongspintransport was achievedby spin drift indmethod. By subtracting the aconstantvoltagesThm
7)~ 80 nm(b) 300 K.
The LHanle-typespin precession
a aspincurrent.
= 4.26µamsemiconductor
0.513)(b)16) conductorn-Si discussed previously.
ferromagnetic
intochannel,at both (a)addition to spin diﬀusion(195 and 460 V at 8 and 300 K, respectively) produced by wereOn the contrary,spin accumulationWhenelsewhere.exhibits
attention. In method
fact, forgraphenelong-rangespin
V = 50 asV
2)
200 nmSiO2electric coupling between the electric pads from the folloThe
is noted as detection
a conductivity
mismatchproblem.
0.0 acid an
measurement which
in nonlocal
geometry(4T-Hanle
substrate was removed
using dilute ~hydrofluoric
(HF)
AP
AP
 was estimated to be 2:0  0:3 and 1:0  0:3 m-800 -400raw data,
0 the
400
800
spin accumulation
voltagesV were obtainedchange-6 300 K,
Si subst.
introductiona sufficiently
largetool
spin-dependentinterfacetransport overmethod)
10 mm,
lifetimeinrespectively.
0.1Ω ofspin
ISDP Applied(A)1andField]
10 using
waswhereas
alsoappliedasa powerfulforgraphene
provingspin solution. In thisstudy, we observed
2  1 and
converted
2 [ Oeinto
R by
an 3injection
current signals
Iinject as a functFigureshows the 4T-Hanle
resistance, such
ISDP
ISDP
0.5
-3
P
AP
7,8) as a tunnel junction and a Schottky barrier,temperature.
Each pointof the nA
curve
1
mA.
changes
R
with
clear
plateaus
wereNonlocal MRIcurves
atof
8(A)
(upperpanel) Steepand 300 (lower
panel) K,in measurement
10
I
Spin
currentinaSichannelwas
injectionandtransport.
reflection
high-energy
electrondiffraction
patternsoftheΩ largez due
is merely about tens picoseconds
mainlyto0.38its
Fig.1. 12(a) Schematicimage
a four-terminal
n-typeSid ofspin
valve.
(b)
Non-local
Schematiccross-sectionalview ofofa Si-basedfour-terminaldegenerate
lateralSD a gap
SD length
has been theoretically
proposed
as a possible
solutionto this Fig.
by the average of the signals obtained by several
m.
The
inset
shows
the
observed in a sample with
1.75
successfully obtained at a temperature of not only 8 K but
Bgap length dependence of nonlocal magnetoresistance R. The red and blue
ments. As the temperature increases,magni
the signal(a) The by
Magnetic
were appliedalong the longof the magnetic
2.49225 fields
successfully demonstrated
theissue
4T-Hanle
method,butinjected
spin device.
Si
surfacebeforetheSigrowthofaxisthelayer.
This8 andalso
wasis xthe detectionof theproblem.3–6)
300
K. (theWith
thelines
increasein temperature,
the
field
for intens
circles panel)indicate data atand
300
K,
respectively.
The dottedare-8 smaller
and the full widthat half
maximummagnetoresistancethe
spin valve
at11,15,16)
8 KMgO(the closed
upper
300
K
lower
The
(y-direction) for a innonlocalmagnetoresistancemeasurement
andFermi velocity
originating
fromsecond
the
Dirac
natureof contacts
awherg10panel).
thefitting-4
lines.
gradually.
theat
4T-Hanle
and accumulated
spin.
Recently,
a four-terminal
nonlocalthetransition in R shiftedslightlyHowever,to thea reverse
lower offield.
I = 1 mA
10valuesofconcurrent generation
was limitedtolow
temperatures
below along
not thedone
previous
studies.
Vz in ourz-direction
for a four-terminal
Hanle-typespin precessionThe(c)clearlyobservedbyapplying
thereversefield,ofeven
V = 4 Vpanel shows gap-length dependence of spin resistanceselAnisotropic
magnetoresistance(AMR) hysteresis, as preinset of theB lower[79]).
detectiontechniqueina lateral spin valve
geometry(NL-MR measurement.
suppreA54 (ref.
This is strong evidence for the spin current
throu
x the Si channelgraphene. Si 150
exhibits
long
spinlifetimeover
several15)I
the otherhand,athree-terminal
Hanle-type
and
9:52

10
ductivity
in
were
1:03

10
K.9–11) Onmethod)wasobservedindummy
samples.
Thus,
are i
viouslyreported,
P
(b)
@
RT
Figure-5 2 shows the results ON
obtained by the NL-MR channel up to 300 K.
has been demonstrated as an electrical detection
Appl. Phys. Express 8, 113004
pap
1 2.49200
1
10(2015)
theconstantchangesinPR voltages
can be -10
explainedby the magnetization
andmethod.
By subtracting
thebackgroundThe spin diffusion
length and otherthetransport
7)I
mmeasured
at
8
and
300
K,
respectively.
Thevaluesspin
precession
measurement(3T-Hanle
method),
in
which
SD
The
Hanle-type
spin
precession
methodforaspincurrent.
L
=
4.26
µ
m
(a)
(b)
10 wereTherefore,
nanoseconds and relatively long spin diffusion length of
300 K, respectively)by(195 and 460 V at 8 andreversal
estimated bywefitting
the analyticalofof each produced
FM electrode.
canwithconcludeV = 50 V
Isd issolutsN
electric coupling
between7.1
the electric pads from the following function:
0.68theµA tunnel
measurement
in nonlocal
geometry(4T-Hanle substrate
was removedarea
usingproductdilute hydrofluoric
acid an(HF)
AP
APthe injectionof the resistanceofcontact
werea single magnetic
contact
is useddetection
for both
0.1 Ω
The
that
the
changesresulted fromtheca.
amount0.68µA in R changed
Z of spin posit-6 the spin accumulation
raw data,
voltages V were obtained-6
P 1 µA underV ðB fromÞΩ andI (A)1andover 1 mm, i.e.,
spinlifetime
diffusion10accumulations
statesmethod)
was also0.1
as a powerfultool for length
proving spin solution. In thisstudy,
we observed
2  1 and
10
2
2
show
effect. Thisis¼’ðtÞ cosð!tÞ
exp
converted
into R by
using an injectiondetectedcurrent I as the Ispin valvePPmmeasured
at
8
and
300
K,
respectively.
and
4.6
K
and long
detectionof thespin, applied
wasappliedtodetectthespinenegativeNðE ÞA

ISD
ISD
0.5
nA undergateK. voltage-3ON at 300
of
1
mA.
Steep
changes
in
R
with
clear
plateauswerelengevidence
of
the
spin
current
throughtheSichannel10
II(A)
in a Si0.38
channelwas
injection and transport.7,8) Spin current12,13)
reflection
high-energy
electrondiffraction
patterns
of
the
-12
Ω
Þ
1
ðx  x signals
AP
2.49175
II
10
successfully
obtainedatatemperature
of
not
only
8
K
but
p
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
ffi
’ðtÞ
¼
exp

;
magnitudeofthesignalsis
attributedSD
successfully coexist.
The butlarge
Figure1 shows
a schematic
view of-8 The
theaccumulation successfully
under theinjectionbycontact.
0:6 spin SD
diffusion length can be accurately
estimated
2.49225 before
4Dt
demonstrated
the 4T-Hanle method,
spin Si surface
the growthof the MgOcross-sectional
layer. This also
was4Dt
300-7K. With the increasein temperature, the field for
10-4
thisgthosemat awheregate
voltagesmallerthanca.
10fromslightly
the gap
lengthofthe frequency,clear= fabricated50 V studies.11,15,16)
is the Larmor
isthtransitionin R shiftedto thelowerdependence
field.
! ¼R,g Bbecause
10values
The(c)of theconcurrent generation
limited to low(RT)temperatures
done in
ourVGprevious
spin ofaccumulation
at room wastemperatureusing below
this notlateraldeviceby electron
beamlithography
for
Vthe
4 as
V curves
SD =R
as m
The chronicle
Si spintronics
substantiallystartedis thespin lifetime,
plateaus
onhysteresis,
antiof result
electron from(usinggsuccessful¼ 2),
Anisotropic
magnetoresistance(AMR)
presuppressed.
Here,the suppressione
VSD = 4 V I AP
9–11)
5
4
modul
On
the
other
hand,
a
three-terminal
Hanle-type
and
9:52

10
ductivityintheSi
channel
were
1:03

10
150
K.
AP
was observedin magnetization
dummy samples.
are integrated
over ofthe Fig.
widthsofthe injector
andhviouslyreported,@RTThus,
P
SD
@ RT
are
parallelalignment.
The
inset
2
shows
3T-Hanle method was an exceptional
discovery madebypatterning.
The
Si
channelwasfabricatedbyamesa-etching
ON
I
-5
-8
-14
@RT
SD
the
parallelandantiparallel
magnetiz1@whichRT
10 The values
2.49200
the changes
inPR can be -10
explained by the magnetization
and D is the spin diffusion constant. We use the re
ISD
10 OFF
10exponentially
2.49150
spin precession measurement(3T-Hanle method),in1 mmeasured at 8 and 300 K, respectively.
Therthat theR curve
decaysincreasing
andIaresdfittingfrom hot-electron
spin
injection
into non-doped
Si (Fig.
¼ ðD Þwith
, thusP, diﬀerence, and gap
preversal of eachconcludeof suppressed,-600-400 -200ferromagnetic
0
200 400 (FM)600
-100FM electrode.
-501050
0 between
50we can100
istheintransIsd
I2sdandDash etal.14)-600
andelectrodes—contact
V Therefore,
0.68theµA tunnel contact
lengthcontacts
Using
a single-400
magnetic
contact is0 used forthe injection
the resistanceareatwoproduct of
were
0.1
Ω
-200
200both 400
600 oftechniqueThe3.fittinglinestheare tunnel
in good barrier,agreement withth
that7.1
thefrom the amountof spin
0.68changesµA in R resulted
-6
as
fun
2
2 VV
7,17)
statesdecreases,
resulting
in
the
103
2 21
(V)
shown
by
thelength;
examplein then,Fig. 3(b).
Theaccumulations
detectedasthe decreases
spin valve as
effect.
This istheatspin30s
Rafunctionofthegap
Magneticfield(Oe)
Currently,
achievingspintransport
atfield
RTunsuccessfulinaSichannelismandcontact
of
2

21

m
—were
2
of
0:5

some

m
measured
at
8
and
300
K,
respectively.
11) 74), although
and challenging
detectionof Magnetic
thespin, butwasappliedtodetect
the
spin
and
4.6
K
(Oe)12,13)
G-12G
ON of theAPlengths
at
8
and
300
K
were
estimated
to
be
2:00

evidence
spin current
through the Si channel at 300 K.
2.49175
signals.equation:
Because 0.5 nA is Iclose
is befittedusing the following
Fito
10datacan
SD -7 view of The
sdareand
TheHere,large
Figure 1byshowsschematicThen,cross-sectional
theaccumulation
injection contact.
consi
spinISD
diffusion
lengthaccurately estimated 0:6  0:2 m, respectively. These valuesof the key
challengesunder
for theSi-spintronics
devices.
formedionamilling.
a I30-nm-thick
SiO
layer
was
2
 by the 10
we method
believethatobtained
withinobta
an erfrom the gap length dependence of R, because the clear
2measurement,
works using onesome
different
approaches
had
been
V
V = 50d NL-MRTheVNL thisPthosespin accumulation
at room temperature(RT) using
this lateral device
fabricatedby electron beamlithography
for
N
the
on
Fig.
4.
Devicecharacteristics
of
the
Si
spin
MOSFET.
left
and
V
=
4
V
as
mentioned
above.
This
indicates
that
our
mea
plateausontheR
curvesresultfromsuccessful
antisigna
exp by over; three orders¼of non-degenerateð1Þn-typ
R¼ The modulated
3. on(a) Magnetoresistance(upper panel)and minor loop
(lower panel)
ofthe
the
Si APspin
MOSFET measured
bythe
the upper
local
3T-MR
method.
=on
4V
weFig.
reportthe first demonstrationof generatinga spindepositedsurfaces,
exceptonfaces
AP deviceFig.
(a)Magnetoresistancein spin-dependent
electric
currentofm@RT
Fisignals
g13.V@RT
SD (a)
inShighly Nin the[thereliabletemperature rangeexpo
of 8parallelmagnetizationalignment.
The inset
of Fig. I2inject
3T-Hanle method was an exceptional discovery madeby patterning.
The1Si3Ichannel
fabricatedby a-8mesa-etching
ISD wasMagnetoresistance-14spin-dependent
andarethespinsignal
right
show
the
source–draincurrent
IshowsOFF axes@ RT
sdgap
reported before.
Theandauthorsof
74along
introduceda(b)hotTherefore,
itmagnitude
is obvious that of
the thespin optimi
transportofthatthe R
decaysexponentiallywith
increasing
external
magneticﬁeld
wasref.
appliedthe y-direction.
Magnetoresistanceof-400theSiferromagnetic
spin
MOSFET
the10verticallocal
2T-50andmethodwith
an10holes
appliedgate
voltagethespinlinea
sign
Isd andcurrent
spin
in highly
doped
Si200
at RT.
Spinof 2.49150
the-600andtwo
FMContacts
4 50curvewere-200
0electrodes.
200
400 (FM)
600 in-1001
100
Dash transport
et al.14)
twoelectrodes—contact
is the inspin
P is antiparallel
thetunnel
spin barrier,polarization,
 Nelectrons
V 0 between
transferredtheSidiffusion
channel is demonstrcontacts
2where
and
Using
the
betweenparallel(P)3.and(AP)
conﬁgurations].
diﬀerenceinGateIsd50length-600 -400 -200
0400
600 technique
MOSFETatroom
temperature.
(b)
voltagedependenceofthesource-draincurrent(theasfunctions
of
the
gate
voltage,aelectric
currentof
non-degeneraten-typespin
2
2
provedV. Currently,
The source–drain(Vsd )werewas
4 V. isThe 2externalﬁeld
wasappliedalong
Themagnitudeof conductivity
thethen,spin(Vg) of +50(V) Al.
length, islength;
thetheK.Si, S is the cross section squaVVR
the of
at 300decreasesasa functionof the gap
Magneticfield(Oe)achievingspintransport
at
RTset
in
atoSi bechannelm SiO
and
3were
ofThe
2 then
21thefilledmy-direction.
—wereof 0:5 magnetic
in21
Gwith
which
Finally,transport
parameters
inwherethe Sicurrent
channelinvestigatedformedtheMagnetic
field
(Oe)
G
2 , contact
electron transistor
structure,
the
wafer
bonding
black
solid
line
and
red theclosedcirclesshow the gate
voltagedependence
data
fitted using
following
Figureshows
the temperaturedependenc
andthe4 spinsignalsboth
valugof the equation:
Si strip, and d is theIsd
betweenthe contacts
2 wereand 3.
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Taharaetsurface
al.
1)
S.
Datta
and
Das,
Appl.
Phys.
Lett.
56
V
V of SiFig.
(a) (a)SpinSpinlogic circuit
spin MOSFET.
(b) MOSFET.
An example XOR
logicexample
operation of
Fig.1414
logic madecircuitmadeof Si spin(b)–6.40
An
XOR
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–3.54
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deﬁne
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Matsuno,Sugahara,and M. 2)
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undertheparallel= 0.3 mA
deﬁne
the
spin
signal
of
the
Si
spin
MOSFET
as thedifwas used, the output spin signal was considerably small injectedcontacts
1 and
2,1theandthe 2,
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Si
spin
MOSFET.
wferenceof the XOR
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0.48
theSiyiSispin
Forcontacts
detail,
see
ref.
[94].
wwSpinin theparalleland antiparallel
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E-mail address: toshuzuki@ait.pref.akita.jp
wasdetected
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intheparallelandantiparallel
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inyT.Fig.
3)
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B.
A.
Filip,
NM2
toshuzuki@ait.pref.akita.jp
detected
contacts 3 and4. insdthe
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I 0 , theHeersche,
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FM-B FM-M conﬁgurations,
–6.45
–3.55
0.47states,
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field.
of address:
picoampereand modulation of spin023003-1was(b)thatis,spinsuccessful
on=oﬀ
as shown
inby the magneticx
milling. The deviceto be an orderE-mailF.
vanmanipulation
Wees, Nature
416,
713(2002).
FM-M
An example
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operationoftheSisuccessful
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FM-A# 2011
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The XORJapan
of Applied
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catingspinthe3)magV↓↓ –6.45<
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In theanalysis,
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Under a gate
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the
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Suzuki,M.
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Physics
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80 nm Society
signalsareobtained
voltage
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Appl.
Phys. Express
2,of053003 (2009).
spin 94).
signalwas
0.68µA.
dABseedthe
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Fig.
3(c).
Under
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gate
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B measured
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13)
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ref.
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4)
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T. KSasaki,
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Sweeping
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V
a
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300
300 K −125 voltage
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the spin signal
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Si substrate[37–40]:no Phys.
signals
Shiraishi, Appl.
Lett. are104, detecte
052404
–3.57
–6.55
0.43
ed the highly dopedpractical application of Si-based spin devices. Thus,
spinsource–drain
voltage –3.58
of –204BVy–10modulatedtheIsdshown(c)(d)
0 10 20–20
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–20 –10
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use
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6)
Sasaki,T. V
Oikawa,T.aSuzuki, M.
Shira
0.441(h)
5)
T.
Despi
B (mT)
Sweeping
thegate Sivoltage
from
toT.Appl.
+125
Bthe
(mT)
B (mT)
300 charge
K at current.
3003002K −125
MOSFET(see
Fig. 4). Becauseof (Bn-type,nel. The contacts hadreliable and reproducibly spin injection and transport
98,
262503A(2011).
–3.82
–3.32
VNLAPtheP λs a(Bz–3.58) −is
VNLP
1 Phys. Lett.
for[37–40]:z)
Sh
try,
devices
and
B
e
2
2
−
–6.55
4 exp
FMincreases-BDevice: FM-A
Injector : (c)(10.43+theω–20
τs –10CIsd, and aofnegative
thespinsource–drain
voltage
4 V modulatedIT.)sdSuzuki,
7)
T. Oikawa,(c) Injector
positive (d)gatevoltage
0 =10voltage
0of10 T.
20Sasaki,–20 –10M.
0 Shira10
m2, respectively. The
I –20 –10 gate
σ20
signalamplitude(theDetector :FM-B
Detector : FM-M
6)
T.d
Si A
–3.34
AB
Appl.
Phys. Express 4, 023003B(2011).
Bconventional
–1.16
–0.90
Bthe
(mT)
(mT)
y (mT) 
in
Si
by
the
other
approachavailable
for
spin

deviceasuppressesMOSFET
Isd. Thus, this exhibited
ne
y
y
I
=
1.0
mA
2
1.0
I = 0.3
mA
I
=
0.6
mA
(see
Fig.
4).
Because
the
Si
is
of
n-type,alargerthaAp8) Y.
Kameno,Ando,
E. Shikoe ferromagnetic conVNLAPP λs AY. is(BAoki,–3.84z )is− VNLPz ) M. device–3.36
2 + 1(B–0.92
2 2 −MOSFET
operation. –1.30
The switching dvoltage
ω2the–1.181 +of
=
(1
+
ωand
τT.s sign)
Shiraishi,
T. Sasaki,
T.and
Oikawa,Suz
tions,
a clear–0.94a negative−(c)DeviceCτIssddevice
7)
T.
M
, and
gate
voltagepositivegate Bvoltage
increases
magnetic electrodes,transistors. The authors introduced the electric nonna
I = 1.0 mA
I =comparatively
1.0 mA
300 K
300 Klarge; in other words,λ the transconductance–3.38
σSidevice
A A. Second,ofI(2012).
2s –1.20
for
–1.32
Ap
–1.16
–0.90
–0.96

this
deviceexhibitedaconventional
suppresses
Isd. Thus,


9)
T. mA
Uemura,K. Kondo,
J. IFujisawa,
K.-I. M
appearedthe device
is not good enough.
TheminimumofIe made from Al andlocal four-terminal method to achieve successful spin
=
1.0
mA
I
=
0.3
mA
I
=
0.6
sd
–3.86
–3.40
device
B
at
I
=
0.3
m



 Lett. 101, 132411 (2012).
8)un
Y.
Appl.
–1.22
–0.98
2 device–0.92is shifted.
(f)(e)
at a gate MOSFET
voltage of –1.34−35
V. These –1.30
performance
character2 2the2τoperation.
Theswitchingvoltageofω
τ1sPhys.
+is1M.slightly
Suc
tween the FM elec–1.18
arctanωτsdd
1 +110)
ω+
sO. −
–3.42
Txoperena,
Gobbi, A. Bedoya-Pint
Sh

–1.00
cosfor



78)
−
×
+
,
istics
were
found
to
be
insuﬃcientcommercialized
Si
300 K
300 K –1.24
300 K
slightdifference
the1
–0.94
I 0.9
= 1.0 mA
I =comparatively
1.0 mA
300 K
, and
Appl.
102,
fou
300 Klarge;
in other2 words,
ofPhys. Lett.in
λs sthe transconductance
2 and F. Casanova,
voltage was appliedinjection and creation of pure spin current in Si
(2
–3.88
–3.44
–1.36
MOSFETs,that
are due
to 0theuseλ–1.02
of –1.20
a–20 –1011)0 10O.2–20
10 20–1.32–20 –1010 20
20
Txoperena,
Y. Song,
L. Qing, and/or
M. Gob–30 –20 –10
0
10
20
30
netic
electrodes–60 –40 and–20 we0 believe20
40 –1060 0 they–0.96
B (mT)
B (mT)
9) T.(
B (mT)Casanova,
B (mT)
B (mT)
the device
deviceis notgood enough.
Thestrucminimumof Isd appeared
he conventional FETroom temperature spin injection/transport/detection in(2) Rev.
Phys.
Lett. 113,
146601
nonoptimized
structure,especiallytheback-gate
polarization
of
FM-M
He


50
–3.03
 andfor
H. N.
Tinkey,P. Li, Phy–1.22 12) I. Appelbaum,–0.98
ture, and(f)the anonuniform
doping proﬁleperpendicular
to thewere investigated by Fig. 2. Schematics of the measurement methods used in this study. The(e) Injector : FM-A
also
decreases
allAp
at
gate
voltageofcurves−35V.) isThese
performance
character–1.34
2I2τ13) forT. Sasaki,Ando,
M. Kameno,Tahaarctanωτd detection
1 + 10)ωT.shoFIG. 3. Vwhere
currents(a)(VatNLPvarious
thecharge
voltageunderDetector: FM-M
left and degenerateright images show theSimeasurement
circuit and the corresponding
XOR -ByVNLAP
s Y.thesO.
with Hanle-typespin precession
300 K
40 channel plane. Although the FET characteristics
theShiraishi,
In–1.00
nonlocal
Si spinof
I = 1.0 mA
×C300measured+KM.
B-M deviceh ST-500), a sourcen-type
andRev. 300A
2–3.04
isticswereA,foundbeinsuﬃcientforcommercialized
Si Phys.limit.
(b)devicetoB, (parallel)and (c)deviceroom
tem-lifetime–1.24
antiparallel
configuration,τsatisthe Suzuki,
spin
Kcos
300
position dependence of an electrochemical potential in the local 3T-MR and2M.µm,
2T. Shin
of
FM-A
FM-B
oranσ
the Si30 spin MOSFET
werenotaschannel,
ideal
as
those
of com14)3.0
Kameno,Y.λAndo,Shikoh,s–1.02E.or
79)perature.
The
distance
between
FM-A
and
FM-B
is
(a)
–1.36
is
the
magnetic
flux
density
along
the
z
in
the
Si
B
z –10
2401), and a digitalwas. Furthermore,
spin
Fig.in the12)
MOSFETs,
and
webelievethat0suﬃciently
they
to
use
of
a–20
localachieved
2T methods. “Spin(seeaccumulation”
lower panels
shows the spin
0.8
–20were10 20 are due–20 –100the
10
20–1011)
0no10
O.
T. Suzuki,
and M.
Shiraishi,Appl.
changed.
When
the
sp
the3.0electric
statesA M mercial devices, (b)µm,direction,andon=oﬀ(c) 21Pµm.
Themagnetization
ofAFM-M
isSuzuki,
fixed–3.05(g)is thespin
polarization,is thecross-sectional
B
(mT)
(h)
B
(mT)
B
(mT)
y
15) back-gate
M. Kameno, fromY. strucAndo,y H.
y0). All measurements accumulation voltages detected by each measurement method.
Ca
8%T.toShinjo,
10%
in Koikthe20
nonoptimized
devicealong
direction.
The experiments.
external
magnetic
density,B
separated,whichmeetsthethe+y
purposeoury,areaof theofstructure,channel,ω = especiallygµ isflux
thetheLarmorfrequency,
B B/Note
injection/transport/detection in non-degenerate n-typetio
Suzuki,and M. Shiraishi, Appl. Phys.
LetI.
is Btoestimatedto12)
changeis swept−30
and 30formT,
isbysufficiently
for
A-M
that thespinsignalswere
also
eﬀectively
modulatedthe–3.06
gnonuniform
is theg factor
thewhichelectrons(g =perpendicular
2 16)
insmallthisstudy),
T. Tahara,
Y.µAndo,M. Kameno, S. Miw
ture,
and
thebetween
dopingproﬁlethe10magnetization
switchingof
FM-M.
precisecontrol
of
the
13)
T.
A-B
FIG.
3.
V
-B
curvesatvariouschargecurrents
for
where
V
(V
)
is
the
nonlocalvoltagethe Bohr magneton,
andysignals
is the Dirac
constant.
Shiraishi, Fromin preparation.
(Fig. 4). Theis magnitudeof theXORspin
NLAP
NLP
anσS
ecting spin signals inSi and subsequent spin signal modulation by gating
300 K gate voltage
Si spinchannelplane.
AlthoughtheFETof at roomI = 1.0 mA
neticelectrodes
and Suthe analysis,λA,τsdeviceare estimatedto (c)
becharacteristics
1.41± 0.16
µm
0
–3.07
s and
device(b)B,
anddeviceCmeasuredt
antiparallel(parallel)
configuration,
τ
is
the
sp
s
–60 –40 –20
0
20
40
60
80,81)by1
2
4
5
the spin
injector andcan be measured
is study. As reportedwere
reliable operation
and2.04± 0.16ns,
which iswith, where theachieved
atdetector
roomelectrodes
temperaturetheSi 3spin
MOSFET
were
notaschannel,
ideal
asoffor com(mT)K14)μ
M
0.7 B 300=
Center-to-center
distance, d (µm)
perature.
The
distance
between
FM-A
and
FM-B
is (a)
3.0
I = 1.0 mA
inrespectively,theSi
Bzconsistentisthosethe magnetic
flux
densitydemandingrequirementheresults
in
Fig.
1(f)
and
those
of
a
previous
study
[31].
a Highly
Doped
Si Channel
dTransport
is another inreliableusing
the local
2T method. Notably, 4anisotropic magneto0.04 mercial devices, the electric on=oﬀ states were suﬃciently
–20
0
20
(b)
3.0 µm,direction,and(c) 21Pthisµm.
ThemagnetizationofAdevices
FM-M
isSufiis thespin
polarization,is thecro
Injector : FM-B
Injector: FM-B(Fig.
13) 81). In
ratioandwasenhanced>10 can(g)B (mT)even forwith
antiparallel
configurations.
However,featureis not(h) and15)maM
ot only1 spin accumu-on/off
resistanceotherspurious signals
superimpose
on the course
Detector : FM-M
Detector: FM-M along
0.02 separated,
0.04
the
+y
direction.
The
external
magnetic
which
meets
the
purposeourapplicablefor theNAND
orOR
operationintheexperiments.
MLG.
isdiscussed
in Sec.
III.
XOR
area
ofOPERATION
theofchannel,
ω =Ifgµisfluxthe density,
LarmorOikawa , Masashi Shiraishi2 , Yoshishige Suzuki2 , and Kiyoshi Noguchi1
Si NoteBσB/SuPspin transport can beof thesignals
detected
using
the
local
method,soexperithese significant studies, a number of detailed FIG. 1. (a) The semiconductor-based MLG
0.00 device proposedis
swept
between
−30
and
30
mT,
which
is
sufficientlysmalati
we spin
use thesignals
NLMR
signalsasacomponent
of
the
MLG,
We
also
demonstra
that
the
were
also
eﬀectively
modulated
by
the
g
is
the
g
factorfortheelectrons
(g
=
2
in
this
In the XOR operation, a direct charge current is applied16) T.
by Dery et al. [11]. (b) Silicon-based multiterminal lateral, Akita
010-1623,
Japan
ce
from
the convenments should be conducted with utmost care. We used boththespindevicefrom
consistsof threecenterswitching
ferromagnetic
electrodes volt[Fig. 3(c)]. A clear X_0.02
magnetization
of
FM-M.
0.00
FM-A
to
FM-B,
and
the
spin-accumulation
is
the
Bohr
magneton,
and

is
the
Dirac
con
XOR
operation.
(c)–(e)NLMR
measured
at
300
K.
The
valvesforSh
gatevoltage
(Fig.
4).
The
magnitude
of
the
spin
signals
spintronic physics in Si were clarified:spin drift in Si
no 385-8555, Japan
0.6
Phys. Express 4 (2011) 023003
T. Suzuki et al. (FM-B, FM-M, and FM-B ) and two outmost nonmagnetic
I = 0.6 mA ≈ I 0 . theSinceversity,
ferromagnetic
elec- methods to corroborate spin transport in theAppl.spin
MOSFETis measured bywithreference to NM2. The_FM-B,
spin injector and detector are0(c) FM-A and20(d) FM-B
0.04
Toyonaka, Osaka 560-8531, Japan
40and age60
80100
 analysis,
theFM-M
λiss fixedandτs aretheestimatedto Thebe
1.41
electrodes(NM-A
and NM-A
large ©
I 0 2015). of
In FM-Mthatcase,
the output(0.6mA)Japan
is o113004-3
FM-M, and (e) FM-A and FM-M, respectively. (f) Dependence
magnetization
direction
along
+y
ﬂow,
acting as a spin at RT.
ity
_0.06
(a)
AP(b)
–0.04
and
2.04
±
0.16
ns,
respectively,
which
is
con
30
voltagedetectedby
FM-M
exhibits
the
0
state
when
the
effectthatshiftsthex
2011; published online February 7, 2011of the12magnitude
of NLMRsignalsonthecenter-to-center
dis0.6
direction. In this situation, the spin-accumulation volt300 K
Vg (V)(b) including
I = 1.0 mA250 K
T= 8 Kthe
300 K

Si is aﬀected by the
Figure 3(a) shows the magnetoresistance,
Fig. 3.

G

N

Fig. 2.

Magnetoresistance (Ω)

ISDP (A)SD

G

injectAPSD

ISD (mA)

ISDP (A)

P
SD
P
SD

ISDP Q ISDAP (A)Magnetoresistance (Ω)

SD

y

15)

G

ISDP Q ISDAP (A)ISD (mA)

y

7,8)

1

2

?

2

inject

F

0

1

2

2

B

sp

N

sp

1=2

N

sp

SD

SD

7,17)

NL

2

N

N

inject

N

2

dd

dd

VXOR (mV)

XOR

dd

dd

XOR

VXOR (mV)# 2011 The Japan Society of App

y

B

BM

y

–3.32

–3.03

–10

0
10
By (mT)

20

–3.44
–60

30

40

∆Vs (µV)

A M

y

–3.06

–40

0.04

–20

0
20
By (mT)

40

y

20

A-M

1

0.02

P

2
3
4
Center-to-center distance, d (µ m)

0.00

_0.04

_0.06

y

–20

–10

VNLA P _ VNLP (mV)

Voltage (mV)

600

20

rot

∆R [mΩ]∆R [mΩ]

10∆R [mΩ]

Fig. 15 Spin lifetime anisotropy in in-plane andage
Fig. 3 | Gate voltage dependence of the spin lifetime anisotropy. The
senperpendicular-to-the-plane spins in Si spin MOSFET
spin lifetime anisotropy ratio ζ is dependent on V , and it is the largest
as a function of gate voltages. The anisotropy exists
spi
and almost unity at Vg=10V, indicating an isotropic spin lifetime. Above
8K
withoutagate
voltagetothebuilt-infield
electrodes
(NM-A
NM-A
).
In
that
case,
the
113004-3-0.6 due
the otherelectrodeis used asmagnetization
theRashba
output andterminal.
Vsummarized↑↓ are
FM-M,
and
(e)
FM-A
and
FM-M,
respectively.
(f)
Dependence
direction
of
FM-M
is
fixed
alo
atou
0 50 100-100 -50 0 50 100 -100 -50
Vg=10V,ζ ofmonotonicallydecreases
with increasing
Vg, whichis situation,a
300 K
voltagebyis
FM-M
exhibits
thestate when
Applied Field[ Oe ] on the center-to-center
themagnitudeofsignals
dis- detected
Applied Field [ Oe
] NLMR
direction.
In
this
the 0spin-accumu
in
the
Si
channel,andtheanisotropy
once
044010-3
tance ofbetweenspin injector and thespinenhancement
detector,d. Thedots ofmagnetization
directionsof FM-Band FM-B
areof(1manifestation
thethegeneration
anda synthetic
Rashbaage,
Vby FM-M
is expressed
XOR , detected
044010-5
are suppressed
experimental data, andred gateline is a voltage
fitting result application
obtainedbythe
the(ref. µ96)).
or (0, 1) and
when
they
(1, 1)σ↓ )],are
where
σ↑ or
(σ↓(0,)(σ↑ µthe↑ + 1σ↓state↓ )/[e(σ↑+SOI field, resulting
emergent
effective
magnetic
field.
The
error
bars
with Eq. (1).in(g) anHanle-effectsignals underparallel (red)andThis gate ductivity
is not a NAND
gate orspinsan ORin gatebuteisissio
anof up (down)
FM-M,
theX
antiparallel(blue)
configurations,
where
the
linearbackgroundisestimated
to bestandard
2:0  0:3 and 1:0  0:3m at 8 and was
0are400
800
estimatedasthefitting.
chargeand µevenis84)
the electrochemical
gate.
words,
though↑ (µ↓ )
82,83)
subtracted.
spin injector
and deviation
the spindependence
detectorin
are theFM-B
and300 K, respectively.
,Thebias
voltageofIn otherspinsignals, we increase thepotnu∆R [mΩ]∆R [mΩ]

400

devices. Here,

0.0
-800

10

1

0.1

2

3
4
d [ µm ]Fig. 3. Hanle curves observed at different temperatures of the sample witha gap length d of 1.75 m. Hanle curves at (a) 8, 50, 100, 150, 200, 250, and(b) 300 K.

-400
Applied Field [ Oe ]N

the(down) spins
the toSi/FM-MWhen
ber of electrodes
from atthree
five, theinterface.
logic operatio
Figure 3respectively.
shows the 4T-Hanle
as a function
the Hanle signal between
FM-M,(h)signals
Difference
in ofthemeasurement
temperature. Each point
curve origin
is shown
Fig. 2. Nonlocal MR curves at 8 (upper panel) and 300 (lower panel) K,
chemicalpotentialSi,beneath FM-M—thaclarification
ofofbythe
thethe “inverted
Hanle”
effectina85)
still
an XOR
gate. Furthermore,
reconstructionof the lotheantiparallel
andparallelsolid(a) Schematicimage
a four-terminal
n-type Si spin valve. (b) Non-local
Fig.1. 12
Fig.
Schematiccross-sectionalview ofofa Si-basedfour-terminaldegenerate
lateralby theaverage of thesignals
obtainedconfigurations.
several measure- The dots and theobserved in a sample with a gap length d of 1.75 m. The inset shows theµ↓ )—is set
beof0three
meV,ferromagneticµ↑ and µ↓ havethe s
gap length dependence of nonlocal magnetoresistance R. The red and blue line
ments.
the experimental
temperature increases,
signaldevice. Magnetic fields were applied along the long axis of the magnetic
areAsthedatatheandthebecomes
fitting curve obtainedwithis impossible
by to
use
electroenhancementof intensity
spinsignals bygate
utilizing
spin
drift
andnamely,
indicateatand
8 and 300
K, respectively.
The dottedlines areFig
. 12 for(a)Schematic
image
ofcircles panel)a datafour-terminal
smaller
and the full width at half maximum
widensmagnetoresistancethe
Simagnetoresistancespin valve atmeasurement
8 K (the closed
upper
300
K (thelower
panel).
contacts(y-direction)
a innonlocalandEq.
(2).The= −µ↓ . I
tudeelectrodes
but opposite
sign; asµ↑ terminals
thefitting lines.
gradually. However, a reverse of the 4T-Hanle signals is
because two
are used
the inputzalong the z-direction
for a four-terminal Hanle-type spin precession
86-88)
clearlyobserved by applying the reverse
at 300 K.
, achievement
clarificationof field,
itsevenunderlying
physics
V =4V
degeneraten-type Si spin valve. (b) Non-local

demonstrated not only generation but also manipulation of SOI

spi

the
inset of the lower panel
shows gap-length dependence of spin resistances[79]).
in(ref.
the
Si MOS
by forgating.
Asthementioned
above,theRashbafield
Athe otherelectrodeis usedas the output
terminal.
measurement. B
This is strong evidence
the spin current through
Si
y

x

SD

Figure 2 shows the results obtained by the NL-MR channel up to 300 K.
Appl. inPhys.theExpress
113004(2015)
T. Tahara
et ,al.investigation of gatingof emergent
thermalspintransport
injectioninSi 89)
magnetoresistance
Si8, spin
atthe constant
8 generates
Kbackground(thevoltages anmethod.valve
By subtracting
The spin
diffusion length and othereffective
parameters
magnetic
field. In our setup, the(a)(b)(195 and 460 V at 8 and 300 K, respectively) produced by were estimated by fitting with the analytical solution of the044010-390),
andthermaleffects(alongeffectsonspinsignals
electric
coupling between
electric pads
fromthefollowing
function:
upper
anddilute
300hydrofluoric
K (the lower
panel).
Thethegate
insetof
substrate
was panel)removed usingacid an(HF)
electric
field
isperpendicular
toannealing
the Si plane 
Z applied
raw data, the spin accumulation voltages V were obtainedchanged
from
ca.
1
µA
under
positivegate
voltages
to
ca.
P
t
V ðB ÞI (A)1and10 using an injection current I
solution. In this study, we observed 2  1 andconverted2¼’ðtÞ cosð!tÞ exp 91,92)
dt;
into R by.
Notableachievements
in Si
on
spin
signals
e
NðE
ÞA

I
I
Ishows gap-length
the
lower
panel
dependence
of
spin
0.5
nA
under
negativegate
voltages.
The
decreaseinthedirection,
as
shown

 in Fig. 1a) and, thus, the effective mag1 mA. Steep changes in R thewith clear z
plateauswere
I of(A)thereflection high-energy electron diffraction 10
patternsI - of1ðx  x Þ
successfully obtained at a temperature of not only 8 K but
ffiffiffiffiffiffiffiffiffiffisignals
ffi exp  is attributed’ðtÞ of¼ pthe;ð2Þ following reason:
magnitude
to the2.49225 before the (ref.
4Dt
spintronics
fromapplication-oriented
viewpoints
Si surface
growth79)).
of the MgO layer. This alsowas4Dt
resistances
300 K. With the increase in netic
temperature, thefield
field foris generated in-plane along the (−y) directionare
because(b)

ISD

VG = 50 V

SD

P

7,8)

SD

P

P
SD
P
SD

-3

-6

injectAPSD?

inject

1

2

2

F

sp

0

1

2

2

ISD

P (A)

ISD (mA)-4
gate
smallerthang isca.
50 V, Isd began to be
10 -8 slightly to the lower field.at awhere
frequency,
the g-factor
transition in R shifted! ¼ voltagegB B is the Larmor
10values of theconnot done in our previous studies.11,15,16) The(c)is the spin lifetime,
x1 and x2 takes place underof electron (using
g ¼ 2),
Anisotropic
magnetoresistance (AMR) hysteresis, as presuppressed.
Here,thespsuppression
equally
5
4
9:52

10
ductivity in the Si channel were 1:03  10 andviouslyreported,15) was observed in dummy samples. Thus, are integrated over the widths of the injector and detector,ON
the andparallelanddiffusion
antiparallel
magnetization
1
10 -5 The values
2.49200
the changesI inPR can be -10
explained by the magnetization
D is the spin
constant. We
use the relationshipalignments. When1 mmeasured at 8 and 300 K, respectively.
SD
10 Therefore, we can conclude of  N ¼ ðDsp Þ1=2 , thus P,  N , and sp are fitting parameters.
reversal of each FM electrode.
I is suppressed, the diﬀerence in Isd between the spin on=oﬀ
0.68theµA tunnel contact wereof the resistance area product of
data, asthat7.1
the
0.68changesµA in R resulted from the amount of spinsd The fitting lines are in good agreement with the-6statesresultingthespinsuppressionof the spin
10
showndecreases,by the example
in Fig. 3(b).inThe
diffusionaccumulations detected as the spin valve effect. This isand 4.6 K m2 measured at 8 and 300 K, respectively.
ON of theAPlengths at
8 and 300 K 0.5
were nA
estimatedtobe 2:00 to 0:03
anddetection limit inspin current-12
through the Si channel at 300 K.
2.49175
signals.
Because
is
close
the
ISD view ofevidence
I
10SD
Figure1showsaschematiccross-sectionalthem,Japanrespectively. These
values are consistent
with 2023
0:6  0:2
The spin
diffusion
lengthcan be accurately estimated-7 JournaloftheMagnetics
Societyof
Vol.47,
No.2,
34 V = 50 V
10thisthosemeasurement,
we method
believeobtained by the NL-MR
within thatan errorthe
range,spin signals weredependence of R, because the clear
G
lateral device
fabricated by electron beam lithographyfrom
forthe gap SDlength=R
4 V curves result from successful anti- as mentioned above. This indicates that our measurements
plateaus onVthe
VSD = 4 V I AP
modulated by over three orders of magnitude. Furthermore,@RT alignment.
SDparallel magnetization
The inset of Fig. 2 shows are highly reliable in the temperature range of 8 to 300 K.
patterning. @RT
The Si channel
was fabricated by a-8mesa-etching
ISDAP
-14
gwith increasing gapI and
10 OFF
10exponentially
2.49150
Therefore,itisobvious
that
the
spin
transport
of
the
that
the
R
curve
decaysthe magnitude of the spin signalsbandwere very consistent0
200 400 (FM)600
-100 -5050
50 contacts
100 2 and 3. Using the tunnel barrier,sd transferredtechnique-600and-400two-200ferromagnetic
electrodes—contact
V 0 between
electrons in the Si channel is demonstrated evenlength
as functionsof the gate voltage, and the on=oﬀ ratios for
7,17)
(V)
VVR
then, theat 300 K.
Magnetic
field(Oe) 3 of 2  21 m2 —werem2 andcontact
2 of 0:5  21GG decreases as a function of the gap length;
data is fitted using the following equation:
Figure4showsthetemperaturedependence
ofthethan 103. Because
and
the
spin
signalswerebothgreaterI
sd
formed by ion milling. Then, a 30-nm-thick SiO layer was

ISDP Q ISDAP (A)0a Si channel isOe)~ 200 nm0Bz (mT)tance between the spin injector and the spin_detector,
d. Thedots
distancemagnetization
directions
ofthe
FM-B
and FM-B
are(1,as0)VXOR
operatioage, Vbyresults
FM-M
is Fig.
expressed= of aXOR
in
1(f)
and
those
previouss
0.08
XOR , detected
10–200.4–10 obtained0(0, 1)10 and20the 1 state when they are (1, 1) or (0, 0).
–20
are experimental
data,200
and0Kthe red line20is a fitting
resultor
ferromagnetic
electrod(σ↑ µandthe con↑ + σantiparallel↓ µ↓ )/[e(σ↑ + σconfigurations.
↓ )], where σ↑ (σ↓ ) is
Bz (mT)Bz (mT)
However,
this featureis150Kwith Eq.
signals under parallel (red)and8 (1). (g) Hanle-effectThisgate ductivity
is not a NAND
realize a high degreegate orspinsan ORin gatebuteisis anof up (down)
FM-M,
theXORelementary
0.2
antiparallel (blue) configurations, where the linear background isapplicableforOR
operationin spinthe absorpt
MLG
III.
XOR
OPERATION
chargeand µevenis thetheelectrochemicalof negligible
upgate. In otherwords,
thoughwe NAND
increaseor
thepotential
num6↑ (µ↓ )
100 K and the spin detector are FM-B
subtracted.
injector
0.0 MLG and
FIG. 1. The(a)spinThe
semiconductor-based
proposed(down)
the toSi/FM-M
Whenelectrowe can freelyaddMadber deviceof electrodes
fromfive, theinterface.
logic
operation
wespins
useatthreethe
NLMR
signals
as thea iscomponentof theFM-M,4 respectively. (h) Difference in the Hanle signal between
In
the
XOR
operation,adirectchargecurrenbyantiparallel
Dery et andal. parallel[11]. (b)Silicon-based
multiterminal
lateralspinchemicalpotential in aSi
beneath FM-M—thatis, (µ↑gates+ other than the
-0.2
still
an XORgate.
reconstructionof centerthe logic
theconfigurations.
The dotsand thesolid
theFurthermore,
deviceconsistsofµthreeferromagnetic
electro
g
50 K
2
from
FM-A
to
FM-B,
and
the
spin-accumu
µ
)—is
set
to
be
0
meV,
µ
and
have
the
same
amplilinearetheexperimental
data
and
the
fitting
curve
obtainedwith↓ K. The↑↓at 300valves for XOR operation. (c)–(e) NLMR measured
can be realized usinggate is impossible
by use of three ferromagnetic
electrodes-0.4(FM-B,
FM-M,
and
FM-B
) ↓andtwocase,outmostnonmagn
Eq.
(2).
= −µ
. In
this
tude
but andopposite
sign; asnamely,µ↑ terminals
8K
0injector and detectorage
ismeasuredby
FM-M
withcharge-current
reference
tode
Thebecause(d)twoelectrodes
are
used
the
input
and
spin
are (c) FM-A and FM-B,
FM-B

25

14,15) in a highly doped Si channel at room temperature (RT) using aspincurrent
ﬁeld
in andthespin
Si,transportminor loop, observed with the 3T-MR method. At 20
an electricdetector consisting of an Fe/MgO tunnel barrier. Spin current was generated using a nonlocalnt
spin
accumulation.
current of 1 mA, the magnitude of the magnetoresistance15
e spin precession were successfully detected at 300 K, thus proving spin injection with the
10 whereomagnetic
electrodes
measuredThemagnetic
m be
and 0.38
1.3 nsΩ.
by theHanle-typespin ﬁelds,
engthand its lifetime
at RT werewas
estimated
to be 0.6to
ety of parallel
Applied Physics
5ﬁeld
to the Si the hysteresis and the minor loop appeared, are consistent

SiO2
Si subst.

5

Injector : FM B
Detector : FM M

_0.02

_0.08

problem. The
ndent interface
chottky barrier,solution to thisof the injected
minal
nonlocalA
metry (NL-MR
trical detection
spin precession
etry (4T-Hanle
or proving spin
Si0.38channelwasΩmethod, but spin
eratures below
nal Hanle-type@ RThod), in whichh the injection
detect the spin
2,13)
The largeRT) using thisovery made
by
@ RT

y

A-B

z

0
ection of the detector (a) between the measurements, showing that the magnetoresist2.5 T= 300 K
beneaththe detector ance is ascribedspin ztransport
in the Si spin
p for SemiconFe to a successful
y
V
2.0
NL
Al
s Si)
an areemerging
controlled toAl MOSFET at RT. The distanceof theferromagnetic
electrodesx
1.5
MgOµm2 and 3a spin
MgOtransportsue
concerning
4
resistancehysteresis. 1was 4.26
of 4.26 µm wasrealized.
~ 20 nm1.0
of spins
ssion
will frombe reported Such~ 60µa µlongspintransport was achievedby spindrift indm
~ 80 nm0.513)
n-Si
ductorchannel,ccumulation
at both addition to spin diﬀusion as discussed previously. When
2)

60

B-M

0.04

0.00

AP

40

0

60

Injector : FM B
Detector : FM M

–0.04

0
20
By (mT)

30

10

VNLA P _ VNLP (mV)

Voltage (mV)

Voltage (mV)–20

∆Vs (µV)ζ (=τs τsǁ)

Voltage (mV)

–3.04

–3.07
–60

–40

50

Injector : FM A
Detector : FM M

–3.05

y

–3.40

VXOR (mV)

–20

y

B M

–3.38

–3.42

–3.88
–30

y

–3.36

Voltage (mV)

Voltage (mV)

–3.86

Injector : FM B
Detector : FM M

–3.34

A B

–3.84

Voltage (mV)

Voltage (mV)

Injector : FM A
Detector :FM B

VXOR (mV)

–3.82

y

VXOR (mV)VXOR (mV)

AB

y

M

NATURE MATERIALS
2

y

XOR

XOR

A



y

2

2

the motion of the propagating spins is along the x direction(Fig. 4a). The in-plane emergent effective magnetic field further
helps spin relaxation of the propagating spins, which enhances
the spin lifetime anisotropy. ζ is close to 1, not at Vg = 0 V but at
V = 10 V; that is, the spin lifetime is isotropic at Vg = 10 V. Thissuggests that a built-in and non-negligible electric field, whose
direction is opposite to that 1 of the positive
external gate electric
13)




obtained transport parameters, together with the 4T-Hanle

na

an

Gi
an
are
fie
pa
tio
res
Δ0

INDEX

demonstration of over 1% magnetoresistance ratio 93) andspin logic operation (Fig. 14) 94). Furthermore, significant
achievements in basic physics viewpoints are spinpumping-induced spin transport in p-type Si 95) andelectric field modulation of spin precession (spinmanipulation without an external magnetic field) due tosynthetic Rashba field in Si/SiO2 96). Especially, spin
manipulation by the gate electric field in Si spin FET
shown in Fig. 15 counters conventional understandingsthat the SOI in Si is negligibly small and the Rashba field
does not play a dominant role in Si. The achievement canbe regarded as one of subsequent studies that gate
control of SOI, resulting in the ISHE, in ultrathin
metallic films 97-99). It is also noted that spin transport in
the other group-IV semiconductor, Ge, was also achievedat room temperature by spin pumping 100), which enables
subsequent studies using Ge towards spin transistor
creation 101,102).
In summary, inorganic semiconductors are playing oneof pivotal roles in spintronics, and its research field
expands to both application-oriented and fundamental
directions. Especially, group-IV semiconductors such as
Si and Ge (and in addition, graphene and diamond) play
an important role in the field.
Acknowledgements The author is indebted to allcollaborators, especially Prof. Yoshishige Suzuki and his
group members in Osaka University, and Dr. Tomoyuki
Sasaki, Mr. Hayato Koike and group members in TDK
corporation. He also acknowledges to his colleagues andstudents of his group in Osaka University (2010-2013)
and Kyoto University (2013-) especially Dr. Eiji Shikoh,
Dr. Yuichiro Ando, Dr. Ryo Ohshima, Dr. Ei Shigematsu
and Dr. Eiiti Tamura, for their strong and supportive
collaboration. Financial supports from the Ministry of
Education, Culture, Sports, Science and Technology ofJapan and the Japan Science and Technology Agency are
deeply appreciated.
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T. Fukushima, K. Sawano, T. Oguchi and K. Hamaya: NPG

Asia Mater. 12, 47 (2020).

R eceiv ed N o v . 1 7 , 2 0 2 2 ; A ccep ted D e c. 1 4 , 2 0 2 2 .

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 38-41 (2023)<Leter>Improvement of GHz Range Electromagnetic Properties of
Ferrite Thin Film Magnetic Core Integrated RF Inductor
T. Nakano*, S. Miyazaki*, Y. Ozaki*, K. Koike*, D. Inokuchi*** Materials Research Center, TDK Corporation, Narita, Chiba, 286-8588, Japan** Evaluation & Analysis Center, TDK Corporation, Ichikawa, Chiba, 272-8588, Japan

Ferrite thin film magnetic core integrated radio frequency inductors (RFIs) were investigated in order to realize
RFIs with a smaller size, higher driving frequency, and higher quality factor (Q). The ferrite thin films were fabricatedby low-temperature spin-spray deposition assuming adaptation to the photolithography process for inductor
fabrication with two different compositions: Ni 0.16Zn0.20Fe2.64O4+δ (NZFO) and Co0.11Fe2.89O4+δ (CFO). The RFI with
CFO had a 34% higher inductance and 43% Q improvement compared with the air core RFI at a frequency of 1 GHz.
It was confirmed that the complex permeability of the films was correlated with the frequency characteristics of the
RFIs with the ferrite thin films. The results suggest that integrating ferrite thin film in RFIs is effective for future
mobile device applications.
Key words: Ferrite thin film, Radio frequency inductor, Spin-spray method, Complex permeability, Photolithography
1. Introduction
In recent years, the fifth-generation wirelesscommunication technology (5G) has been used. The
electric components used in radio frequency (RF) frontend circuits such as antennas, amplifiers, filters, andinductors must be miniaturized and the driving
frequency and quality factor (Q) increased. The air core(non-magnetic material) type of structure is selected formass-produced RF inductors (RFIs) to satisfy therequirements of cost, inductance tolerance, and high Q.
However, to satisfy 5G demands, further improvements
to the structure and process of RFIs are required.
Therefore, photolithography and Cu plating have been
examined for fabricating future RFIs to improve the wire
resistance and shape, which can increase Q.
Inserting a magnetic core can solve the above problems
and has been studied with various magnetic materials 1)5). The magnetic core must have a high natural resonancefrequency (fr) and electric resistance in order to maintain
constant permeability while preventing increasing coreloss until the driving frequency of RFIs (ex. 0.45 to 6 GHz
for 5G sub-6 bands). Ferrite film is a possible candidate
for the magnetic core as it has both shape magnetic
anisotropy and a higher electric resistance. Low
temperature processes (<100 °C) are also desirable forfabricating the magnetic core assuming adaptation to thephotolithography process. Spin-spray deposition, which
was proposed by M. Abe et al 6)-8), is a ferrite thin-film
fabrication process that uses a low temperature, requires
no vacuum, and has a high deposition rate for various
substrates such as glass, silicon, and organic material.
Corresponding
author:Takuma.Nakano@tdk.com).

38

T.

NakanoHowever, there have been few reports on ferrite thin film
integrated RFIs that compare both RFI and film
properties in the GHz bands 3)-5), 8), 9).
In this work, Ni0.16Zn0.20Fe2.64O4+δ (NZFO) andCo0.11Fe2.89O4+δ (CFO) ferrite thin films are fabricated byspin-spray deposition and ferrite thin films integrated
RFIs are fabricated, and the electromagnetic propertiesof both the films and the RFIs are examined.
2. Experimental
2.1 Ferrite thin film deposition
Ferrite thin films with compositions of NZFO and CFO
were fabricated by spin-spray deposition as shown in Fig.
1. A reaction solution and oxidizing solution were
sprayed simultaneously on rotating substrates heated atselected temperatures between 70 °C and 90 °C. The
substrate was selected from a quartz or photoresist
coated Si wafer, which is described later. For the(e-mail:Fig. 1 Schematic images of spin spray deposition.

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

INDEX

3. Result and discussion
3.1 Film properties
Figure 3 shows cross-sectional SEM images of theferrite thin films. Dense and >2 μm thick films wereachieved. Figure 4 shows out-of-plane XRD spectra. All
diffraction peaks corresponded to a spinel structure, andthus, the films were crystalized with low-temperature
spin-spray deposition. A structure perpendicular to thesubstrate surface was confirmed in SEM images, and acrystalline orientation to the (111) plane was also
confirmed, which have been reported for other ferrite
films fabricated by spin-spray deposition 6).
The values of the saturation magnetization (MS) andcoercivity examined by VSM were 415 emu/cc and 27 Oe
for NZFO and 403 emu/cc and 107 Oe for CFO as shownin Fig. 5. It is reported that ferrite thin films fabricatedby spin-spray deposition have a higher MS compared withgeneral bulk ferrites (ex. 300~350 emu/cc for
Ni0.5Zn0.5Fe2O4 9), 12)) as they contain a large amount of
Fe2+ 6). Figure 6 shows the frequency dependences of thecomplex permeability measured by a short-circuited
microstrip line. The values of the real part of complex
permeability (μr’) for the NZFO and CFO were 30 up to
0.5 GHz and 8 up to 2 GHz, respectively, and then bothdecreased as the frequency increased. The imaginary
part of complex permeability (μr”) for NZFO indicated abroad peak over the entire range of the frequency and

333

220

311

440

(a) NZFO

222

111

Fig.3 Cross-sectional SEM images of (a) NZFO and(b) CFO.

Intensity(arb. unit)

deposition of NZFO, the reaction solution contained 20
mM FeCl2･4H2O, 5 mM NiCl2･6H2O, and 0.1 mM ZnCl2
in deionized water, and the oxidizing solution contained
5 mM KNO2 and 65 mM CH2COONH4 in deionized water.
For the deposition of CFO, the reaction solution
contained 20 mM FeCl2･4H2O and 1 mM CoCl2･6H2O indeionized water, and the oxidizing solution contained 5mM KNO2 and 65 mM CH2COONa･3H2O in deionizedwater. All reagents were purchased from Wako Pure
Chemical Industries.
2.2 Measurement
The film structure and composition were examined by
X-ray diffraction (XRD) with Cu Kα and a scanningelectron microscope (SEM) after an ion milling polish andinductively coupled plasma mass spectrometry.
Magnetization curves were taken on 5 mm × 5 mmsamples using a vibrating sample magnetometer (VSM).
Complex permeability and fr were measured using ashort-circuited microstrip line (KEYCOM, PER01) 10)
with which accuracy of the complex permeability is
within 5%, and a flexible microstrip line-type probe 11).
2.3 Inductor fabrication
Solenoid RFIs were fabricated on a Si wafer using aphotolithography process and consisted of four parts of
Cu components, which were lower wiring, connection via,
upper wiring, and upper electrode, as shown in Fig. 2. A
2μm thick ferrite thin film was inserted between thelower and upper wiring for the magnetic core integrated
inductors. Each Cu component was fabricated as follows:
sputtered Cu seed layer deposition, lapping andpatterning of the negative dry film resist (RY-5115 fromShowa Denko Materials), Cu electroplating, seed layerand dry film resist removal, and filling of gaps with apermanent photoresist (SU-8 3005 of Nippon Kayaku).
The ferrite thin films were patterned into a 400 μm wide× 1000 μm long rectangular bar using photolithography
and etched in a 36 wt% HCl solution.

(b) CFO

10

20

30

40

50

2theta (deg.)

60

70Fig. 4 Out of plane XRD spectra of (a) NZFO and (b)
CFO.
600

Magnetization(emu/cc)

400
200

NZFO
CFO

0

-200
-400
-600
-4000

Fig. 2 Schematic images of ferrite thin film integrated
RFI with (a) perspective and (b) cross-sectional view.

-2000

0

Magnetic field (Oe)

2000

4000

Fig. 5 In plane M-H curves of NZFO (red solid line)
and CFO (blue dashed line).

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

39

INDEX

contained two peaks, which may suggest the presence ofat least two magnetic anisotropy fields and/or domain
wall resonance 8), 13). The peak of μr” for CFO was alsobroad and observed at around 2 GHz. It is reported thatferrites containing cobalt have a large damping constant(α>0.1) due to a large magnetic anisotropy disarmament
magnetoelastic effect 14), 15). Low signal to noise ratioaround lower frequency (< 0.5 GHz) was caused bysensitivity of vector network analyzer. Peaks of μr’ and μr”
around 10 GHz arose from measurement equipment.
Figure 7 shows the relationship between the fr andstatic μr’ of the bulk and film ferrites. The values for thebulk ferrites were evaluated by complex permeability
measurement of sintered toroidal cores fabricated byusing a conventional solid phase method 16) with various
ferrite compositions. The static μr’ of the film ferrites are
excerpted from μr’ at 100 MHz in Fig. 6. The values of fr
for the film ferrites were estimated using the following
equation based on FMR measurement with various inplane external magnetic fields using a flexible microstrip
line-type probe 17), 18).

𝑓𝑓FMR = 𝛾𝛾⁄2𝜋𝜋 √(𝑀𝑀s ⁄𝜇𝜇0 + 𝐻𝐻k + 𝐻𝐻ex )(𝐻𝐻k + 𝐻𝐻ex ), (1)Real
Imaginary

NZFO

zzzz

CFO
0.1

1

Frequency (GHz)10

Fig. 6 Frequency dependences of real (solid lines) andimaginary part (dotted lines) of complex permeabilityof NZFO (red) and CFO (blue).

Real part of static
permeability

100

Film

10

1

Bulk

1

10

Natural resonance frequency,
fr (GHz)100

Fig. 7 Relationship between natural resonancefrequency and real part of static permeability of bulk
(black) and film ferrites (blue).

40

Fig.8 (a) Top and (b) cross-sectional views of air coreand magnetic core solenoid RFIs.
Inductance, L (nH)

40
35
30
25
20
15
10
5
0

3.2 Inductor properties
Figure 8 shows top views taken by an optical
microscope and cross-sectional views taken by SEM of
the air-core and magnetic-core solenoid RFIs. The ferrite
thin films were successfully deposited and patterned
between the lower and upper wiring with the lowtemperature process.
The frequency dependence of inductance (L) and Q are
shown in Fig. 9. For the air core RFI, the value of L wasalmost constant up to approximately 3 GHz, and a peakin the self-resonance frequency (SRF) was observed at 10
GHz. By integrating NZFO and CFO, the values of L
increased compared with that of the air core RFIs up to 4
and 8 GHz, respectively, and the values of Q increased up
to 1 GHz for NZFO and 2 GHz for CFO. Table I
summarizes the L and Q values of the fabricated RFIs,

Quality factor, Q

Complex permeability

where 𝑓𝑓𝐹𝐹𝐹𝐹𝐹𝐹 is the ferromagnetic resonance frequency,
𝛾𝛾 is the gyromagnetic ratio, 𝑀𝑀s is the saturation
magnetization, 𝜇𝜇0 is the permeability of free space, 𝐻𝐻kis the magnetic anisotropy field, and 𝐻𝐻ex is the external
magnetic field. The relationship between the fr and static
μr’ of the bulk ferrite (solid line in Fig. 7) corresponds to
Snoek’s limitation rule. The result shows that therelationship of the film ferrite (dotted line) exceeded
Snoek's limit for bulk ferrite, with the effect of shapemagnetic anisotropy 18). This result will need to befurther discussed including the modeling of magnetic
anisotropy.

5

Air core RFI
RFI with NZFO
RFI with CFO

4
3

(a)

2
1
0

0.1

8

1
Frequency (GHz)

10

(b)

Air core RFI
RFI with NZFO
RFI with CFO

6
4
2
0

0.1

1
Frequency (GHz)10

Fig. 9 Frequency dependence of (a) inductance and (b)quality factor of RFIs.

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

10

50%

8

40%

6

30%

4

20%

2

10%

0

0.1

1

10

0%

Rate of increase of
inductance from
inserting CFO

Real part of complex
permeability

INDEX

Frequency (GHz)

Fig. 10 Comparison of frequency dependence of realpart of complex permeability (black, left axis) and rateof increase of inductance from inserting CFO (blue,
right axis).
Table I Summary of inductance and quality factor of
air core and ferrite thin film integrated RFI.
Inductance, L (nH)
Air core
RFI with CFO
𝛥𝛥𝛥𝛥CFO
RFI with NZFO𝛥𝛥𝛥𝛥NZFO

1 GHz
1.37
1.84
34%
2.82
106%

5 GHz
1.52
1.82
20%
1.20
-21%

Quality factor, Q
1 GHz 5 GHz
1.3
6.5
1.9
2.1
43%
-67%
1.3
0.8
-3%
-88%

Qmax
7.0
2.7
-62%
1.5
-79%

and the rate of increase of L and Q from inserting theferrite thin films [𝛥𝛥𝑉𝑉NZFO or CFO = (𝑉𝑉NZFO or CFO − 𝑉𝑉air )⁄𝑉𝑉air ,where 𝑉𝑉NZFO or CFO is the L or Q of RFI with NZFO or
CFO and 𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎 is the L or Q of air core RFI]. The RFI with
CFO had a 34% higher inductance and 43% Q
improvement compared with the air core RFI at afrequency of 1 GHz. It was confirmed that both GHz-band
L and Q are enhanced by integrating ferrite thin films,
especially using CFO.
Figure 10 shows a comparison of μr’ and 𝑅𝑅CFO of L. The
frequency dependences of both decreased as thefrequency increased with almost the same slope above 2
GHz. This result indicates that integrating ferrite thinfilm in RFI is effective for improving RFI properties withGHz bands. In addition, the slope of the dependence ofthe rate of increase of L was shifted toward higher
frequencies compared with the slope of μr’. This may be
due to the effect of SRF, stress, or deficiencies induced
during the RFI process and/or shape difference of CFO
samples. The CFO sample for permeability measurement
was 5 mm × 5 mm, and that for RFI was 1 mm × 0.4 mm,
of which the long side was perpendicular to the solenoid
coil length (see Fig. 2). Therefore, there was uniaxial
magnetic anisotropy perpendicular to a high frequency
magnetic field 1).
4. Conclusion
This paper discussed the electromagnetic properties offerrite thin film fabricated radio frequency inductors(RFI). Spin-spray deposition and shape patterning of
Ni0.16Zn0.20Fe2.63O4+δ and Co0.11Fe2.89O4+δ (CFO) wereconducted at low temperature (<100°C) assuming
adaptation to the photolithography process. The RFI

with CFO achieved a 34% higher inductance (L) and 43%
quality factor (Q) improvement at a frequency of 1 GHz
and superior values for both L and Q up to 2 GHz
compared with the air core RFI. Moreover, the frequency
dependences of both the real part of complex
permeability and L improvement from integrating theferrite thin film showed a similar trend, which can meanthat integrating ferrite thin film is an effective method
for future RFI.
Acknowledgements
The NZFO film fabrication of thispaper was performed by the Matsushita Laboratory at
the Tokyo Institute of Technology. The measurement of
the high-frequency magnetic properties was performedby Tohoku-TMIT. The authors would like to thank Prof.
M. Matsushita of the Tokyo Institute of Technology andProf. S. Yabukami, Assoc. prof. Y. Endo, and Dr. K. Okita
of Tohoku-TMIT for the fruitful discussion.
References
1) A. El-Ghazaly, R. M. White and S. X. Wang: IEEE Trans.
Microw. Theory Tech., 65, 4893 (2017).
2) K. Sato, K. Sugimura, T. Sato, M. Sonehara and H. Takeuchi:
T. Magn. Soc. Jpn. (Special Issues)., 1, 44 (2017).
3) N. Sangeneni, N. Bhat, and S. A. Shivashankar: IEEE 17th
Int. Conf. on Nanotech., NANO 2017, 762 (2017).
4) X. Wang, H. Chen, X. Shi, Y. Gao, H. Lin, J.G. Jones, B.M.
Howe, G.J. Brown and N.X. Sun: AIP Advances, 7, 056606(2017).
5) K. Hagita, Y. Yazaki, Y. Kondo, M. Sonehara, T. Sato, T. Fujii,
K. Kobayashi, S. Nakazawa, H. Shimizu, T. Watanabe, Y.
Seino, N. Matsushita, Y. Yanagihara, T. Someya, H. Fuketa,
M. Takamiya and T. Sakurai: J. Magn. Soc. Jpn., 39, 71(2015).
6) N. Matsushita, M. Abe, K. Kondo, S. Yoshida, T. Sato and K.
Okada: J. Surf. Finish. Soc. Jpn., 6, 425 (2010).
7) K. Kondo, S. Yoshida, H. Ono and M. Abe: J. Magn. Soc. Jpn.,
101, 4 (2007).
8) N. Matsushita, T. Nakamura and M. Abe: IEEE Trans. Magn.,
38, 3111 (2002).
9) D. Guo, Z. Zhang, M. Lin, X. Fan, G. Chai, Y. Xu and D. Xue:
J. Phys. D, 42, 12 (2009).
10) S. Takeda, T. Hotchi, S. Motomura and H. Suzuki: J. Magn.
Soc. Jpn., 39, 227 (2015).
11) S. Yabukami, K. Nozawa, L. Tonthat, K. Okita and R. Sai:
IEEE Trans. Magn., 57, 1 (2021).
12) N. Hiratsuka, M. Shimizu, M. Fujita and M. Sugimoto: J.
Jpn. Soc. Powder Powder Metallurgy, 39, 152 (1992).
13) T. Tsutaoka: J. Appl. Phys, 93, 2789 (2003).
14) B. Kuanr, S. R. Mishra, L. Wang, D. Delconte, D. Neupane,
V. Veerakumar and Z. Celinski: Mater. Res. Bull, 76, 22(2016).
15) E. L. Verde, G. T. Landi, M. S. Carrião, A. L. Drummond, J.
A. Gomes, E. D. Vieira, M. H. Sousa and A. F. Bakuzis: AIP
Advances, 2, 032120 (2012).
16) T. Yamaguchi: J. Jpn. Soc. Powder Powder Metallurgy, 12,
62 (1965).
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18) K. Oota, Jikikougaku no kiso II, Kyoritsu shuppan, Tokyo(1973) (in Japanese).
Received Sep. 15, 2022; Accepted Dec. 13, 2022

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 42-51 (2023)<Paper>Reluctance Network Model of IPM Motor Representing Dynamic Hysteresis
Characteristics for High-Accuracy Iron Loss Calculation Considering
Carrier Harmonics
Y. Hane and K. Nakamura

Graduate School of Engineering, Tohoku Univ., 6-6-11 Aoba Aramaki, Aoba-ku, Sendai 980-8579, Japan

It is essential to establish a simple and practical method for quantitatively estimating the iron loss considering
the dynamic hysteresis behavior to further improve the efficiency of electric machines. In a previous study, a novel
simple magnetic circuit model representing the dynamic hysteresis characteristics was presented by incorporating aplay model, one of the phenomenological dc hysteresis models, and a Cauer circuit, which can consider the skin effect.
It was demonstrated that this magnetic circuit model could accurately calculate the hysteresis loops and iron loss
even under PMW excitation for magnetic reactors made of several types of core materials in a short time. However,this method can only be used for an object with a simple shape, such as a ring core. Hence, this paper describes thatthe previously proposed magnetic circuit model is extended to a reluctance network analysis (RNA) to expand theapplication range. Furthermore, the proposed method was experimentally validated using an interior permanent
magnet (IPM) synchronous motor driven by a PWM converter as the examination target.
Key words: interior permanent magnet (IPM) motor, reluctance network analysis (RNA), play model, Cauer circuit,dynamic hysteresis characteristics
1. Introduction
In recent years, the efficiency improvement of electricmachines, especially an electric motor, has been strongly
desired from the viewpoint of global environmental
protection and energy conservation. Among a variety ofelectric motors, utilization of an interior permanent
magnet (IPM) synchronous motor has been dramaticallyincreasing because of its high torque density andefficiency characteristics. To further enhance theperformance of an IPM motor, it is necessary to
optimally design not only a motor structure but also awhole motor drive system. However, in many cases ofmachine design using a finite element method (FEM), it
takes a lot of calculation time and computer memory sothat the coupled analysis with an external driving
circuit and a motion equation is not necessarily easy.
To overcome this issue, a reluctance network analysis(RNA) has been proposed so far 1), simulating flux
distribution inside an analytical object by expressing it
as one reluctance network. In the RNA, all thereluctances are determined by the magnetic propertiesof materials and dimensions of divided elements. The
RNA can be one of the practical solutions because of
several advantages, such as a straightforward analyticalmodel, short calculation time, relatively high calculation
accuracy, and easy coupling with an external driving
circuit and a motion equation. In previous studies, theRNA has been utilized for characteristic calculations ofvarious electric machines, including an SPM motor 2)-4).
Moreover, although there are very few studies on the                     Corresponding author: Y. Hane (e-mail: yoshiki.hane.e2@
tohoku.ac.jp).

42

derivation of the RNA model for an IPM motor 5) becauseof its complicated flux distribution, Ref. 6) indicated themodeling technique of the RNA model for an IPM motorwith a relatively small number of divided elements.
However, Ref. 6) indicated that the conventional RNA
model cannot calculate the iron loss with sufficiently
high accuracy because carrier harmonics generated by
PWM voltage excitation cannot be considered. Since an
IPM motor is generally driven by a PWM converter, it isessential to accurately calculate the iron loss even undera complicated exciting waveform.
In previous studies, a novel RNA model incorporatinga play model 7), which is one of the phenomenological dc
hysteresis models, was presented 8)–10). The play model
can express an arbitrary hysteresis loop with not only
high accuracy but also high speed. Although the playmodel generally requires a lot of measured dc hysteresis
loops with various flux density amplitudes, the dc
hysteresis
loops
calculatedbyasimplified
Landau-Lifshitz-Gilbert (LLG) equation 11), which is oneof the physical hysteresis models, can be substituted forthe measured ones 12). The calculation accuracy of thepreviously
proposed
RNA
model
has
been
experimentally proved by analyzing various devices,
including an SPM motor 8)-10). However, all the above
studies are limited to characteristic calculations undersimple excitation conditions such as sinusoidal andsquare waveforms. In this model, the calculation
accuracy of iron loss is insufficient under PWM
excitation because the influence of the skin effect caused
by carrier harmonics is neglected.
One of the most attractive eddy current loss models
in recent years is a Cauer circuit 13), 14), which expresses
the frequency characteristic of complex permeability by

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

INDEX(())

a ladder-type electric equivalent circuit composed of =p j ( B,  j ) max min p j 0 ( B,  j ), B +  j , B −  j(1)multiple resistance and inductance elements. Using theN
Cauer circuit, the one-dimensional electromagnetic field
H dc =
f j p j ( B)(2)
j =1
analysis can be performed with minimal calculation timeand cost. Moreover, Ref. 15) indicated that the playwhere an integer from 1 to N is j, the play hysterons at
model can be combined with the Cauer circuit bycurrent time step and 1 time step ago are pj and pj0, a
excluding the first inductance element. Furthermore, inwidth of the play hysteron is  j, the shape function is fj,
Ref. 16), a novel simple magnetic circuit model
respectively. The values of play hysterons are
representing the dynamic hysteresis characteristics was
overwritten at each time step. Although the derivation ofpresented, incorporating the play model and the Cauer
the shape function generally requires many measured dc
circuit (converted to a magnetic circuit). Using thehysteresis loops with various flux density amplitudes,
previously proposed magnetic circuit model, it is possible
they can be substituted by the calculated ones acquired
to accurately calculate hysteresis loops and iron loss
from the simplified LLG equation 11) so that only a few
even under PWM excitation for ring cores made ofdc hysteresis loops have to be measured 12). Fig. 2 shows
16)
several core materials in a short calculation time
the comparison of the measured dc hysteresis loops and.
calculated ones obtained from the simplified LLG
However, it is difficult to apply this model to analyze aequation of non-oriented electrical steel (NOES), whose
device with a complicated flux distribution, including an
thickness is 0.35 mm. In the experiment, ac hysteresis
IPM motor.
loops at a very low frequency of f = 5 Hz were regarded
Therefore, this paper describes that the simple
as dc ones. As shown in Fig. 2, the measured andmagnetic circuit model proposed in Ref. 16) is extended
calculated values agree with each flux density amplitude.
to the RNA model. The proposed RNA model is
In addition, as shown in Fig. 3, many dc hysteresis loops
experimentally validated by using an IPM motor driven
used for deriving the play model can be acquired byby a PWM converter as the examination target. It wasusing the simplified LLG equation without experiment.
proven that the iron loss could be accurately estimatedSecondly, the classical eddy current loss is
by taking carrier harmonics under PWM excitation into
represented by a ladder-shaped part composed of
account with a reasonable calculation time.
repeatedly connected magnetic circuit elements, which
2. Previously Proposed Simple Magnetic Circuit Modelis equivalent to the part of the first resistance element
Representing Dynamic Hysteresis Characteristics
and after in the original Cauer circuit 13), 14), as shown in
Fig. 4. This part represents the frequency characteristic
This chapter describes a principle of the previouslyof complex permeability due to the skin effect in the
proposed simple magnetic circuit model representing thephysical meaning. The parameters Rm and Lm are defined
dynamic hysteresis characteristics 16), as shown in Fig. 1,
which is the basis of the proposed RNA model describedas follows:
later. In the following, it is explained how to represent
1 l
Rm=

each component in this model.
L S(3)Firstly, the dc hysteresis characteristics are
1 l=
expressed by the play model 7), which can represent an S
arbitrarily shaped hysteresis loop by combining thelmultiple play hysterons with different widths and the
Lm= R S
shape function. Here, the magnetic flux density B is the
(4)
d2 l
input and the dc hysteresis component of magnetic field=4 S
Hdc is the output, respectively. The behavior of the playmodel can be described by the following equations: (Fig. 1)

Previously proposed simple magnetic circuit model representing the dynamic hysteresis characteristics.

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

43

INDEX

Fig. 2 Comparison of the measured and calculated dc
hysteresis loops of NOES.

H
dB
dt

R1 (= 7 R)

R0 (= 3R)

L1 (= L / 5)

L0 (= L)

Fig. 4

Fig. 3 Calculated dc hysteresis loops of NOES with flux
density amplitudes from Bm = 0.04 T to 1.6 T at intervalsof 0.04 T.

R2 (= 11R)
L2 (= L / 9)=
Ln ( L / (4n + 1))

Original Cauer circuit.

where the coefficients of the original Cauer circuit are L
and R, the magnetic path length is l, the averagecross-sectional area is S, the permeability is μ, theconductivity is σ, and the thickness of a steel sheet is d,respectively.
Thirdly, the anomalous eddy current loss isrepresented by a dependent-source element, which
outputs the magnetomotive force (MMF) proportional tothe input |d /dt|0.5. Its coefficient γ2 can be determined byapproximating the measured core loss curves of thematerial by the least squares method, as shown in Fig. 5,
using the following equation 17):

 2 d 2 Bm2
 B1.5Wi=
const. +f + 8.763 2 m f 0.5
6qi
f
qi

R=
n ( (4 n + 3) R )(a) external view(b) specifications(5)

where the iron loss is Wi, the frequency is f, themaximum flux density is Bm, and the mass density ofcore material is qi, respectively.
3. Conventional and Proposed RNA Models of IPM
Motor Representing Dynamic Hysteresis Characteristics
Fig. 6(a) and (b) show specifications and a rotor
structure of an IPM motor with polar anisotropic bonded

Fig. 5
Measured core loss
approximate curves of NOES.

44

curvesand

theirFig. 6(c) rotor structure
IPM motor used in the consideration.

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Nd-Fe-B magnets used in the consideration. The relative
recoil permeability and coercive force of magnets are
1.275 and 461 kA/m, respectively. Also, as shown in Fig.
6(b), rotor magnets are magnetized in not the generalradial or parallel directions but the arcuate one.
In the following, it is described how to construct theconventional and proposed RNA models. Firstly, ananalytical object is divided into a multiple number of
elements. Then, each divided element is replaced with aunit magnetic circuit composed of three or four
reluctances, as shown in Fig. 7. The stator core isdivided into six regions in the circumferential direction(excluding stator pole tips), which is the same number as
slots. On the contrary, stator pole tips, air gaps, and arotor are divided into 360 elements in increments of 1
degree in the circumferential direction since their flux
distribution is more complicated than that of stator poles
and yoke. Here, the analytical model is halved in the rand z-axis directions, respectively, considering flux
distribution symmetry.
Figs. 8 and 9 show the conventional and proposed
RNA models of one stator pole of an IPM motor(simplified schematic). The difference between these twomodels is the method for giving the reluctances in a
stator core. In the conventional RNA model, eachreluctance in a stator core is determined byapproximating the initial magnetization curve of thecore material as shown in Fig. 10, using the following
equations 6):=
H 1B +  m B mcalculate the iron loss, the magnetic inductance element
given by the following equation should be connected inseries with each reluctance given by Eq. (9):

Lmc =

1l
S

(9)

where the coefficient is 1, which can be determined byapproximating the following equation using the leas t

Rr
Rq

Fig. 7

Unit magnetic circuit.

(6)

 l  l
f m  1 + mm  m −1  
=
(7)
S
S


1l  ml m−1
+ m
R=
(8)
mc
S
S
where the coefficients are 1 and m, the order is m, the
MMF is fm = Hl, the magnetic flux is  = BS, and thenonlinear reluctance is Rmc, respectively. In addition, toSimplified schematic diagram of theFig. 8
conventional RNA model of one stator pole of an IPM
motor.

Fig. 9 Simplified schematic diagram of the proposed RNA model of one stator pole of an IPM motor representing the
dynamic hysteresis characteristics.

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INDEX

square method:2 2 1 2 2
Wi =
f Bm
qi

(10)

In this way, the iron loss can be simply calculated withthe accuracy equivalent to the Steinmetz’s empiricalequation 18) without the post-processing in the RNA 6).
However, its calculation accuracy is not sufficiently highunder PWM excitation. On the other hand, in the
proposed RNA model, each reluctance denotes the dc
hysteresis characteristics by the play model, theclassical eddy current loss by a ladder-shaped partcomposed of inductance and resistance elements, whichis equivalent to the Cauer circuit, and the anomalous
eddy current loss by a dependent-source, respectively, ineach divided element. Here, when a ladder-shaped partis truncated at 1st stage, the proposed method isequivalent to the previous one presented in Refs. 8)–10).
Besides, the MMF generated from the armature winding
current is concentrated at the center of each stator pole,
where the armature winding is applied 6). In contrast,
the reluctances in a rotor core are regarded as zero, thatis, these magnetic paths are short-circuit in this model
because these reluctances are extremely smaller thanthose in magnets 6) so that the calculation accuracy of
the reluctance torque is not affected in this way.
Next, the reluctances in air gaps and air region
surrounding a stator core, where the leakage flux flows
from each stator pole, can be expressed by the following
equation 6):

Ra =

l

(11)

0 S

where the vacuum permeability is  0.
Moreover, the reluctance Rp and the MMF Fc in arotor magnet are connected in series in each element of amagnet and given by the following equation 6):

Rp (q ) =| lp (q ) |0  r S

Fc (q ) = Hclp (q )In this chapter, the above-derived RNA model is used
for the characteristic calculation of an IPM motor tovalidate the proposed method. The RNA is performed
using Ansys Twin Builder 2021 R1, one of thegeneral-purpose circuit simulators. The validity of thecalculation results is proved by comparing them with theexperimental ones, which are acquired by measuring
input current and power under variously loaded
conditions (the load torque of from 0 mN·m to 200 mN·m

Fig. 10curve.

B-H curve of core material and its approximated(13)(a) where lp(q ) pointsN a cos2(2 j − 1)q
j =1

j

(14)

where arbitrary coefficients are aj and N = 15,
respectively. In this manner, even the generally
complicated flux distribution of an IPM motor can be
expressed by a simple model with a minimum number of
elements compared with a finely divided FEM model.
Further, when an analytical object has an overhang
structure, a 3-D analytical model is generally adopted tosimulate the flux distribution strictly. However, here, toavoid an increase in the calculation time as the RNA

46

4. Simulation Results by Using Conventional and
Proposed RNA Models(12)

where the relative recoil permeability is  r and thecoercive force is Hc, respectively. In addition, theeffective magnet length in the arc-shaped magnetized
direction is lp(q ), which changes corresponding to a rotor
position angle q , as shown in Fig. 11(a) and (b). Here,lp(q ) can be approximately given by the following Fourier
series 6):=
lp (q )

model scales up, this structure is expressed byconnecting each circumferential element in protruding
rotor magnets and the lamination plane on stator poletips facing each other, and the reluctances whichleakage flux flows from all the other elements in thecircumferential direction, as shown in Fig. 12 6).

(b) relationship between the rotor position angle q andthe effective length lp(q )Fig. 11 Effective length lp(q ) of the permanent magnet
corresponding to the rotor position angle q .

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INDEX

Fig. 12Magnetic circuit in an overhang part.

Fig. 13

Experimental setup.

at intervals of 20 mN·m) while driven by a PWM
converter at the constant rotational speed of 12600 rpm,
using the experimental system shown in Fig. 13. In theanalysis, the measured exciting current waveforms,
whose carrier frequency is 20 kHz and current phaseangle is 18 deg., are input. Fig. 14(a) and (b) show
examples of the measured exciting current waveforms.
4.1 Simulation results by using conventional RNA model
In this section, the conventional RNA model
described in the chapter 3 is analyzed before theproposed one, to point out its challeges. For reference,
the RNA model is analyzed is performed by inputting
the ideal sinusoidal ones with the rms values of 0 A to 7
A at intervals of 1 A, in addition to the measured ones
mentioned above. The parameters of magnetic circuit
elements are  1 = 51,  m = 2.5, m = 15, and  1 = 0.0438,
respectively. Moreover, the FEM model of an IPM motor
is also analyzed under sinusoidal excitation as well,using JMAG-Designer Ver. 20.0, one of thegeneral-purpose electromagnetic field analysis software.
Fig. 15 shows the comparison of the measured andcalculated winding rms current density versus torquecharacteristics. In the analysis, the torque is calculated
by using the following equation, with a very thin torquecalculation layer of 10 m provided on the rotor surface
as shown in Fig. 16 6), 19):m =2nq nq



fq 
j =1

s j srj(a) load torque is 20 mN·m(b) load torque is 200 mN·m
Fig. 14 Measured exciting current waveforms input inthe analysis.

(15)

where the number of divided elements in thecircumferential direction is nq , the MMF of each elementon the rotor surface generated in the circumferential
direction is fsq j, and the flux of each element on the rotor
surface flowing in the radial direction is fsrj, respectively.
In addition, the calculated values are corrected bysubtracting the loss torque value due to the measured
mechanical loss, which cannot be considered in theanalysis. Here, the values of the measured mechanicalloss and its loss torque are 5.8 W and 4.4 mN·m,
respectively, at 12600 rpm. From the figure, it is clearthat the calculated values of the RNA when excited by
the measured current waveforms are in good agreementwith the measured ones, while the calculated values for
the RNA and the FEM under sinusoidal excitation havea little errors with respect to the measured ones due toFig. 15 Comparison of the measured and calculated
windingrms
current
densityversustorquecharacteristics (conventional RNA model).

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47

INDEXFi g . 1 6

Enlarged view of the rotor surface of the RNA model.

the low-order harmonic components included in themeasured current waveforms as shown in Fig. 14.
Fig. 17 shows the comparison of the measured andcalculated iron loss characteristics. In the FEM, the ironloss is obtained using the Steinmetz’s empirical equation
for post-processing 18). In the experiment and analysis,
the iron loss is acquired by subtracting the machine
output, copper loss, and mechanical loss (only for themeasurement) from the electrical input. Since almost no
eddy current is generated in the bonded magnet, themagnet eddy current loss is regarded as zero. From thefigure, it is understood that the calculated values for the
RNA and the FEM under sinusoidal excitation are
underestimated compared with the measured ones since
the carrier harmonics are not taken into consideration.
On the contrary, the calculated values of the RNA when
excited by the measured current waveforms areoverestimated compared with the measured ones since
the dependence of the minor loop loss on the dc flux
component and the skin effect are not considered.
Fig. 18 shows the comparison of the measured andcalculated efficiency characteristics. The calculation
values are obtained, including the measured mechanicalloss. As shown in the figure, due to the errors in thetorque and iron loss characteristics mentioned above,the calculated values for the RNA and the FEM undersinusoidal excitation are a little overrated while thecalculated values of the RNA when excited by themeasured current waveforms are underrated, comparedwith the measured ones.

Fig. 17 Comparison of the measured and calculated
iron loss characteristics (conventional RNA model).

48

Fig. 18 Comparison of the measured and calculated
efficiency characteristics (conventional RNA model).
4.2 Simulation results by using proposed RNA model
In this section, the validity of the proposed RNAmodel is experimentally verified. The analysis isperformed by exciting the measured current waveforms
shown in Fig. 14. Moreover, a ladder-shaped part istruncated in the analysis at the first, second, or third
stages, that is, Lm0, Lm1, or Lm2, respectively. The
parameters of magnetic circuit elements are σ = 2.2×106,
d = 3.5×10-4, and γ2 = 0.467, respectively. Besides, theparameter μ is approximately given by the
instantaneous value of the differential permeability on
the centerline of a dc hysteresis loop 16).
Fig. 19(a) – (c) show the comparison of the measured
and calculated winding rms current density versus
torque characteristics. In the analysis, the torque iscalculated by using Eq. (15). From the figures, it is clearthat the measured and calculated results are in good
agreement regardless of the number of ladder stages.
Fig. 20(a) – (c) show the comparison of the measured
and calculated iron loss characteristics. As shown in the
figures, the calculated values are closer to the measured
ones as the number of ladder stages increases. It is clearthat both results are almost in good agreement when aladder circuit has three stages. However, there is still a
possibility that the proposed model will improve thecalculation accuracy because slight errors can be seen at
low load conditions when carrier harmonics are larger.
Possible causes of these errors seem to be methods forgiving the parameter μ 16) and expressing the anomalous
eddy current loss, and neglect of the rotational magnetic

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

INDEX

field 20) and the edge effect 21).
Fig. 21(a) – (c) show the comparison of the measured
and calculated efficiency characteristics. These figures
reveal that the measured and calculated values are ingood agreement when a ladder circuit has 2 stages or
more.
Furthermore, Fig. 22 shows an example of thecalculated hysteresis loop in a stator core obtained fromthe proposed RNA model. This figure indicates that the
proposed method can draw such a local complicatedly
distorted hysteresis loop due to PWM excitation, eventhough the dynamic hysteresis behavior inside of a coreis generally difficult to acquire by the experiment andanalysis. Its calculation accuracy should be verified by
the experiment (such as the H-coil method) in the future.
Finally, Table 1 shows the calculation time of the
proposed method per one cycle of electric angle for eachcase. Here, the PC used for the analysis has a 12-core
CPU and 48 GB of memory, respectively, and theanalysis is performed non-parallel. From the table, it
can be seen that the proposed model can perform theiron loss analysis under PWM excitation considering
carrier harmonics in a reasonable time. In addition, in
Ref. 6), it is indicated that the FEM takes about 217
times longer calculation time than the RNA whenanalyzing the same analytical object. Therefore, if this(a) truncated at the 1st stage(b) truncated at the 2nd stage(c) truncated at the 3rd stage
Fig. 19 Comparison of the measured and calculated winding rms current density versus torque characteristics(proposed RNA model).

(a) truncated at the 1st stage(b) truncated at the 2nd stage(c) truncated at the 3rd stage
Fig. 20 Comparison of the measured and calculated iron loss characteristics (proposed RNA model).

(a) truncated at the 1st stage(b) truncated at the 2nd stage(c) truncated at the 3rd stage
Fig. 21 Comparison of the measured and calculated efficiency characteristics (proposed RNA model).

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

49

INDEX

Fig. 22

Calculated hysteresis loop in the element of a stator core of the proposed RNA model.

Table 1 Calcalation time per one cycle of the RNA.
Torque (mN・・ m) 1st stage (h) 2nd stage (h) 3rd stage (h)
20
4.6
8.1
10.2
40
4.5
8.1
10.0
60
4.9
8.2
10.2
80
4.9
8.2
10.1
100
4.7
8.1
10.1
120
4.8
7.9
9.9
140
4.7
8.0
9.8
160
4.8
7.7
9.6
180
4.6
7.7
9.6
200
4.1
7.8
9.7
motor is analyzed by the FEM in consideration of the
dynamic hysteresis characteristics, the estimatedcalculation time per cycle is 891 hours in the shortest
case and 2217 hours in the longest case, which suggeststhat there is a huge practical problem.
5. Conclusion
This paper described that a novel RNA model isderived by incorporating the play model and Cauer
circuittorepresentthedynamic
hysteresis
characteristics. The novelties in this paper are as
follows:(1) Based on the RNA, a device with a complicated flux
distribution, such as an IPM motor, can be analyzed bytaking the dynamic hysteresis characteristics including
the skin effect into consideration, which has not beenachieved in Refs. 8)–10) and 16).
(2) The calculation accuracy of the proposed RNA model
representing the dynamic hysteresis characteristics is
examined by comparing the calculated results with themeasured ones when an IPM motor is driven by a PWM
converter, which has not been achieved in Ref. 22). As aresult of the examination, it became clear that the
proposed RNA model can calculate the iron loss
characteristic with higher accuracy by considering theinfluence of carrier harmonics, as the number of ladder
stages is larger. Also, the proposed model can accurately
calculate the torque and efficiency characteristics
regardless of the number of ladder stages.

50(3) The proposed RNA model can draw a local
complicatedly distorted hysteresis loops inside a core,
which is difficult to measure and calculate in general.
(4) The calculation time and cost of the proposed RNAmodel are practical, which has not been achieved in Ref.
22), while it is estimated that a considerable amount ofcalculation time is required in the FEM.
In the future, we plan to further increase thecalculation accuracy of the current RNA model byidentifying the causes of errors at low load conditions
and experimentally validate the local hysteresis loops
inside of an iron core.
Acknowledgements This work was supported by JSPS
KAKENHI Grant number JP22K14232 and research
grant from Japan power Academy.
References
1) K. Nakamura and O. Ichinokura: IEEJ Trans. FM, 128, 506(2008).
2) K. Nakamura, K. Kimura, and O. Ichinokura: J. Magn. Magn.
Mat., 290-291, 1309 (2005).
3) M. Fukuoka, K. Nakamura, and O. Ichinokura: IEEE Trans.
Magn., 47, 2414 (2011).
4) K. Nakamura, K. Honma, T. Ohinata, K. Arimatsu, T.
Shirasaki, and O. Ichinokura: J. Magn. Soc. Jpn., 38, 174(2014).
5) Y. Kano and N. Matsui: IEEE Trans. Ind. Appl., 44, 543(2008).
6) Y. Hane, Y. Uchiyama, and K. Nakamura: J. Magn. Soc. Jpn.,
45, 125 (2021).
7) S. Bobbio, G. Miano, C. Serpico, and C. Visone: IEEE Trans.
Magn., 33, 4417 (1997).
8) Y. Hane and K. Nakamura: Proc. IEEE Int. Magn. Conf.
(INTERMAG 2018), 1800038 (2018).
9) Y. Hane, K. Nakamura, T. Ohinata, and K. Arimatsu: IEEE
Trans. Magn., 55, 8401306 (2019).
10) Y. Hane, K. Mitsuya, and K. Nakamura: Proc. IEEE Int.
Magn. Conf. (INTERMAG 2021), 2100016 (2021).
11) H. Oshima, Y. Uehara, K. Shimizu, K. Inagaki, A. Furuya, J.
Fujisaki, M. Suzuki, K. Kawano, T. Mifune, T. Matsuo, K.
Watanabe, and H. Igarashi: J. Jpn. Soc. Pwdr. Metall., 61,
S238 (2014).
12) H. Tanaka, K. Nakamura, and O. Ichinokura: J.Phys.: Conf.
Ser., 903, 012047 (2017).
13) Y. Shindo and O. Noro: IEEJ Trans. FM, 134, 173 (2014).

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14) Y. Shindo, A. Kameari, and T. Matsuo: IEEJ Trans. PE, 137,
162 (2017).
15) Y. Shindo, T. Miyazaki, and T. Matsuo: IEEE Trans. Magn.,
52, 6300504 (2016).
16) Y. Hane and K. Nakamura: IEEE Trans. Magn., 58,
7300412 (2022).
17) G.Bertotti: IEEE Trans. Magn., 24, 621 (1988).
18) C. P. Steinmetz: Proc. IEEE, 72, 197 (1984).
19) K. Nakamura and O. Ichinokura: Int. Power Electron.

Motion Contr. Conf. (EPE-PEMC 2008), 441 (2008).
20) E. Dlala, A. Belahcen, and A. Arkkio: Physica B, 403, 428(2008).
21) L. Cheng, S. Sudo, Y. Gao, H. Dozono, and K. Muramatsu:
IEEE Trans. Magn., 49, 1969 (2013).
22) O. Messal, F. Dubas, R. Benlamine, A. Kedous-Lebouc, C.
Chillet, and C. Espanet: Preprints (2017).
Received Sep. 19, 2022; Revised Nov. 2, 2022; Accepted Nov. 22,
2022

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Copyright ©2023 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
http://creativecommons.org/licenses/by/4.0/

J. Magn. Soc. Jpn., 47, 52-56 (2023)<Paper>Magnetic Moment Method with the Idea of
Magnetic Surface Charge Method
H. Yano, and K. Sugahara*

ELF Corporation, 3-5-24 Miyahara, Yodogawa, Osaka 532-0003, Japan*Faculty of Science and Engineering, Kindai Univ., 3-4-1 Kowakae Higashiosaka 577-8502, Japan

Magnetic Moment Method (MMM) is well known for its ”lightweight” and simplicity of implementation; however,meshing must be carefully treated to obtain accurate results. In this paper, the MMM with the idea of the Magnetic
Surface Charge method is proposed that is free from the meshing problem. Accelerator magnets; a C-shaped dipole
and a quadrupole magnet, are analyzed, and it is shown that the proposed method outperforms currently available
finite-element packages with respect to the CPU time and accuracy of the magnetic field.
Keywords: electromagnetic field analysis, accelerator magnets, magnetic moment method, magnetic surface charge
method, meshing
1. Introduction
Most of the accelerator magnets are designed bymeans of electromagnetic simulations employing threedimensional finite element method. OPERA-3D(TOSCA) is one of the major software for modelingaccelerator magnets 1), 2). The name TOSCA comes fromtwo scalar potentials, namely, reduced potentials andtotal potentials. The method has the following
advantages. (i) Because it is based on the
two-scalar-potential formulation, the number of degrees
of freedom is small, and the magnetostatic analysis isfast. (ii) Coils are modeled as Biot-Savart sources and do
not have to be meshed; therefore, the mesh quality ofthe magnetic core can easily be controlled.
Another famous software to model accelerator
magnets is RADIA 3)–5), which is freely distributed as
Mathematica's add-on by ESRF: the European
Synchrotron. The method has the following advantages.
(i) Because it is based on the Magnetic Moment Method(hereafter MMM 6),7)), no air-mesh is required, and no
special technique is required to emulate open
boundaries. (ii) Because only the magnetic core ismeshed, it is fast and ”lightweight,” namely the size ofthe data is small. One problem of the MMM, which isalso stated on Radia’s website 3), is the meshing problem.
Figures 1 show a C-shaped electromagnet subdivided
into (a) parallelepiped mesh and (b) mesh parallel toflux lines. If the iron core is subdivided into
parallelepiped mesh, as shown in Fig. 1 (a), it is known
that an inaccurate magnetic field is obtained. To avoid
it, the iron core must be meshed parallel to flux lines, as
shown in Fig. 1 (b), however, flux-line distributions
must be known before solving the problem.
In this paper, the MMM with the idea of the Magnetic
Surface Charge method (hereafter MMM with MSC) is                     magnetic core

coil

coil

(a) parallelepiped mesh(b) parallel to flux lines
Fig. 1 Two different types of mesh for MMM.
proposed that is free from the above-mentioned meshingproblem. Unknown variables in the MMM with MSC
are surface magnetic charges on each face of theelements, whereas unknown variables in the MMM aremagnetic moment vectors in each element. The negative
magnetic point charges are placed at the center of thegravity of the element to guarantee Gauss’s law in eachelement whose magnitudes are equal to the surface
integral of each surface charge. By doing so, the bent of
the magnetic flux in each element can be reproduced
more naturally than the conventional MMM, even withcoarse mesh. Accelerator magnets, such as a C-shaped
dipole and a quadrupole magnet, are analyzed, and it isshown that the proposed method outperforms currently
available finite-element packages with respect to the
CPU time and accuracy of the magnetic field.
2. Formulation
2-1. Conventional Magnetic Moment Method
A magnetic moment M in the element produces
magnetic field H at observation point r by taking
integrals as (1) where r', is the displacement s' is thesurface, V ', is the volume of the element, and ns' is thenormal vector of each surface5).

Corresponding author: H. Yano(e-mail: yano@elf.co.jp).

52

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

(1)

Schematic of MMM’s concept.

10 mmFigure 2 shows a schematic the concept of the MMM.
Unknown variables in the MMM are magnetic moments
M and thus the number of degrees of freedom is three
per element. If M is assumed to be uniform inside theelement, the first integral term in (1) vanishes;
therefore, the matrix representation of the conventional
MMM is derived from (2). The magnetic field produced
by M is computed with the equivalent surface magnetic
charges M  n s . When the point matching method is
employed, (2) is evaluated at the center of gravity of theelement to construct a matrix equation.
(2)
2-2. Magnetic Moment Method with the Idea of Surface
Magnetic Charge Method
Figures 3 show schematic of the concept of the MMM
with MSC. Hexahedral elements are subdivided into six
pyramids and unknown variables are surface magnetic
charge densities σn on each pyramid’s bottom surface.
Negative magnetic point charges mn whose magnitudes
are equal to the surface integral of the σn are placed atthe vertex of each pyramid so that the total charges ineach element are zeros in total. The number of degrees
of freedom is six per element which is double the MMM.
The magnetic fields H are evaluated at mid-points
between the center of the surface and the center ofgravity. The first integral term in (1) corresponds to thenegative magnetic point charges and the second term tosurface magnetic charges. The permeability is assumed
to be constant, whereas the magnetic flux is not uniform
and can bend in the element.
Figure 4 shows a simple two-dimensional
magnetostatic problem. Two permanent magnets withthe remanence of 0.2 T are attached to two adjacentedges of the iron core whose relative permeability is

2

2

3

6

5

4

m2 m

1

H1

1
Fig. 3

H2

1

Schematic of MMM with MSC’s concept.

Fig.

4

-9.82

3.34
-3.33

-1.79

3.31
-3.36

-0.40

0.40

-8.43

1.79

1.08

-1.70

-3.31
3.36

1.70

-1.08

-3.34
3.33

6.29
-1.08

-5.67
1.70

8.43

5.67
-1.70

-6.29
1.08

9.82

-6.29

5.67

-5.67

6.29

10 mm

10 mm

10 mm

MagnetMagnetFig. 2

10 mm

INDEX

10 mm

(a) MMM(b) MMM with MSC
Simple two-dimensional static problem
indicating the existence of the theoretical limitthat can be achieved by the MMM.

1000. The iron core is subdivided into four squares. The
obtained equivalent surface magnetic charge densities σ[Wb/m2] are shown in Fig. 4. If the permeability is
uniform in the iron core, the equivalent magnetic charge
densities on the inner surfaces of two adjacent elements
must theoretically be zero in total. For example, in the
MMM, at the bottom edge of the upper left square, σ =-6.29 Wb/m2, and at the top edge of the lower left square,
σ = 1.08 Wb/m2, thus, they do not cancel each other. In
the MMM with MSC, at the bottom edge of the upper
left square σ = -3.34 Wb/m2, and at the top edge of thelower left square, σ = 3.33 Wb/m2, they are almost zeroin total. This indicates that there is a theoretical limit
to the accuracy that can be achieved with the MMM
whereas the MMM with MSC is free from it.
3. Numerical results
3-1. T-Shaped magnet
Figures 5 show the T-shaped magnet; a typicalexample of which the MMM becomes inaccurate. A
cuboid magnet is attached to a T-shaped magnetic core.
The relative permeability of the magnetic core is 1000.
and composed of four cubes with an edge length of 1 mm.
The size of the permanent magnet is 1 mm × 1 mm × 2
mm and the and its remanence is 0.2 T The surface
magnetic field distributions obtained by the MMM andthe MMM with MSC are shown in Fig. 5. Upper figures
are when the subdivision number N = 1 and lower
figures are with N = 3. The result obtained by FEM withthe 5 million mesh is used as the reference solution.
Figure 6 shows the convergence of the surface magnetic
field at the observation point P in increasing N. Even
with N = 3, accurate results within sub-percent error
can be obtained by MMM with MSC whereas theconvergence of the MMM is slow and not simply
monotonic.
3-2. C-Shaped magnet
A C-shaped magnet is a typical accelerator magnet,
and an example model of RADIA is provided by ESRF3).
Figures 7 show the three types of mesh of t h e
C-shaped magnet: (a) parallelepiped coarse mesh, (b)parallelepiped fine mesh, and (c) mesh along flux lines.

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

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INDEX

problem discussed in the introduction. The computing
time for analyzing the C-shaped magnet with Intel Corei7-9700K CPU at 3.60 GHz is shown in Table 1.
Although the computing time for the MMM is shorter
than the MMM with MSC when the number of elements
is the same, the results obtained by the MMM with
MSC is more accurate especially when the mesh iscoarse.

10 mm
210 mmmagnetic core

coil

15 mm
182.5 mm(a) parallelepiped coarse meshFig. 5T-shaped magnet example.

(b) parallelepiped fine meshFig. 6

Fig. 7

Various mesh types of the C-shaped magnet.

Fig. 8B-H curve of the iron core.

Fig. 9Magnetic ﬁeld and its errors at the gap center.

Surface magnetic ﬁeld at the point P.

The B-H curve of the magnetic core is shown in Figure
8.
The size of the magnetic core is 182.5 mm × 210 mm.
The iron core gap is 10 mm and the magnetic field at
the gap center is evaluated with various coil currents
from 1000 to 10000 AT. The result obtained by
OPERA-3D is used as the reference solution. 8-layer
IABC 8), 9) was required to obtain a self-consistent open
boundary solution in OPERA-3D. Figures 9 show themagnetic field at the center of the gap and those errors
with three types of mesh. Even with mesh type (a), theerror of the magnetic field obtained by the MMM with
MSC is about 4% at maximum. Both with mesh type (b)and (c), the error of the magnetic field obtained by the
MMM with MSC is within sub percent, which indicatesthat the MMM with MSC is free from the meshing

54(c) mesh along flux lines

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Table 1 CPU time for analysis of C-shaped magnet.

coil

magnetic core

30 mm(a) parallelepiped mesh3-3. Quadrupole magnet
A quadrupole magnet is also a typical accelerator
magnet, and an example model of RADIA is provided by
ESRF3). Figures 10 show the mesh of the quadrupole
magnet. The size of the magnetic core is 176 mm × 176
mm. The B-H curve of the magnetic core is again shownin Fig. 8. Since the magnetic ﬁeld at the center gap iszero in a quadrupole magnet, magnetic ﬁeld at the Bohrradius is evaluated with various coil current densities
from 0.5 to 5.0 mega ampere per square meter. The
error of the magnetic ﬁeld obtained by the MMM with
MSC is within sub percent as shown in Figures 11. The
computing time for analyzing the quadrupole magnet
with Intel Core i7-9700K CPU at 3.60 GHz is shown in
Table 2.
Table 2 CPU time for analysis of quadrupole magnet.

(b) mesh along flux lines

Fig. 10

Two different types of the mesh of thequadrupole magnet.

Fig. 11

Magnetic ﬁeld and its errors at Bohr radius.
4. Conclusion

The Magnetic Moment Method with the idea of theMagnetic Surface Charge method is proposed that is
free from the meshing problem. Unknown variables are
surface magnetic charges on each face of the elements
and the negative magnetic point charges are placed at
the center of the gravity of the element. Accelerator
magnets are analyzed, and it is shown that the proposed
method outperforms currently available ﬁnite-element
packages with respect to the CPU time and accuracy ofthe magnetic ﬁeld. The proposed method isimplemented in the commercial software ELF/MAGIC 10).
Acknowledgments This work was supported in part by
the Japan Society for the Promotion of Science underGrants-in-Aid for Scientiﬁc Research (C) JP 20K04454.
References
1) Opera website: https://www.3ds.com/products-services/sim
ulia/products/opera/ (As of Jan. 24, 2023).
2) J. Simkin and C. W. Trowbridge: IEE Proc., Part B, Electric
power applications., 127, 368 (1980).
3) Radia website: https://www.esrf.eu/Accelerators/Groups/Ins
ertionDevices/Software/Radia/ (As of Jan. 24, 2023).
4) O. Chadebec, J. L. Coulomb, and F. Janet: IEEE Trans.
Magn., 42, 515 (2006).
5) O. Chubar, P. Elleaume, and J. Chavanne: Journal ofsynchrotron radiation., 5, 481 (1998).
6) F. Janet, J. L. Coulomb, C. Chillet, and P. Mas: IEEE Trans.
Magn., 41, 1428 (2005).

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

55

INDEX

7) T. Le Duc, O. Chadebec, J. M. Guichon, G. Meunier, andY. Lembeey: COMPEL - The international journal forcomputation and mathematics in electrical and electronicengineering., 32, 333 (2012).
8) D. Meeker: IEEE Trans. Magn., 49, 5243 (2013).
9) K. Sugahara: IEEE Trans. Magn., 53, 7205604 (2017).

10) ELF/MAGIC website: https://www.elf.co.jp, (As of Jan. 24,2023).

Received Nov. 16, 2022; Revised Dec. 16, 2022; Accepted Jan.
22, 2023

56

Journal of the Magnetics Society of Japan Vol.47, No.2, 2023

INDEX

Editorial Committee Members・Paper Committee Members
T. Kato and S. Yabukami (Chairperson), K. Koike, K. Kobayashi and Pham NamHai (Secretary)
T. Hasegawa
K. Hioki
S, Inui
K. ItoK. KamataH. Kikuchi
S. Kokado
Y. Kota
T. Kouda
A. Kuwahata
S. Muroga
Y. Nakamura
H. Nakayama
T. Narita
K. Nishijima
D. Oyama
T. SatoT. Suetsuna
T. Takura
K. ThamN. Wakiya
T. Yamamoto
K. Yamazaki

Y. Kamihara
K. Masuda
T. Nozaki
T. Tanaka

N. Adachi
T. GotoH. KuraE. Shikoh
M. Toko

M. GotoT. Kojima
M. Sekino
K. Tajima
S. Yoshimura

H. AokiS. Honda
T. MakiK. Suzuki
S. YakataK. Bessho
S. Isogami
M. NaoeI. TagawaS. Yamada

M. DoiM. Iwai
M. OhtakeY. Takamura
A. YaoT. DoiN.Kikuchi
S. Seino
M. Takezawa
M. Yoshida

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編 集 委 員・論 文 委 員
加 藤 剛 志 （理事） 薮 上
伊藤啓太
乾
成里
小田洋平
佐藤
拓
成田正敬
西島健一
脇谷尚樹

信 （理事） 小 池 邦 博 （幹事） 小 林 宏 一 郎 （幹事） Pham NamHai（幹事）
小山大介
鎌田清孝
神原陽一
菊池弘昭
桑波田晃弘
神田哲典
末綱倫浩
田倉哲也
田中哲郎
Kim Kong Tham
仲村泰明
野崎友大
長谷川崇
日置敬子
増田啓介
室賀
翔
山崎慶太

青木英恵
後藤太一
土井正晶
山田晋也

磯上慎二
鈴木和也
都甲
大
吉村
哲

安達信泰
仕幸英治
土井達也
吉田征弘

岩井守生
清野智史
直江正幸

大竹
充
関野正樹
別所和宏

菊池伸明
高村陽太
本多周太

藏
裕彰
田河育也
槙
智仁

小嶋隆幸
竹澤昌晃
八尾
惇

古門聡士
中山英俊
山本崇史

後藤
穣
田島克文
家形
諭

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