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Vol.48 No.2
JournalJournal of the Magnetics Society of Japan
Electronic Journal URL: https://www.jstage.jst.go.jp/browse/msjmag

2024

Hard and Soft Magnetic Materials
Enhancement of Coercivity for Sm(Fe-Co)12-B Thin Films by Introduction of Sm Seed Layer
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Y. Mori, S. Nakatsuka, S. Hatanaka, M. Doi, and T. Shima…17

Microwave Transmission Theory for On-Chip Ultrastrong-Coupled Magnon-Polariton in Dynamical Inductors
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Evaluation of Spin Hall Eﬀect in Ferromagnets by Means of Unidirectional Spin Hall Magnetoresistance in Ta/Co
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M. Aoki, R. Ohshima, T. Shinjo, M. Shiraishi, and Y. Ando…28

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INDEX

Journal of the Magnetics Society of Japan
Vol. 48, No. 2

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

CONTENTS
Hard and Soft Magnetic Materials
Enhancement of Coercivity for Sm(Fe-Co)12-B Thin Films by Introduction of Sm Seed Layer……………………………………… Y. Mori, S. Nakatsuka, S. Hatanaka, M. Doi, and T. Shima

17

Spintronics
Microwave Transmission Theory for On-Chip Ultrastrong-Coupled Magnon-Polariton in
Dynamical Inductors……………………………………………… T. Chiba, T. Komine, and T. Aono

21

Evaluation of Spin Hall Effect in Ferromagnets by Means of Unidirectional Spin Hall
Magnetoresistance in Ta/Co Bilayers……………………………………… M. Aoki, R. Ohshima, T. Shinjo, M. Shiraishi, and Y. Ando28

Measurement Technique, High-frequency Devices, Magnetic Imaging
Domain Wall Displacement Modulation GMR Sensors with Closed-Loop Current-Field Feedback……………………………………………………………………K. Komuro, D. Oshima, and T. Kato

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INDEX

Copyright ©2024 by the Magnetics Society of Japan.
This article is licensed under the Creative Commons Attribution International License (CC BY 4.0)
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J. Magn. Soc. Jpn., 48, 17-20 (2024)<Paper>E n h a n c e m e n t o f c o e r c i v i t y f o r S m ( F e - C o ) 12- B t h i n f i l m s
by introduction of Sm seed layer
Y. Mori†, S. Nakatsuka, S. Hatanaka, M. Doi, and T. Shima

Graduate School of Engineering, Tohoku Gakuin Univ., Shimizukoji , Sendai 984-8588, JapanTo improve the coercivity of Sm(Fe-Co)12-B thin film, a Sm seed layer was introduced between a V buffer layer anda Sm(Fe-Co)12-B layer, and the thickness of the Sm(Fe-Co)12-B layer was varied. From the result of XRD patterns
measured in an out-of-plane configuration, peaks from (002) and (004) of the ThMn12-type crystal structure wereobserved for all samples. The intensity of these peaks was reduced by decreasing the thickness of the Sm(Fe-Co)12-B
layer; however, it was recovered by introducing a Sm seed layer. Although the coercivity was decreased due to the
reduction in the thickness of the Sm(Fe-Co)12-B layer, a large coercivity of 1.87 T was obtained in an Al-diffused thinfilm, which was thinned to 50 nm while introducing a Sm seed layer.
Keywords: coercivity, ThMn12 compound, Sm(Fe-Co)12-B film, grain boundary diffusion, seed layer
1.

Introducti on

RFe12 (R: rare earth element) compounds with atetragonal ThMn12-type crystal structure are candidates
for new high-performance permanent magnetic
materials
because
of
their
high
saturation
magnetization due to a composition with a high Fe
content. SmFe12-based compounds possess superior
intrinsic magnetic properties compared with Nd2Fe14B
sintered magnets at room and elevated temperatures1)-7).
For example, saturation magnetization (µ0Ms = 1.78 T),
a high anisotropy field (µ0HA = 12 T) at room
temperature, and a high Curie temperature (TC = 879
K) have been realized for Sm(Fe0.8Co0.2)12 thin film
deposited on a MgO single crystal substrate with a V
buffer layer2). However, stabilizing elements such as Al,
Si, Ti, V, Co, W, and Zr must be substituted with a partof Fe sites since RFe12 compounds are well known to
exhibit thermo-dynamical instability in bulk form8)-10).
Recently, Sepehri-Amin et al. reported that theachievement of a high coercivity of 1.2 T and formationof a columnar structure in which anisotropic SmFe12
grains are enveloped by an amorphous grain boundary
phase with a width of 2 ~ 3 nm were successfully
realized for Sm(Fe0.8Co0.2)12B0.5 thin film11),12); however,the value of the coercivity was about 10% of theanisotropy field of Sm(Fe0.8Co0.2)12 thin film. Dempsey et
al. reported that a coercivity of 2.8 T, which is 37% of
the anisotropy field of the Nd2Fe14B phase, wasobtained for Nd-Fe-B thick film13). The main differencein microstructure between Nd-Fe-B thick film andSm(Fe0.8Co0.2)12B0.5 thin film is the composition of thegrain boundaries6), and the grain boundary phase ofSm(Fe0.8Co0.2)12B0.5 has a large Fe composition (72 at.%)that is higher than Nd-Fe-B thick film (60 at.%)6); thus,
further
improvement
tothecoercivityofSm(Fe0.8Co0.2)12B0.5 thin film was suggested by reducing
the Fe content in the grain boundary phase6).

Corresponding author: Y. Mori(e-mail: s236532001@g.tohoku-gakuin.ac.jp).

Grain boundary diffusion using non-magnetic
elements is expected to improve magnetic properties,
and many achievements have been made to improvethese properties14)~17). For example, Bolyachkin et al.
reported that the coercivity was increased by
infiltration of a Si cap layer into the grain boundary
phase of Sm(Fe0.8Co0.2)12B0.5 (100 nm) thin film16). Then,microstructural observation by cross-sectional STEMEDS revealed that the penetration depth of the diffused
Si was found in a region approximately 25 nm from the
top surface of the Sm(Fe0.8Co0.2)12B0.5 layer16). In
addition, micromagnetic simulation based on the resultsof microstructural observation and magnetic properties
predicts that a coercivity of 1.9 T will be obtained when
diffused Si reaches 90 nm below the top surface of theSm(Fe0.8Co0.2)12B0.5 layer; furthermore, if the formationof soft magnetic phases such as α-Fe or α-(Fe-Co)
existing in the initial interface between the V buffer
layer and the Sm(Fe0.8Co0.2)12B0.5 layer are suppressed
completely, the coercivity will be enhanced toapproximately 6.0 T16). Thus, to obtain a large coercivity
in Sm(Fe-Co)12B thin films, it is necessary to sufficiently
diffuse non-magnetic elements into the grain boundary
phase while controlling the microstructure at thebottom of the Sm(Fe-Co)12B layer. Recently, we reported
that the formation of an α-Fe phase can be suppressed
while maintaining a high coercivity by introducing a Sm
seed layer between the V buffer layer and the Sm(FeCo)12-B layer19). In this study, to improve the coercivityof Sm(Fe-Co)12-B thin film, a Sm seed layer was
introduced into Sm(Fe-Co)12-B thin films with the
diffusion of a Si or Al cap layer. Furthermore, thethickness of the Sm(Fe-Co)12-B thin films was varied.
Their magnetic properties and crystal structures were
investigated in detail.
2.

Ex p e r i me n t a l p r o c e d u r e

The samples were prepared by using an ultra-highvacuum magnetron sputtering system with a basepressure of less than 4.0 × 10-7 Pa. First, a V buffer
layer of 20 nm and a Sm seed layer of 2 nm were

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

17

INDEX(ii) Sm/ Sm(Fe-Co)12-B(t nm)(ii) Sm/ Sm(Fe-Co)12-B(t nm)

Main-phase(1-12)(ii) Sm/ Sm(Fe-Co)
12-B(t nm)
Sub-phase (α-Fe,
α-FeCo)Main-phase(1-12)(b) 50 nm(b') 50 nm(b) 50 nm(c') 70 nm(d) 100 nm(d') 100 nm

40

50

60

2 theta (deg.)

70

80

20 30

:
:

0.0
40 50 60 70 80-1.0
2 theta (deg.)

40 50 60 70 80
2 theta (deg.)

1.0

Magnetization (T)deposited
onto a MgO (100) single
crystal substrate at a
0.0
0.0
µ0HA = 0.9 Tµ0MsT=s 1.64
T
1.43 T 12of -1.0
400ºC.
Then, a Sm(Fe-Co)
substrate
temperature-1.0µ0Hc = 0.57 T
1.02 Tbyco-sputteringwith
B -2.0layer of t nm wasMdeposited%
59.1 Sm,%r/ Ms = 38.7
-2.0
3
2.0
and
t
was
changedtoFe,2.0Fe(b)350Co
20 targets,
5050
nmand Fe80B
(d)
100
nm
2.15 MJ/m
3.25 MJ/m
30,1.050, 70, and 100 nm. Film
1.0compositions at each film
thicknesswere determined0.0to be Sm5.4Fe74.2Co18.6Bx
0.0(at.%) µ(0tHA=≈ 1230T nm), Sm
Fe73.9Co19.2Bx (t = 50
1.526.9
T-1.0
1.48nm),T-1.0
0.82nm),T
1.15 T
Sm7.4Fe73.7Co18.9Bx (t = 70
andSm
7.2Fe74.2Co18.6Bx (t47.4 %-2.0
72.9 %-2.0= 100 nm) by energy dispersive-6 X-ray-4 -2analysis
0
2 (EDX).
4
6
Magneticﬁeldthe(T) detection limit ofHowever, it is noted that
due tolight elements, the composition of B cannot be
determined by EDX. Subsequently, an Al cap layer of 35
nm and a Si cap layer of 8 nm were deposited at a Ts of
400ºC onto the Sm(Fe-Co)12-B layer, and sufficient postannealing was performed to fully diffuse the cap layermaterials. The annealing temperature was set to 400ºC
for 4 hours (Al-diffused film), and additional post
annealing was not performed on the Si-diffused film.
Finally, a V layer with a thickness of 10 nm wasdeposited as a protective layer to prevent oxidation. The
crystal structures were analyzed by X-ray diffraction(XRD) with Cu-Kα radiation employing an out-of-planeconfiguration. The magnetic properties were evaluatedby using a superconducting quantum interference
device (SQUID) magnetometer. All measurements were
performed at room temperature.
3.

Resul t s and di s c us s i o n

X-ray diffraction patterns for Sm(Fe-Co)12-B (t nm)
and Sm(2 nm)/Sm(Fe-Co)12-B(t nm) thin films withdifferent thicknesses for the magnetic layer (t) are
shown in Fig. 1. Peaks from (002) and (004) for theThMn12-type crystal structure are clearly observed forall samples. Note that the peak position shown by thebroken line represents the literature value of the
SmFe12 compound without B addition2), and it has
18

0.0µ0HA ≈ 12 T

-2.0
2.0 (c) 70 nm
1.0

Fig. 1. XRD patterns for Sm(Fe-Co)12-B thin films withdifferent thicknesses of magnetic layer (t) between 30
and 100 nm. (i) denotes samples without Sm seed layer,
while(ii)t shows
those where
Sm seed layer has3
2.0 (a)2.03= 30 nm2.45 MJ/mthickness1:12
of 2 nm. Ku = -0.12 MJ/m (c) 70 nm
1.0

-2.0
2.0 (b) 50 nm
1.0
-1.0

(c) 70 nm

20 30

(004)

(004)

V (200)MgO (200)(a) t =
30 nm(d) 100 nm(c) 70 nm

30

:
:

-1.0

Magnetization, µ0M (T)(a') t =30 nm

V (200)
(002)

(002)

(a) t =
30 nm

20

1.0

0.0
Sub-phase (α-Fe, α-FeCo)µ0HA = 0.9 T(004)

V (200)MgO (200)

Intensity (log. scale)(002)

Main-phase (1-12)
Sub-phase (α-Fe, α-FeCo)

MgO (200)(i) Sm(Fe-Co)12-B(t nm)

3

KuSm(Fe-Co)= 2.65 MJ/m(ii) Sm/(i) Sm(Fe-Co)12-B(t nm)(a) t = 30 nm
12-B(t nm)
3
2.0 (a) t = 30 nm Ku = -0.12 MJ/m
: 3 (a') t = 30 nm
Ku = 2.65 MJ/m::
µ0HA ≈ 12 T :µ M = 1.54 Tµ0HA ≈ 12µT0H s = 0.76 T
0 cµ0Ms = 1.54 T
Mr/ Ms = µ85.5%
0Hc = 0.76 T
Mr/ M3s = 85.5%(b) 50 nmµ0Ms = 1.64 Tµ0Hc = 0.57 T
Mr/ Ms = 38.7%
3

2.15 MJ/m

1.52 T
0.82 T
47.4%(b') 50 nm(c) 70nm
32.45 MJ/m

1.43 T
1.02 T
59.1%(c') 70 nm

4.74 MJ/m

34.74 MJ/m

1.50 T
0.95 T 1.50 T
88.0 % 0.95 T

3 88.0%4.63 MJ/m

3

4.63 MJ/m

1.49 T 1.49 T
1.00 T 1.00 T
84.2 % 84.2%

-2.0
3
3
3
(d) 100nm
2.0 (d) 100 nm
4.70 MJ/m(a) t = 30 nm3.25(c)MJ/m
70 nm (d') 100 nm 4.70 MJ/m(b) 50 nm(d) 100 nm
1.0
0.0
1.48 T
1.15 T
72.9%

1.48 T 1.48 T
0.97 T 0.97 T
80.2 % 80.2%-2.0-6 -4 -2 0 2 4 -6 6 -4 -6-2 -40 -22 0 4 2 6 4 6
ﬁeld,
Magnetic ﬁeld, µ0H (T) MagneticMagnetic
ﬁeld, µ0H(T) µ0H (T)-1.0

Fig. 2. Magnetization curves for Sm(Fe-Co)12-B thinfilms with different thicknesses of magnetic layer.
Filled and open circles denote curves measured inperpendicular and parallel directions to film plane,
respectively.

already been reported that the peak position is shiftedto the high angle side by co-deposition with B12). The
intensities of the (002) and (004) peaks were reduced bydecreasing the thickness of the magnetic layer for the
sample without a Sm seed layer. However, it was
confirmed that by introducing the Sm seed layer, the(002) and (004) peaks could be clearly observed, and theintensity of the peak around 65º corresponding to an αFe phase was remarkably reduced. These results
indicated that the introduction of the Sm seed layer
improved the crystal orientation and suppressed theformation of the α-Fe phase. It has already beenreported that a Fe-V(Co) phase was formed at theinterface between the Sm(Fe-Co) layer and the V buffer
layer5). Therefore, it is thought that inserting the Sm
seed layer at the interface suppressed the formation of
the α-Fe(-Co) phase.
Magnetization curves for Sm(Fe-Co)12-B (t nm) andSm(2 nm)/Sm(Fe-Co)12-B(t nm) thin films with different
thicknesses for the magnetic layer are shown in Fig. 2.
The filled and open circles denote the curves measured
in perpendicular and parallel directions to the film
plane, respectively. In the samples without the Sm seedlayer, µ0Hc, the uniaxial magnetic anisotropy (Ku) andsquareness (Mr/Ms) were increased by increasing t, andit was confirmed that the direction of the easymagnetization changed from in-plane to perpendicular
as the film thickness increased. A high µ0Ms of 1.48 T,high µ0Hc of 1.15 T, high Mr/Ms of 72.9%, and moderate
Ku of 3.25 MJ/cm3 were obtained for the film with t =100 nm. On the other hand, when the Sm seed layer
was introduced, perpendicular magnetic anisotropy wasconfirmed even at t = 30 nm, and a µ0Hc of

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

INDEX

:
:

0.0
-2.0
2.0
Magnetization, µ0M (T)2.49 MJ/m60

2 theta (deg.)

70

80

20

30

40

50

60

2 theta (deg.)70

80

Fig. 3. XRD patterns for Sm(Fe-Co)12-B/Si thin films
with different thicknesses of magnetic layer (t) between
30 and 100 nm. Thickness of Si cap layer was fixed at 8
nm.

approximately 1 T and high Ku of 4.7 MJ/cm3 wereobtained above t = 50 nm. Therefore, it was confirmedthat the introduction of the Sm seed layer plays animportant role in improving the magnetic properties
and crystallographic orientation of the 1:12 phase.
To improve µ0Hc, diffusion of a Si and Al cap layer
followed by appropriate post-annealing were performed.
XRD patterns for (i) Sm(Fe-Co)12-B(t nm)/Si (8 nm) and(ii) Sm(2 nm)/Sm(Fe-Co)12-B(t nm)/Si(8 nm) thin films
with different t are shown in Fig. 3. The intensity of thepeaks from the 1:12 phase was increased remarkably byintroducing the Sm seed layer. Also, in the case of thefilm with t = 30 nm, the peak position of the α-Fe phase
was slightly shifted to a higher angle, suggesting that
the Si that diffused into the Sm(Fe-Co)12-B layer
reached the bottom.
Magnetization curves for (i) Sm(Fe-Co)12-B(tnm)/Si(8 nm) and (ii) Sm(2nm)/Sm(Fe-Co)12-B(t nm)/Si(8nm) thin films with different t are shown in Fig. 4. It
was confirmed that µ0Hc was increased by increasing t
for the films without a Sm seed layer, and a high µ0Hc of
1.30 T was obtained for the film with t = 100 nm.
However, when the Sm seed layer was introduced, theµ0Hc was increased for the films with t = 30 and 50 nm,
but the µ0Hc of the films with t = 70 and 100 nm wasdecreased. Furthermore, in the film with the Sm seedlayer introduced, µ0Hc changed from increasing todecreasing as the film thickness increased.
XRD patterns for Al-diffused Sm(Fe-Co)12-B thinfilms with and without a Sm seed layer are shown in
Fig. 5. t was changed between 30 and 100 nm, while thethickness of the Al cap layer was fixed at 35 nm.
Remarkable peaks from (002) and (004) from the 1:12
phase began to be observed above t = 50 nm, and theirintensity was increased by increasing t for the film
without the Sm seed layer. In addition, it was confirmedthat the (002) and (004) peak position in the Al-diffused
films were shifted to a lower angle compared with the

-2.0
2.0
1.0

3

3.86 MJ/m(d) 100 nm

1.45 T
1.16 T
69.9%

3

4.08 MJ/m(d') 100 nm

0.0
1.45 T
1.30 T
74.2%

-1.0
-2.0

-6

-4 -2 02
46Magnetic ﬁeld, µ0H (T)-6

1.43 T
1.12 T
77.6%-4 -2 02
46Magnetic ﬁeld, µ0H (T)Fig. 4. Magnetization curves for Sm(Fe-Co)12-B/Si thinfilms with different thicknesses of magnetic layer (t).
(ii) Sm/ Sm(Fe-Co)12-B/ Al(i) Sm(Fe-Co)12-B/ Al

Main-phase (1-12)
Sub-phase (α-Fe, α-FeCo)
Fe3Al (200)Main-phase (1-12)
Sub-phase (α-Fe, α-FeCo)
Fe3Al (200)(a) t =
30 nm(a') t =30 nm(b) 50 nm(b') 50 nm(c) 70 nm(c') 70 nm

30

50

60

(d') 100 nm(d) 100 nm

20

(004)

50

1.35 T
1.30 T
66.6%

V (200)40

34.52 MJ/m(c') 70 nm

MgO (200)30

5.40 MJ/m

(002)

20

(d') 100 nm

3(b') 50 nm

0.0

-1.0

V (200)(d) 100 nm

1.0

3.01 MJ/m

MgO (200)(c') 70 nmµ0Ms = 1.39 Tµ0Hc = 0.89 T
Mr/ Ms = 46.8%

1.40 T
1.20 T
64.7%
3(c) 70 nm

3

Ku = 5.00 MJ/m

1.40 T
1.17 T
55.4%

(002)

(c) 70 nm::

3(b) 50 nm

0.0

-2.0
2.0

Intensity (log. scale)(b') 50 nm(ii) Sm/ Sm(Fe-Co)12-B/ Si(a') t = 30 nmµ0Ms = 1.39 Tµ0Hc = 0.46 T
Mr/ Ms = 20.9%-1.0(b) 50 nm

3

Ku = 0.52 MJ/m

-1.0

1.0

(a') t =30 nm(a) t =30 nm

1.0(i) Sm(Fe-Co)12-B/ Si(a) t = 30 nm(004)

V (200)

(002)

(004)

Main-phase (1-12)
Sub-phase (α-Fe, α-FeCo)(004)

V (200)MgO (200)

Intensity (log. scale)(002)

Main-phase (1-12)
Sub-phase (α-Fe, α-FeCo)

2.0(ii) Sm/ Sm(Fe-Co)12-B/ Si

MgO (200)(i) Sm(Fe-Co)12-B/ Si

40

50

60

2 theta (deg.)

70

80

20

30

40

2 theta (deg.)70

80

Fig. 5. XRD patterns for Sm(Fe-Co)12-B/ Al thin films
with different thicknesses of magnetic layer (t).
Thickness of Al cap layer was fixed at 35 nm.

Si-diffused film (Fig. 3). This is considered to be due tothe interstitial diffusion of Al element into the 1:12
phase, increasing the lattice spacing. Furthermore, as
the film thickness increased, their peak positions
shifted to a higher angle, which is thought to be due tothe fact that the amount of diffusion in the Al elementfrom the cap layer decreased with the increase in film
thickness.
Magnetization curves for Al-diffused Sm(Fe-Co)12-B
thin films with and without a Sm seed layer are shownin Fig. 6. Magnetic properties such as a µ0Ms of 1.17 T,high µ0Hc of 1.78 T, Mr/Ms of 69.0%, and Ku of 3.88
MJ/cm3 were obtained for the Sm(Fe-Co)12-B(100nm)/Al(35 nm) thin film. The coercivity was decreased

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

19

INDEX(i) Sm(Fe-Co)12-B/ Al

1.0

3

2.64 MJ/m

-2.0
2.0
1.0

50

1.0

µ0Ms = 0.76 Tµ0Hc = 1.83 T
Mr/ Ms = 76.4%(b') 50 nm

2.75 MJ/m

3.44 MJ/m(c') 70 nm

1.14 T
1.60 T
62.4%(d) 100 nm

60

2 theta (deg.)

70

3

3

1.17 T
1.78 T
69.0%

-1.0
-6

3

3.73 MJ/m

1.04 T
1.78 T
75.6%

80 3.88 MJ/m

0.0

-2.0

µ0HA ≈ 12 T

0.93 T
1.87 T
75.2%
3(c) 70 nm

0.0

-2.0
2.0

3

Ku = 2.31 MJ/m::

1.08 T
1.06 T
49.7%

-1.0

8040

(ii) Sm/ Sm(Fe-Co)12-B/ Al(a') t = 30 nmµ0HA ≈ 12 T

-1.0

m

7030

0.0

µ0Ms = 0.73 Tµ0Hc = 0.57 T
Mr/ Ms = 35.6%

(004)

-2.0
2.0 (b) 50 nm

Magnetization, µ0M (T)

30 nm

-1.0

MgO (200)

(004)
(002)

Fe, α-FeCo)

V (200)2.0
3Main-phase(1-12)(a) t = 30
nm
Ku = 0.14 MJ/m
Sub-phase(α-Fe,
α-FeCo):1.0
Fe3Al (200)
:
0.0

ane
-12)

-4 -2 02
46Magnetic ﬁeld, µ0H (T)(d') 100 nm-633.63 MJ/m

1.09 T
1.50 T
80.5%-4 -2 02
46Magnetic ﬁeld, µ0H (T)Fig. 6. Magnetization curves for Sm(Fe-Co)-B (t nm)/Al(35 nm) thin films with and without Sm seed layer. t
was changed from 30 to 100 nm.

to 1.50 T by the introduction of the Sm seed layer.
However, the highest µ0Hc of 1.87 T was obtained for the
Sm/Sm(Fe-Co)12-B/Al thin film with t = 50 nm. The
penetration depth of Al diffusion into Sm(Fe-Co)12-B(100 nm)/Al (35 nm) was reported to be about 50 nm20).
Hence, the enhancement in µ0Hc is thought to be due tothe increase in the volume ratio of an Al-diffused grainboundary phase in the Sm(Fe-Co)12-B layer. However,there was a kink where the hysteresis loops were
measured in the perpendicular direction at near zeromagnetic field. This can be attributed to the formationof a ferromagnetic Fe3Al compound present in theregion of the Al cap layer or the Al-diffused grainboundary phase.
4.

Concl usi on

The effects of introducing a Sm seed layer between a
V buffer layer and a Sm(Fe-Co)12-B layer on crystal
structures and magnetic properties for Sm(Fe-Co)-B,
Sm(Fe-Co)12-B/Si, and Sm(Fe-Co)12-B/Al thin films were
investigated in detail. Since µ0Hc was increased to 1.30
T (Si diffusion) and 1.78 T (Al diffusion) at t = 100 nm,
each cap layer material is thought to have infiltrated
into the grain boundary phase in the Sm(Fe-Co)12-B
layer. Magnetic properties such as µ0Hc, Mr/Ms, and Ku
and the intensities of (002) and (004) peaks for the 1:12
phase of the Sm(Fe-Co)12-B thin film were decreased bydecreasing t. However, the µ0Hc of Sm/Sm(Fe-Co)12-B/Si
and Sm/Sm(Fe-Co)12-B/Al thin films held a maximum
value at t = 50 nm, and the highest µ0Hc of 1.87 T was
obtained for Sm(Fe-Co)12-B/Al thin film with a Sm(220nm) seed layer. The enhancement of µ0Hc wasconsidered to be due to the increment of the volume
ratio of the Al-diffused grain boundary phase in theSm(Fe-Co)12-B layer, and it is considered that the resultof diffusion/infiltration in the grain boundary phase canpave the way to realizing applications of Sm(Fe-Co)12based permanent magnets.
Acknowledgements This work was performed at the
Research Institute for Engineering and Technology(High-Tech Research Center) at Tohoku Gakuin
University. This work was partially supported by MEXT
Program: Data Creation and Utilization-Type Material
ResearchandDevelopment
Project(Digital
Transformation Initiative Center for Magnetic
Materials) Grant Number JPMXP1122715503.
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Received Oct. 30, 2023; Accepted Dec. 12, 2023

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Copyright ©2024 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., 48, 21-27 (2024)<Paper>Microwave Transmission Theory for On-Chip Ultrastrong-Coupled
Magnon-Polariton in Dynamical Inductors
Takahiro Chiba1,2, Takashi Komine3, and Tomosuke Aono3

Sendai, Miyagi 980- 8578, Japan
Sendai, Miyagi 980-8579, Japan
3Graduate School of Science and Engineering, Ibaraki Univ., Hitachi, Ibaraki, 316-8511, Japan

1Frontier Research Institute for Interdisciplinary Sciences (FRIS), Tohoku Univ.,

2Department of Applied Physics, Graduate School of Engineering, Tohoku Univ.,

We present a microwave transmission theory for recently proposed ultrastrong-coupled magnon-polariton (MP) in
dynamical inductors which consist of a coil involving a magnetic insulator. Combining with the RLC-circuit andLandau-Lifshitz-Gilbert equations, we formulate the electric impedance of MP as a coupled oscillator under thecorresponding principle. Based on the transmission (ABCD or F) matrix approach, we further calculate S21 being ascattering parameter for the microwave transmission measurement passing through an RLC-circuit with the
dynamical inductor. By tunning the size of the dynamical inductor, we theoretically demonstrate an on-chip
ultrastrong-coupled MP at room temperature, which reaches a coupling ratio about 0.55 and cooperativity about 2×105
with material parameters of Y3Fe5O12. This work paves the way for quasi-two-dimensional circuit/wave-guide basedmagnonics for quantum information technology.
Keywords: hybrid quantum systems, magnons, polaritons, magnetic insulators, ferromagnetic resonance, microwave
techniques, quantum information technology
1. Introduction
A strong microwave-magnet interaction gives rise to a
hybrid quantum system with energy levels distinct fromthose of the microwave (photon) or the magnet (magnon),namely, magnon-polariton (MP) with a level repulsion
characterized by Rabi-like energy splitting.1) In such a“strong coupling” regime, quantum information can beeasily transferred from the microwave to the magnet andvice versa, whose feature is useful in quantum
information technologies, such as magnon-based sensors,2) memories,3,4) transducers,5,6) and masers.7) However,
without a few exceptions utilizing planar resonators,8-11)
most experiments have so far focused on strong couplingfor cavity magnonic systems based on three-dimensional
microwave cavities with several-tens millimetersscales.12–15) For practical applications based on solidstate devices, a realization of on-chip MPs at room
temperature is highly desired.
Recently, quantum magnonic systems with on-chipsuperconducting/ferromagnetic
multilayers
haveachieved ultrastrong coupling (USC) with the coupling
ratio 𝑔𝑔/𝜔𝜔r ≈ 0.6 below several Kelvins,16,17) where 𝑔𝑔
denotes the coupling strength and 𝜔𝜔r is the transition(resonance) angular frequency of the system. The USC(defined for 𝑔𝑔/𝜔𝜔r ≥ 0.1) could enhance the performanceof quantum devices, e.g., enabling fast transfer ofquantum information before decoherence of quantum
states. Furthermore, in the USC regime, the breakdownof the standard quantum-optical approximation (therotating-wave approximation, RWA) allows eigenstates
to combine higher/lower states with different particle
Corresponding author:
Takahiro Chiba (e-mail: takahiro.chiba.e2@tohoku.ac.jp).

numbers, which produces exotic quantum effects.18)
Very recently, an ultrastrong-coupled MP with 𝑔𝑔/𝜔𝜔r ≈0.28 has been demonstrated at room temperature by atheory that utilizes a dynamical inductor consisting of asmall coil involving a magnetic insulator (MI) in an RLCcircuit.19) The microwave-magnet interaction, which isgovern by the magnetic-dipole (Zeeman) interaction, i.e.
the inner product of the microwave magnetic field andmagnetization of the magnet, is enhanced by the coil thataligns the microwave magnetic field and generates
strong overlap among the magnon-photon. In order togenerate a coherent magnon-photon coupling (magneticdipole interaction) inside the coil, the magnetization of
MI is required to be normal to the microwave magnetic
field, so that in the previous work19) an interfacial
magnetic anisotropy induced by a topological insulator
contact20–22) and an external static magnetic field normal
to the microwave field have been utilized. It is worth tonote that an in-plane static magnetic field normal to themicrowave field also could drive the ultrastrong-coupledMP.
Towards the experimental realization of the proposedroom temperature ultrastrong-coupled MP, the above
setup could be generalized to other potential magnonic
systems. An alternative is strain-induced interfacial
magnetic anisotropy in garnet thin films on a controlled
substrate, such as Y3Fe5O12 (YIG)/Gd3Ga5O12 (GGG)21)
and Bi-doped YIG/GGG.24) Also, two-dimensional van der
Waals magnets with a strong perpendicular magnetic
anisotropy25) may be potential candidates. Thus, theultrastrong-coupled MP in the dynamical inductor could
be ubiquitous for a number of magnonic systems. On theother hand, the previous work19) has presented atheoretical model of an ultrastrong-coupled MP in the
dynamical inductor by treating the RLC-circuit as an

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

21

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transmission measurements, which measure a scatteringparameter S21 in a two-port network by using the vector
network analyzer (VNA). Therefore, from the viewpointof the experiment, it is desirable to model the scatteringparameter based on the microwave circuit theory.
In this paper, we develop the theory of recently
proposed ultrastrong-coupled MP in dynamical inductors
by taking into consideration of a practical two-port
microwave network. Combining with the RLC-circuit andLandau-Lifshitz-Gilbert (LLG) equations, we formulate
the electric impedance of MP as a coupled oscillator
under the corresponding principle. We further calculate
S21 for the microwave transmission passing through an
RLC-circuit with the dynamical inductor using thetransmission (ABCD or F) matrix approach. By tuning
the size of the dynamical inductor, we theoreticallydemonstrate an on-chip ultrastrong-coupled MP withrealistic material parameters at room temperature. In
addition, we discuss a way to achieve the deep-strong
coupled MP in the dynamical inductor.
2. Theoretical Model

Fig. 1(a) Schematics of a two-port microwave
network with a RLC-circuit that consists ofa dynamical inductor 𝐿𝐿(𝜔𝜔) and a capacitor
C, in which 𝑟𝑟circuit is the resistance due toleads and electrodes, the parameter 𝑁𝑁1 /𝑁𝑁2
indicates the inductive coupling between theport and the RLC-circuit, and 𝑍𝑍0
represents the impedance of the microwave
feedline. Also, VNA denotes the vector
network analyzer. The dynamical inductor
consists of a magnetic insulator (MI)embedded within a coil. The red arrow is theprecessional magnetization directions 𝐦𝐦(𝑡𝑡)at the resonance driven by a microwave
magnetic field 𝐇𝐇(𝑡𝑡) due to alternating
current 𝐼𝐼(𝑡𝑡).
(b) Schematic structure of the dynamical inductorthat consists of a coil involving a MI thin filmwith thickness 𝑑𝑑M . The coil is assumed to bewound around the thin film of MI.
(c) Corresponding cascade connection of two-port
networks characterized by the transmission(ABCD or F) matrix. (𝑉𝑉𝑖𝑖 , 𝐼𝐼𝑖𝑖 ) , (𝑉𝑉𝑟𝑟 , 𝐼𝐼𝑟𝑟 ) , and(𝑉𝑉𝑡𝑡 , 𝐼𝐼𝑡𝑡 ) are microwave power vectors forincident, reflection, and transmission waves,respectively.
electric admittance. This formulated observable(admittance) is inconvenient for standard microwave

22

2.1 Coupled magnon-photon oscillator
Here, we describe a MP as a coupled magnon-photon
oscillator under the corresponding principle.1,19) The
system is schematically shown in Fig. 1 (a) as a two-port
microwave network with an RLC-circuit, in which theperpendicular magnetization of the inserted MI, which isstabilized by an external static magnetic field, is excitedby the microwave magnetic field H(t) with a resonantmode of the RLC-circuit. The circuit mode is coupled to
the Kittel mode of magnetization dynamics m(t) withzero magnon wavenumber via the magnetic-dipole(Zeeman) interaction that is responsible for the coherent
magnon-photon coupling.
Inside the coil inserted MI, the magnetization
dynamics is described by the LLG equation

𝑑𝑑𝑑𝑑
1 𝛿𝛿𝛿𝛿m𝑑𝑑𝑑𝑑= −𝛾𝛾𝛾𝛾 × −+ 𝜇𝜇0 𝐇𝐇(𝑡𝑡) + 𝛼𝛼𝛼𝛼 ×
𝑑𝑑𝑑𝑑
𝑑𝑑𝑑𝑑
� 𝑀𝑀s 𝛿𝛿𝛿𝛿�

(1)

𝑈𝑈m = −𝜇𝜇0 𝑀𝑀s 𝐦𝐦 ⋅ 𝐇𝐇0 + 𝜇𝜇0 𝑀𝑀s2 𝑚𝑚2𝑧𝑧 /2 + 𝐾𝐾𝑢𝑢 �1 − 𝑚𝑚2𝑧𝑧 �(2)m(t)) is the unit vector along the magnetization
where m(=mdirection of MI with the saturation magnetization Ms, γ
is the gyromagnetic ratio, 𝜇𝜇0 is the permeability of freespace, and α is the intrinsic Gilbert damping constant.
Here, the total magnetic energy is assumed bywhere 𝐇𝐇0 = 𝐻𝐻0 𝐳𝐳̂ is the external static magnetic field forthe perpendicular magnetization configuration and Ku is
uniaxial magnetic anisotropy energy. Note that thesecond term in Eq. (2) describes the demagnetization
field for a thin film of MI. Also, 𝐇𝐇(𝑡𝑡) ≈ 𝑛𝑛𝑛𝑛(𝑡𝑡)𝐱𝐱̂ is the
microwave magnetic field induced by an alternating
current 𝐼𝐼(𝑡𝑡) via Ampère’s law inside the coil with a turnnumber density 𝑛𝑛, which is governed by the RLC-circuit
equation (Kirchhoff’s voltage law)

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

INDEX
𝑑𝑑Φ(𝑡𝑡)
𝑄𝑄(𝑡𝑡)+ 𝑟𝑟circuit 𝐼𝐼(𝑡𝑡) += 𝑉𝑉 (𝑡𝑡)
𝑑𝑑𝑑𝑑
𝐶𝐶

(3)

where Q(t) is the accumulated charge on the capacitor
with an electrostatic capacitance C, rcircuit represents theresistance due to leads and electrodes in the RLC-circuit,and 𝑉𝑉 (𝑡𝑡) = 𝑉𝑉0 𝑒𝑒−𝑖𝑖𝑖𝑖𝑖𝑖 is an applied ac voltage with anangular frequency ω (experimentally due to input signal
from the VNA). Here, for H(t)-linear magnetization
dynamics:
𝐦𝐦(𝑡𝑡) = �𝛿𝛿𝛿𝛿𝑥𝑥 (𝑡𝑡), 𝛿𝛿𝛿𝛿𝑦𝑦 (𝑡𝑡), 1� ∝ 𝐇𝐇(𝑡𝑡)with|𝛿𝛿𝛿𝛿𝑥𝑥 |, �𝛿𝛿𝛿𝛿𝑦𝑦 � ≪ 1 , the magnetic flux in the dynamical
inductor is given by

Φ(𝑡𝑡) = 𝐿𝐿0 𝐼𝐼(𝑡𝑡) + 𝐿𝐿0 𝑀𝑀s (𝐦𝐦 ⋅ 𝐱𝐱̂ )/𝑛𝑛 ≈ 𝐿𝐿(𝜔𝜔)𝐼𝐼(𝑡𝑡)(4)

where 𝐿𝐿0 ≡ 𝐿𝐿(𝜔𝜔 = 0) = 𝜇𝜇0 𝑛𝑛2 𝑙𝑙𝑙𝑙𝑙𝑙 is a static (bare)inductance with the length 𝑙𝑙, width 𝑤𝑤, and thickness d(See Fig. 1 (b) for the coil geometry). Note that the coil isassumed to be wound around a thin film of MI with the
thickness 𝑑𝑑M ≈ 𝑑𝑑 . In Eq. (4), the term 𝐿𝐿0 𝑀𝑀s (𝐦𝐦 ⋅ 𝐱𝐱̂ )/𝑛𝑛
induces a voltage in the RLC-circuit via Faraday’s law.
By combining the RLC-circuit and LLG equations forthe circuit current 𝐼𝐼(𝑡𝑡) = 𝑑𝑑𝑑𝑑/𝑑𝑑𝑑𝑑 = 𝐼𝐼0 𝑒𝑒−𝑖𝑖𝑖𝑖𝑖𝑖 and thelinearized dynamical magnetization 𝑚𝑚⊥ = 𝛿𝛿𝛿𝛿𝑥𝑥 − 𝑖𝑖𝑖𝑖𝑖𝑖𝑦𝑦
with a harmonic time dependence 𝑒𝑒−𝑖𝑖𝑖𝑖𝑖𝑖, respectively, we
get an eigenvalue equation for a coupled magnon-photon
oscillator:Ω̅(𝜔𝜔)

with

𝐼𝐼0𝑖𝑖𝑖𝑖𝑖𝑖0 /𝐿𝐿0=
�𝑀𝑀 𝑚𝑚 � � 0 �s⊥Ω̅(𝜔𝜔) = �𝜔𝜔 − 𝜔𝜔c + 2𝑖𝑖𝑖𝑖𝑖𝑖c
𝑛𝑛𝑛𝑛M
2

2

𝜔𝜔2 /(2𝑛𝑛)𝜔𝜔 − 𝜔𝜔m + 𝑖𝑖𝑖𝑖 �

(5)

(6)

where 𝜔𝜔c = 1/√𝐿𝐿0 𝐶𝐶 and 𝛽𝛽 = 𝑟𝑟circuit √𝐶𝐶/𝐿𝐿0 /2 are theresonance angular frequency and the intrinsic dampingof the (bare) RLC-circuit, respectively. Also, 𝜔𝜔m = 𝜔𝜔H −𝜔𝜔M + 𝜔𝜔K is the Kittel (magnon) mode, where 𝜔𝜔H = 𝛾𝛾𝛾𝛾0 𝐻𝐻0 ,𝜔𝜔M = 𝛾𝛾𝛾𝛾0 𝑀𝑀s , and 𝜔𝜔 = 2𝛾𝛾𝛾𝛾𝑢𝑢 /𝑀𝑀s . Hence, the hybridized
eigenmodes are calculated by solving the determinant of
Eq. (6):det �Ω̅(𝜔𝜔)� = 0.

(7)

The influence of hybridization is usually most noticeable
in a region near the crossing point, 𝜔𝜔m = 𝜔𝜔c , where themagnon and photon subsystems have similar resonanceproperties. Therefore, writing 𝜔𝜔 = 𝜔𝜔c + 𝛿𝛿 with 𝛿𝛿 ≪ 𝜔𝜔 ,we can neglect terms of order 𝛿𝛿 2 or 𝛿𝛿/𝑛𝑛. In addition, byimplementing a classical version of the RWA, 𝜔𝜔2 − 𝜔𝜔2c ≈2𝜔𝜔c (𝜔𝜔 − 𝜔𝜔c ) , we obtain the analytic dispersion for the
hybridized modes𝜔𝜔± = �(𝜔𝜔�c + 𝜔𝜔�m ) ± �(𝜔𝜔�c − 𝜔𝜔
�m )2 + 𝜔𝜔c 𝜔𝜔M � /2,(8)

�m = 𝜔𝜔m − 𝑖𝑖𝑖𝑖𝑖𝑖c . Therefore, we
where 𝜔𝜔�c = 𝜔𝜔c − 𝑖𝑖𝑖𝑖𝑖𝑖c and 𝜔𝜔
can write the effective non-Hermitian Hamiltonian of thecoupled magnon-photon oscillator as� = ℏ𝜔𝜔
𝐻𝐻
�c 𝑎𝑎̂† 𝑎𝑎̂ + ℏ𝜔𝜔�m 𝑚𝑚� † 𝑚𝑚� + ℏ𝑔𝑔̃�𝑎𝑎̂† 𝑚𝑚
� + 𝑚𝑚� † 𝑎𝑎̂�,(9)𝑔𝑔̃ ≡ �𝜔𝜔+ − 𝜔𝜔− �/2 = �−𝜔𝜔2c (𝛽𝛽 − 𝛼𝛼)2 + 𝜔𝜔c 𝜔𝜔M /2.

(10)where ℏ is the reduced Plank constant, 𝑎𝑎̂† (𝑎𝑎̂) and𝑚𝑚�† (𝑚𝑚�) are the creation (annihilation) operators forphotons and magnons, respectively, andNote that 2𝑔𝑔 = Re�𝜔𝜔+ � − Re�𝜔𝜔− � ≈ √𝜔𝜔c 𝜔𝜔M /2 is the Rabilike splitting at the modes crossing point.
2.2 Scattering parameter
Using the coupled oscillator model in the previous
section, we formulate the electric impedance of MP in an
RLC-circuit with the dynamical inductor. We further
calculate 𝑆𝑆21 being a scattering parameter for the
microwave transmission measurement passing throughthe RLC-circuit.
A microwave network can be expressed in terms of
scattering parameters, namely, the so-called Sparameters. The commonly used S-parameter for
ferromagnetic resonance is 𝑆𝑆21 that can be interpreted
as the power ratio of an incident wave (𝑎𝑎1 ) at port 1 andoutgoing one (𝑏𝑏2 ) at port 2. For a two-port network withan input signal only in the port 1, it follows that 𝑆𝑆21 =𝑏𝑏2 /𝑎𝑎1 . Based on the standard microwave circuit theory,26)
we calculate 𝑆𝑆21 in our setup shown in Fig. 1 (a). Then,
it is necessary to know the total impedance of the
microwave circuit responsible for the resonance field
inside the coil, which has contributions due to the current
related with Ampère's law and the current induced via
Faraday's law. The impedance of the RLC-circuit withcurrent and field due to Ampère's law is given by Eq. (6),𝑍𝑍A (𝜔𝜔) = −𝑖𝑖

𝐿𝐿0 22�𝜔𝜔 − 𝜔𝜔c + 2𝑖𝑖𝑖𝑖𝑖𝑖c 𝜔𝜔�.
𝜔𝜔

(11)

𝜔𝜔𝜔𝜔0
𝜔𝜔M
.
2 𝜔𝜔 − 𝜔𝜔m + 𝑖𝑖𝑖𝑖𝑖𝑖(12)

𝐴𝐴 = 𝐹𝐹 ̅ 𝐹𝐹 ̅
̅ −1
𝑀𝑀 𝑅𝑅𝑅𝑅𝑅𝑅 (𝜔𝜔)𝐹𝐹𝑀𝑀
𝐶𝐶�

(13)

𝑁𝑁1 /𝑁𝑁20(14)

According to Eq. (4), an induced voltage due to the
Faraday's low is 𝑉𝑉F = −𝑖𝑖𝑖𝑖𝑖𝑖0 𝑀𝑀s 𝑚𝑚⊥ /(2𝑛𝑛). Then, for 𝑚𝑚⊥ =−𝛾𝛾𝛾𝛾𝛾𝛾0 /(𝜔𝜔 − 𝜔𝜔m + 𝑖𝑖𝑖𝑖𝑖𝑖), its impedance is calculated as

𝑍𝑍F (𝜔𝜔) = 𝑖𝑖

Now, we can calculate 𝑆𝑆21 based on the transmission(ABCD or F) matrix approach. As shown in Fig. 1 (c), by
coupling to the input and output through a cascade of therelevant matrix elements and treating the RLC-circuit asa shunt admittance, the transmission (ABCD or F)
matrix can be calculated aswith𝐹𝐹 ̅ (𝜔𝜔) = �𝐴𝐴𝐶𝐶0,𝑁𝑁2 /𝑁𝑁1 �
10̅
𝐹𝐹𝑅𝑅𝑅𝑅𝑅𝑅(𝜔𝜔) = �1/𝑍𝑍 (𝜔𝜔) 1� ,
𝑡𝑡
̅ =
𝐹𝐹𝑀𝑀
�

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

(15)

23

INDEX
where 𝑍𝑍𝑡𝑡 (𝜔𝜔) = 𝑍𝑍A (𝜔𝜔) + 𝑍𝑍F (𝜔𝜔) is the total impedance of
the RLC-circuit and 𝑁𝑁1 /𝑁𝑁2 indicates the inductive
coupling between the port and the RLC -circuit. Next, we
relate the transmission matrix to the S-parameter. To
this end, as shown in Fig. 1 (c), we assume microwave
power vectors for incident, reflection, and transmission
waves as (𝑉𝑉𝑖𝑖 , 𝐼𝐼𝑖𝑖 ), (𝑉𝑉𝑟𝑟 , 𝐼𝐼𝑟𝑟 ), and (𝑉𝑉𝑡𝑡 , 𝐼𝐼𝑡𝑡 ), respectively, which
satisfy the following conditions:

𝑉𝑉𝑖𝑖 + 𝑉𝑉𝑟𝑟
𝑉𝑉
= 𝐹𝐹 ̅ (𝜔𝜔) 𝑡𝑡
� 𝐼𝐼 − 𝐼𝐼 �� 𝐼𝐼 �
𝑖𝑖

𝑟𝑟

𝑡𝑡

(16)

with 𝑉𝑉𝑖𝑖 /𝐼𝐼𝑖𝑖 = 𝑉𝑉𝑟𝑟 /𝐼𝐼𝑟𝑟 = 𝑉𝑉𝑡𝑡 /𝐼𝐼𝑡𝑡 = 𝑍𝑍0. Here, 𝑍𝑍0 is the impedanceof the microwave feedline. Regarding 𝑆𝑆21 = 𝑉𝑉𝑡𝑡 /𝑉𝑉𝑖𝑖 in our
two-port network and solving Eq. (16), the S-parameterfor the microwave transmission measurement istherefore

𝑆𝑆21 =2𝑍𝑍0

𝐴𝐴𝐴𝐴0 + 𝐵𝐵 + 𝐶𝐶𝐶𝐶02 + 𝐷𝐷𝐷𝐷0𝛽𝛽ex = 𝑁𝑁22 𝑍𝑍0 /�8𝑁𝑁12 𝜔𝜔c 𝐿𝐿0 �=

𝑍𝑍t (𝜔𝜔), (17)𝑍𝑍t (𝜔𝜔) + 4𝛽𝛽ex 𝜔𝜔𝑐𝑐 𝐿𝐿0

where
is the extrinsic damping
parameter of the RLC-circuit.
3. Results and Discussion
Towards the experimental demonstration of the room
temperature ultrastrong-coupled MP, we use realistic
parameters for MI, which are those of yttrium iron garnet(YIG)23,27) with 𝛾𝛾 = 1.76 × 1011 T -1 s-1 , 𝛼𝛼 ≈ 10−4 , and 𝑀𝑀s ≈120 kAm-1 . We also disregard the very low in-planemagnetocrystalline anisotropy field∼ 0.3 mT reported.28)
Note that YIG is typically used in magnonics as a highperformance material.29-31) For dimensions etc. of the coil,
we assume 𝑙𝑙 = 𝑤𝑤 = 1.0 mm and 𝑛𝑛 = 100 mm-1 , which
gives 𝐿𝐿0 ≈ 1.3 nH for 𝑑𝑑M = 100 nm . Also, 𝐶𝐶 = 1.0 pF isused within realistic values.
Figure 2 shows calculated eigen-frequency (Re�𝜔𝜔± �) of
the MP hybridized mode with/without RWA for different
values of 𝑑𝑑M . The results for with/without RWA are
calculated by Eqs. (8) and (7), respectively. Also, thesecalculated results are also highlighted in Tables I and II.
In the case for 𝑑𝑑M = 10 nm, one can see a huge level
repulsion characterized by the Rabi-like splitting 2𝑔𝑔/
(2𝜋𝜋) ≈ 7.9 GHz for w/o RAW and 7.7 GHz for w/ RWA,
whose values are more than a half of the circuit mode𝜔𝜔c /(2𝜋𝜋) ≈ 14.2 GHz. Then, the coupling ratio is 𝑔𝑔/𝜔𝜔c ≈0.28 (0.27) without (with) RWA, which means that the
MP based on the dynamical inductor is in the USC
regime. Accordingly, the MP has the cooperativity
𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑔𝑔 2 /�𝛼𝛼𝛼𝛼𝛼𝛼2c � ≈ 1.7 × 104 for both cases with 𝛽𝛽 =4.5 × 10−2. In the USC regime, the breakdown of the RWA
makes the system possess eigenstates combined byvarious states with different particle numbers, which
modifies the Rabi spiting via the Bloch-Siegert shiftmechanism. However, the RWA in the current systemstill keeps the meaning because of a relatively small
coupling ratio ( 𝑔𝑔/𝜔𝜔c ≲ 0.28 ) even for the USC regime,
which is supported by the Dicke model.18),32) In the casefor 𝑑𝑑M = 100nm, the magnitude of 2𝑔𝑔/(2𝜋𝜋) is around 4.9

24

Table 1 Calculated results for dM = 10 nm.
Indexes

w/o RWA

w/ RWA

2𝑔𝑔/(2𝜋𝜋) [GHz]

7.9

7.7

𝑔𝑔/𝜔𝜔c0.28

0.27

𝜔𝜔c /(2𝜋𝜋) [GHz]𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑔𝑔 2 /�𝛼𝛼𝛼𝛼𝜔𝜔2c �

14.2
1.7 × 104142.
1.7 × 104

Table 2 Calculated results for dM = 100 nm.
Indexes

w/o RWA

w/ RWA

2𝑔𝑔/(2𝜋𝜋) [GHz]

4.9

4.4

𝑔𝑔/𝜔𝜔c0.55

0.49

𝜔𝜔c /(2𝜋𝜋) [GHz]𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 = 𝑔𝑔 2 /�𝛼𝛼𝛼𝛼𝜔𝜔2c �

4.5

2.1 × 105

4.5

1.7 × 105

GHz for w/o RAW and 4.4 GHz for w/ RWA, whose values
are comparable to that of the circuit mode 𝜔𝜔c /(2𝜋𝜋) ≈4.5 GHz. Then, the coupling ratio is 𝑔𝑔/𝜔𝜔c ≈ 0.55 (0.49)
without (with) RWA, which indicates that the dynamical
inductor-based MP approaches to the deep-strong
coupling regime (defined for 𝑔𝑔/𝜔𝜔c ≳ 1 ).18) Also, thecorresponding cooperativity 𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 ≈ 2.1 (1.7) × 105 isenhanced for each case with 𝛽𝛽 = 1.4 × 10−2. In contrast to
the result for 𝑑𝑑M = 10 nm, the RWA appears to break
down, resulting in a larger shift of the Rabi-like spiting.
Figure 3 shows the computed scattering parameter(|𝑆𝑆21 |2 ) of the MP hybridized mode without RWA basedon Eq. (17) for different values of 𝑑𝑑M . The impedance ofthe microwave feedline 𝑍𝑍0 = 50 Ω is assumed to belarger than the circuit one (𝑟𝑟circuit = 1.0 Ω). Also, we set
the inductive coupling 𝑁𝑁1 /𝑁𝑁2 = 0.3. These parameters
lead to 𝛽𝛽 = 4.5(1.4) × 10−2 and 𝛽𝛽ex = 5.0(1.6) × 10−2 forgiven 𝐿𝐿0 with 𝑑𝑑M = 10(100) nm and C = 1.0 pF. As seenin these figures, an input microwave power is absorbedby the MP, i.e., |𝑆𝑆21 |2 rapidly decreases at the eigenfrequency ( Re�𝜔𝜔± � ) displayed on Fig. 2. Since the level
broadening in 𝑆𝑆21 depends on the magnitude of the
intrinsic damping ( 𝛽𝛽 ), |𝑆𝑆21 |2 for 𝑑𝑑M = 100 nm has anarrower linewidth than that for 𝑑𝑑M = 10 nm. Therefore,by tunning the size (𝑑𝑑M ) of the dynamical inductor, theexperiment might realize an ideal ultrastrong-coupled
MP which possesses a larger coupling ratio (𝑔𝑔/𝜔𝜔c ) andhigher cooperativity ( 𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 ) at room temperature. In
actuality, a similar MP near the USC regime is observedin a metamolecule consisting of a coil involving a ferrite(YIG) rod.33) For such a measurement, the capability ofthe magnetic damping constant (α) could be up to anorder of 10-2, whose value is comparable to that of thecircuit mode (β). For circuit parameters used here, input
microwave power is an order of mW which needs to excite

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Fig. 2

Calculated eigen-frequency (Re�𝜔𝜔± �) of the MP
hybridized mode as a function of an external
magnetic field ( 𝜇𝜇0 𝐻𝐻0 ) for (a) 𝑑𝑑M = 10 nm
and (b) 𝑑𝑑M = 100 nm. In these plots, 𝑟𝑟circuit =1.0 Ω is used.

the ferromagnetic resonance of MI and the estimatedinductance is an order of nH, so that for a resonancefrequency even with 14.2 GHz (for MI with 10 nm) the
corresponding impedance is several tens Ω, whose value
is comparable to that of the microwave feedline (50 Ω isassumed). Hence, the reflection of the input microwave
would not suffer from the so-called impedance mismatch
problem.
In addition, we mention a guideline to achieve thedeep-strong coupled MP in the dynamical inductor. To
this end, we show computed coupling ratio (𝑔𝑔/𝜔𝜔c ) as afunction of 𝜔𝜔c /(2𝜋𝜋) in Fig. 4. As we have discussed above,the magnitude of the Rabi-like splitting (∝ 𝑔𝑔) increases
with decreasing the size of the coil (𝑑𝑑M ). In contrast, thecoupling ratio shows the opposite trend, i.e., 𝑔𝑔/𝜔𝜔c is
1/4
roughly proportional to 𝑑𝑑M
via 𝐿𝐿0 in the circuit modeωc . Accordingly, a plausible strategy for deep-strong
coupling is to enhance the coupling ratio by a reduced
resonance frequency, which could be easily conducted by

Fig. 3

Computed |𝑆𝑆21 |2 as functions of an external
magnetic field ( 𝜇𝜇0 𝐻𝐻0 ) and a microwave
frequency (𝜔𝜔/(2𝜋𝜋)) for (a) 𝑑𝑑M = 10 nm and (b)𝑑𝑑M = 100 nm. The details of the calculations
are given in the text.

tuning the coil size. As shownin Fig. 4, the estimated coil
|𝑆𝑆 |2
size is around 𝑑𝑑M = 1 μm to reach the deep-strong
coupling regime in the dynamical inductor. This strategy
is sharp contrast to that of cavity/planar-resonator basedmagnonics which attempt to enhance the coupling ratioby scaling down the mode volume.16,17)
Finally, we briefly mention potential applications of
the proposed ultrastrong coupled MP toward thequantum information technology. The candidate one isquantum handling of the single magnon excitation using
the box cavity demonstrated by Tabuchi et al. in Ref. 5.
For the magnetic flux type qubits, an added coil to theRLC-circuit in Fig. 1 (a) might be used for a magnonqubit coupling. Then, USC of the proposed MP could
allow us to conduct a much faster measurement andcontrol for the single magnon excitation. Note that weneed to replace circuit components (leads etc.) by
superconducting ones. Other candidate is MP based

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25

INDEX

References

Fig. 4 Computed coupling ratio (𝑔𝑔/𝜔𝜔c ) of the MP
hybridized mode as a function of 𝜔𝜔c /(2𝜋𝜋). The dashed
red line is a fitting function for the w/o RWA case by
𝑓𝑓 (𝑥𝑥) = 𝑎𝑎/√𝑏𝑏 + 𝑐𝑐𝑐𝑐 + 𝑑𝑑𝑑𝑑2 with 𝑥𝑥 = 𝜔𝜔c /(2𝜋𝜋). In this plot,
𝑟𝑟circuit = 1.0 Ω is used.

masers,7) coherent microwave emitters, for control of𝑔𝑔/𝜔𝜔quantum information devices. Instead of the box cavity
used in Ref. 7, the proposed dynamical inductor with theultrastrong coupled MP might be useful to stabilize thecoherent microwave emission.
4. Summary
In summary, we have presented a microwave
transmission theory for an ultrastrong-coupled MP in
dynamical inductors which consist of a coil involving amagnetic insulator. Combining with the RLC-circuit and
LLG equations, we formulated the electric impedance ofMP as a coupled oscillator under the corresponding
principle. Based on the transmission (ABCD or F) matrix
approach, we further calculate a scattering parameter forthe microwave transmission measurement (𝑆𝑆21 ) passing
through an RLC-circuit with the dynamical inductor. By
tunning the size (𝑑𝑑 ≈ 𝑑𝑑M ) of the coil, we theoreticallydemonstrated an on-chip ultrastrong-coupled MP atroom temperature, which reaches a coupling ratio 𝑔𝑔/𝜔𝜔c ≈0.55 and cooperativity 𝐶𝐶𝑅𝑅𝑅𝑅𝑅𝑅 ≈ 2 × 105 with material
parameters of YIG. In addition, we showed a strategy toachieve the deep-strong coupled MP in the dynamical
inductor.
Acknowledgments The authors thank Satoshi Tomita,
Toshiyuki Kodama, Jun-ichiro Ohe, Hiroaki Matsueda,
and Ryunosuke Suzuki for valuable discussions. This
work was supported by Grants-in-Aid for Scientificresearch (Grants No. 22K14591, No. 20H02196, and No.
20K03814) from the Japan Society for the Promotion of
Science.

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Received Oct. 13, 2023; Accepted Dec. 13, 2023

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Copyright ©2024 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., 48, 28-33 (2024)<Paper>

Evaluation of Spin Hall Effect in Ferromagnets by Means of
Unidirectional Spin Hall Magnetoresistance in Ta/Co Bilayers
M. Aokia),b) †, R. Ohshima a),b), T. Shinjo a), M. Shiraishi a),b), and Y. Ando a),b),c)a) Department of Electric Science and Engineering, Kyoto Univ., Kyoto Univ. Katsura, Nishikyo-ku, Kyoto, Kyoto 615-8510, Japanb) Center for Spintronics Research Network, Institute of Chemical Research, Kyoto Univ., Gokasho, Uji, Kyoto 611-0011, Japanc) PRESTO, Japan Science and Technology Agency, 4-1-8 Honcho, Kawaguchi, Saitama 332-0012, Japan

We investigate unidirectional spin Hall magnetoresistance (USMR) in Ta/Co bilayer systems with various Co
thicknesses. A negative USMR is observed when the thickness of Co is thin due to the negative spin Hall angle of Ta,
as expected from the conventional framework. However, as the Co thickness increases, the amplitude of USMR
becomes strongly suppressed, and the sign of USMR becomes positive, which cannot be explained by theoretical
calculation considering only the spin Hall effect (SHE) in the Ta layer. We successfully explain the anomalous
thickness dependence of USMR by considering USMR induced by SHE in the Co layer. This work verifies thesignificant influence of SHE in ferromagnets on the measurement of USMR and will contribute to a better
understanding of USMR.
Keywords: spintronics, spin Hall effect, unidirectional spin Hall magnetoresistance, spin current
1. Introduction
Magnetoresistance (MR) effects have been intensively
investigated since the 19th century, and a variety of MR
effects have been observed in ferromagnetic materials(FM)1), topological insulators2),3), Weyl semimetals4), andtwo-dimensional materials5). In most cases, the sign andmagnitude of MR do not change under sign reversal of amagnetic field/magnetization, i.e., an even function of amagnetic field/magnetization. Therefore, whereas mostMR effects are applicable to the detection of magnetic
field/magnetization rotation by 90 degrees, they cannot
be used for the detection of such rotation by 180 degrees,i.e., magnetization/magnetic field reversal. Since thedetection of magnetization reversal by MR can be applied
to the reading process of magnetoresistive random accessmemory without the need to fabricate additional
electrodes6), MR, which has an odd function ofmagnetization, is attracting much attention. A
representative example of such odd-function MR effects
is unidirectional spin Hall magnetoresistance (USMR) 7)–
12) in a nonmagnetic material (NM)/FM bilayer system.
Figures 1(a) and 1(c) show schematics of themechanism of USMR when the electric current in the NM
layer, Jc(N), is positive and negative, respectively. Jc(N) is
converted to spin current, Js(N), via the spin Hall effect(SHE)13). Then, injection of spin into FM causes
fluctuation in the population of spins parallel or antiparallel to the magnetization, M, in the FM layer. Since
parallel and anti-parallel spins do not degenerate in FM
and have different electron mobilities with each other,fluctuation of parallel- or anti-parallel-spin populations
results in fluctuation in the resistivity in the FM10).
Injected spin polarization, i.e., parallel or anti-parallel
spins, is reversed when the direction of Jc(N) or
magnetization of the FM is reversed, meaning that theresistance of the NM/FM bilayer changes depending on
the direction of Jc(N) and magnetization.
Aiming at application for the detection of magnetization                     Corresponding author:
M. Aoki (e-mail: aoki.motomi.53r@st.kyoto-u.ac.jp).

28

reversal, researchers have focused on NMs with a large
spin Hall angle (SHA), which is an indicator of themagnitude of SHE, such as heavy metals and topologicalinsulators14), because they enable larger spin-current
injection and larger USMR. However, SHE in the FM
layer has been overlooked. Recent findings on sizable
SHE in FM15)–19) indicate that USMR would also be
induced by SHE in the FM layer [self-induced USMR,(SI-USMR)] as explained as follows.
Figures 1(b) and 1(d) show schematics of the mechanismof SI-USMR when the electric current in the FM layer,
Jc(F), is positive and negative, respectively. Jc(F) isconverted to spin current, Js(F), via the SHE in the FM
layer. Then, extraction of spin from FM causes

Fig. 1 Schematics of the mechanism of (a) USMR when
Jc(N) is positive, (b) SI-USMR when Jc(F) is positive, (c)USMR when Jc(N) is negative, and (d) SI-USMR when
Jc(F) is negative. In these schematics, SHAs of NM and
FM are positive.

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fluctuation in the population of spins parallel or antiparallel to M in the FM layer, resulting in a change inresistivity in the same manner as USMR originatingfrom SHE in the NM layer. Since injection of parallel(anti-parallel) spins into the FM and extraction of antiparallel (parallel) spins from the FM are attributed to thepositive (negative) SHA in the NM and FM with apositive electric current, respectively, relationships
between signs of the SHA and fluctuation of theresistivity are the same in USMR and SI-USMR.
Although SI-USMR is predicted to exist theoretically12),it has not been experimentally unveiled yet if it is present
in NM/FM systems.
In this research, we estimated the influence of SI-USMR
in Ta/Co bilayer systems, where sizable self-induced
spin-orbit torque (SI-SOT) due to SHE in the Co layer
was confirmed in our previous work20). We compared thethickness dependence of experimentally observed USMR
signals with theoretical models that do and do notconsider SHE in the FM layer. As a result, a theoreticalmodel considering SHE in the Co layer well explains
experimental results, indicating the existence of SIUSMR due to SHE in the Co layer. From analysis usinga model equation, we estimate the SHA of Ta and Co tobe −0.2 and 0.05, respectively. Our result shows thesignificant influence of SHE in FM on USMR in NM/FM
systems and will contribute to a better understanding of
USMR in NM/FM bilayer systems.

system (Quantum Design PPMS), where the angle
between Hext and x axis was defined as . All
measurements were carried out at room temperature.
3. Observation of unidirectional spin Hall
magnetoresistance by second harmonic measurements
3.1 Longitudinal measurements2𝜔𝜔Figure 2(b) shows 𝑅𝑅𝑥𝑥𝑥𝑥
as a function of  with 0Hext =4 T for the Ta(5)/Co(5) device. A black line indicatesfitting using10),21),2𝜔𝜔
𝑅𝑅𝑥𝑥𝑥𝑥= (𝑅𝑅USMR + 𝑅𝑅ANE(L) + 𝛼𝛼ONE(L) 𝐻𝐻ext )sin𝜑𝜑+𝑅𝑅FLT(L) sin𝜑𝜑cos2 𝜑𝜑 + 𝑅𝑅PNE(L) cos2(𝜑𝜑 − 𝜑𝜑0 ),(1)

where RUSMR, RANE(L), ONE(L)Hext, RFL SOT, and RPNE(L) are
longitudinal second harmonic resistance generated by
USMR, the anomalous Nernst effect (ANE), the ordinary
Nernst effect (ONE), field-like torque (FLT), which
includes both the field-like SOT and torque due to the

2. Device fabrication and experimental procedure
Figure 2(a) shows schematics of the device structureand electrical circuits used in this study. Hall bars madeof Ta(5)/Co(tF)/SiO2(7) layers were fabricated using
electron-beam (EB) lithography and DC magnetron
sputtering. Then, electrode structures were drawn by EB
lithography, and a SiO2 layer was etched by Ar+ ion
milling to make an Ohmic contact. Samples weretransported to an EB deposition system without breaking
the vacuum, and a Ti(3)/Au(70) electrode was deposited.
Here, numbers in brackets are the thickness innanometers. We measured longitudinal and transverse2𝜔𝜔
2𝜔𝜔
second harmonic voltages, 𝑉𝑉𝑥𝑥𝑥𝑥
and 𝑉𝑉𝑥𝑥𝑥𝑥, using a lock-in
amplifier (Stanford SR 830) and AC-DC current source(Keithley 6221).
Here, we explain the advantage of using lock-in
technique for the experiment of USMR. In principle,
USMR can be detected even by using a DC current and a
DC voltmeter. However, large offset coming from thelongitudinal resistance makes it difficult to estimate
USMR. In contrast, harmonic measurement by applying
an AC current with a frequency of ω enables us to remove
such a large offset because voltage induced by USMR is
proportional to the square of the current and oscillatewith 2ω, whereas voltage from the longitudinal
resistance is linear to the current and oscillate with ω.
Longitudinal (transverse) second harmonic resistance,
2𝜔𝜔
2𝜔𝜔
2𝜔𝜔
2𝜔𝜔
𝑅𝑅𝑥𝑥𝑥𝑥( 𝑅𝑅𝑥𝑥𝑥𝑥), was calculated by 𝑅𝑅𝑥𝑥𝑥𝑥(𝑅𝑅𝑥𝑥𝑥𝑥
)=
2𝜔𝜔
2𝜔𝜔 ⁄
𝑉𝑉𝑥𝑥𝑥𝑥 (𝑉𝑉𝑥𝑥𝑥𝑥 ) √2 𝐼𝐼ac , where Iac is the amplitude of the AC
current, which was fixed at 10 mA for devices with tF = 4
nm and 5 nm, whereas it was fixed at 20 mA for devices
with tF ≧ 7 nm to increase the current density. The
frequency of Iac was fixed at 17 Hz. A magnetic field, Hext,
was applied in-plane in a physical property measurement

Fig. 2 (a) Schematics of device structure andmeasurement circuit used in this study. (b)Longitudinal and (c) transverse second harmonic
resistance as function of  measured for Ta(5)/Co(5)bilayer system with 0Hext = 4 T. (d) Transverse
resistance as function of 0Hext applied out-of-plane.
DC electric current with amplitude of 1 mA wasapplied in this measurement. Black lines indicate
linear fittings, where magnetization was and was not
saturated. Magnetic field at intercept of two fittinglines corresponds to 0Hk. (e) Rcos as function of 0Hext
measured for Ta(5)/Co(5) system. Red dots aremeasured signal, and black curves indicate fitted
result.

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

29

INDEX

Oersted field, and the planar Nernst effect (PNE),
respectively. Offset angle, 0, is considered in the PNE
contribution because direction of in-plane thermal
gradient is not well-defined. Although FLT and PNE are2𝜔𝜔eliminated by measuring 𝑅𝑅𝑥𝑥𝑥𝑥
as a function of , ANE
and ONE cannot be eliminated because they have thesame  dependence as that of USMR.
3.2 Transverse measurements2𝜔𝜔2𝜔𝜔
To extract RUSMR from 𝑅𝑅𝑥𝑥𝑥𝑥, we measured 𝑅𝑅𝑥𝑥𝑥𝑥
as a2𝜔𝜔
function of . Figure 2(c) shows 𝑅𝑅𝑥𝑥𝑥𝑥 as a function of with 0Hext = 4 T for the Ta(5)/Co(5) device. A black line
indicates fitting using21):2𝜔𝜔
𝑅𝑅𝑥𝑥𝑥𝑥= 𝑅𝑅cos𝜑𝜑 cos𝜑𝜑 + 𝑅𝑅FLT(T) (2cos3 𝜑𝜑 − cos𝜑𝜑)+𝑅𝑅PNE(T) sin2(𝜑𝜑 − 𝜑𝜑0 ),(2)

where RFLT(T) and RPNE(T) are transverse second harmonic
resistance generated by FLT and PNE. Rcos is expressedas22):
𝑅𝑅cos𝜑𝜑 =𝛼𝛼DL+ 𝑅𝑅ANE(T) + 𝛼𝛼ONE(T) 𝐻𝐻ext ,𝐻𝐻ext + 𝐻𝐻k(3)

where Hk is the in-plane anisotropy field. DL/(Hext + Hk),
RANE(T), and ONE(T)Hext are transverse second harmonic
resistance generated by damping-like SOT (DL SOT),
ANE, and ONE, respectively. Here, Hk was
independently estimated from the measurement of theanomalous Hall effect as shown in Fig. 2(d). Although DL
SOT, ANE, and ONE have the same  dependence, they
have different dependences on Hext, meaning that RANE(T)and ONE(T) can be estimated from the Hext dependence ofRcos as shown in Fig. 2(e).
3.3 Contribution of anomalous Nernst effect
From the measurements in Section 3.1 and 3.2, RUSMR+ RANE(L) + ONE(L)Hext, RANE(T), and ONE(T)Hext are
estimated. To estimate RUSMR, RANE(L) and ONE(L)Hext
need to be converted from RANE(T) and ONE(T)Hext,

respectively. Figures 3(a) and 3(b) show the relationshipbetween thermoelectric voltages generated alongtransverse and longitudinal directions, respectively. An
electric field due to ANE and ONE, EANE+ONE, is produced
along the cross product of magnetization, M, andtemperature gradient, ∇T. We note that ANE and ONE
has the same symmetry with  in this experimentbecause amplitude of Hext is large enough to alignmagnetization along Hext. Since ∇T generated by Joule
heating and the heat-sink effect of the MgO substrate isindependent of the magnetization direction, themagnitude of EANE+ONE is also independent of themagnetization direction. Therefore, longitudinal andtransverse thermoelectric resistances are simply
correlated by the geometry of the Hall bar7). When we
define distances between the two electrodes used inlongitudinal and transverse measurements as l and w,
respectively, RANE(L) + ONE(L)Hext is simply calculated by:
𝑅𝑅ANE(L) + 𝛼𝛼ONE(L) 𝐻𝐻ext =𝑙𝑙(𝑅𝑅+ 𝛼𝛼ONE(T) 𝐻𝐻ext ).
𝑤𝑤 ANE(T)(4)

Figures 3(c) and 3(d) show the contributions from USMR
2𝜔𝜔and ANE + ONE in 𝑅𝑅𝑥𝑥𝑥𝑥/𝐼𝐼𝑎𝑎𝑎𝑎 for Ta(5)/Co(5) andTa(5)/Co(17.5) devices, respectively. In both cases,
signals were well fitted by Eq. (1), and the contribution
from USMR was successfully separated from that fromthermoelectric effects.
2𝜔𝜔
𝑅𝑅𝑥𝑥𝑥𝑥shows complicated  dependence at tF = 17.5 nm asshown in Fig. 3(d) because contributions from Oersted
field (sin2 sin) and PNE (cos2) becomes salient as tF
increases. However, we emphasize that contribution
from the USMR is properly estimated even at tF = 17.5
nm because the measured plots are well fitted by Eq. (1).

Fig. 3 (a) Schematics of generation of thermoelectric signals when M is along longitudinal direction of Hall bar and2𝜔𝜔(b) transverse direction of Hall bar. In our experiment, l and w were 45 m and 40 m, respectively. (c) 𝑅𝑅𝑥𝑥𝑥𝑥/𝐼𝐼ac asa function of  for Ta(5)/Co(5) and (d) Ta(5)/Co(17.5) devices. Contributions from thermoelectric signals and USMR
are shown as green and blue curves, respectively.

30

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INDEX

4. Theoretical analysis of thickness dependence of
unidirectional spin Hall magnetoresistance
4.1 Thickness dependence of unidirectional spin Hall
magnetoresistance
We estimated the USMR for Ta/Co devices withdifferent tF following the procedure in Section 3. Figure4(a) shows the USMR coefficient normalized by current
amplitude, USMR / Iac = RUSMR / (IacR), as a function of tF,
where R is the four-terminal resistance of the Ta/Co
devices. USMR / Iac showed a negative value when tF wasthin, which is consistent with the scenario that USMR is
induced by SHE in Ta because USMR ~ N, where N is
the SHA of the NM layer (−0.1 ~ −0.2 in Ta)8),11). However,USMR / Iac was strongly suppressed and became almost
zero when tF was thicker than ~ 14 nm, indicating thatthe contribution of SHE in Ta became suppressed as tF
got thicker. Given that the SHA of Co is positive16) andcancels the contribution from the negative SHE in Ta23),
it is likely that SI-USMR originating from Co wasenhanced and caused anomalous suppression of the net
USMR as tF became thicker.
One might think that positive USMR at tF = 17.5 nm is
attributed to imperfection in the conversion ofthermoelectric signals. If the conversion coefficient fromtransverse to longitudinal thermoelectric signal issmaller than l / w because of misalignment in the
fabrication process, sign of USMR could be negative evenat tF = 17.5 nm. However, to make USMR / Iac positive at
tF = 17.5 nm, the conversion coefficient needs to be lessthan 60 % of the actual value of l / w. Given that we use
EB lithography in all the drawing processes of the Hallbar structure and the misalignment of the drawing istypically less than 100 nm, which is much less than 1 %of the value of l and/or w, we conclude that imperfection
in device structure cannot explain sign reversal of the
USMR at tF = 17.5 nm.
4.2
Analysiswithout
considering
self-induced
unidirectional spin Hall magnetoresistanceTo support our assumption that the strong suppressionof USMR when tF is thick is due to SI-USMR originatingfrom Co, we compared experimental results andtheoretical calculations. Figure 4(b) shows the thickness
evolution of USMR / Iac calculated by8),12):𝑡𝑡
𝑒𝑒(𝑝𝑝𝜎𝜎 − 𝑝𝑝N )tanh ( F )𝛼𝛼USMR
𝜆𝜆F
=
𝑡𝑡
𝑡𝑡
𝜎𝜎 𝜆𝜆
𝐼𝐼ac
1 + (1 − 𝑝𝑝𝜎𝜎2 ) ( F N ) tanh ( F ) coth ( N )𝜎𝜎N 𝜆𝜆F𝜆𝜆F
𝜆𝜆N
𝜃𝜃N 𝜆𝜆N
𝑡𝑡N
𝜃𝜃F 𝜆𝜆F
𝑡𝑡F
3𝑅𝑅
(5)
× [(
) tanh ()+() tanh (
)] ×
,
𝜀𝜀F
2𝜆𝜆N
𝜀𝜀F
2𝜆𝜆F
2𝑙𝑙

where e is elementary charge, p is conductivity spin
asymmetry, pN is the asymmetry of the spin population,
N (F) is the spin diffusion length of NM (FM), N (F) isthe SHA of NM (FM), and F is the Fermi energy of FM.
The parameters used in the calculation are shown in
Table 19),10),23),24). In the calculation of Fig. 4(b), F was set
to zero, i.e., SI-USMR was neglected. Although the USMR/ Iac plotted as function of tF assuming N = −0.1 is theclosest to the experimental results, the modulation of
USMR / Iac with respect to tF is too weak. For example, theexperimental results at tF ≦ 5 nm and tF = 17.5 nm
strongly deviate from the calculation result. Therefore,
we concluded that a theoretical model that does notconsider SI-USMR cannot explain the thickness
dependence of USMR in Ta/Co bilayer systems.
4.3 Analysis considering self-induced unidirectional spin
Hall magnetoresistance
Figure 4 (c) shows the thickness evolution of USMR / Iac
using Eq. (5) with F = 0.05, i.e., SI-USMR originatingfrom SHE in Co is considered. The calculation result
considering SI-USMR showed a stronger modulation of
USMR with respect to tF and nicely explains theexperimental results when N was set to −0.2. Indeed, F= 0.05 and N = −0.2 were consistent with previous works.
F of Co was estimated to be +0.1 with the spin valve
method16) and +0.05 with our SOT measurement20),
whereas the N of Ta has been reported to be −0.1~−0.2
in previous works23),25). Note that our Ta film has N = 4.3
× 105 (Ωm)−1, which corresponds to the value of beta Ta
having a large N26),27). All these facts demonstrate theconsistency of our conclusion that SI-USMR exists in
Ta/Co bilayer systems.

Fig. 4 (a) USMR / Iac as function of tF for Ta(5 nm)/Co (tF nm) bilayer system. (b) USMR / Iac as function of tF calculated
by solving spin-diffusion equation with different values of N when F was set at 0 and (c) 0.05. Experimental datais also shown as red dots as reference.
Table 1 Parameters used in calculation of thickness dependence of USMR using Eq. (5).
ParametersppN

F (nm)N (nm)F (m)−1

N (m)−1

F (eV)

0.5

0

18

1.8

1.0 × 106

4.3 × 105

0.5

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31

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4.4 Comparison of self-induced spin-orbit torque andunidirectional spin Hall magnetoresistance
Finally, we compare the SI-USMR observed in thisresearch and the SI-SOT observed in our previous
research20). One might think that it is obvious that SIUSMR is present in a NM/FM bilayer system in the samemanner as SI-SOT. However, there are two notabledifferences between SI-USMR and SI-SOT.
First, the relaxation mechanism of the spin current in
the FM layer is different. In the case of USMR, spin
relaxation is dominated by the longitudinal spin diffusion
length28) because USMR is induced by the projection ofspin to the axis parallel to magnetization 8),9). In the caseof SOT, spin relaxation is dominated by the transverse
spin diffusion length29)–31), which is much shorter thanthe longitudinal spin diffusion length because SOT is
induced by the projection of spin to the axis
perpendicular to magnetization20),32).
Second, not only SHE but also the spin anomalous
Hall effect (SAHE) contributes to SI-USMR. In a FM, in
addition to SHE, where injected spin-polarization isparallel or anti-parallel to Jc(F) × Js(F) irrespective of themagnetization direction, SAHE also generates a spincurrent, where spin polarization is parallel or antiparallel to magnetization18),33). Although the spin current
generated by SAHE does not produce torque onmagnetization, it causes the spin polarization tofluctuate, which is parallel or anti-parallel tomagnetization, resulting in USMR.
In our previous work, we found that SI-SOT
significantly affects the SOT measurements in Ta/Co
bilayer systems, where the sign of the net SOT reverses
at around tF = 10 nm due to SI-SOT originating from SHE
in Co20). On the other hand, a sign of USMR / Iac is stillnegative up to tF = 14 nm, indicating that the thickness
evolution of SI-USMR is more gradual than that of SISOT. This is consistent with the fact that thelongitudinal spin diffusion length (> 10 nm)9),28) that
dominates SI-USMR is longer than the transverse spin
diffusion length that dominates SI-SOT (< 5 nm)19),30).
Regarding the estimated value of F, it is estimated tobe ~ 0.05 in both SI-USMR and SI-SOT measurements20),
meaning that SAHE that contributes only to SI-USMR isless significant than SHE that contributes to both SIUSMR and SI-SOT. Indeed, theoretical work hasrevealed that SHE is large in hcp-Co18). In addition,
previous experiments on anomalous SOT have shownthat torque efficiency is much larger than the value
expected only from anomalous Hall conductivity19), i.e.,
SHE is much larger than the anomalous Hall effect in Co.
Both works suggest that SHE is dominant over SAHE in
Co, consistent with our result.

model calculated by a spin diffusion equation thatconsiders the SHE in Co relatively well-reproduced thethickness evolution of USMR in Ta/Co systems. A
comparison between SI-USMR and the SI-SOT in ourprevious work revealed that the longitudinal spin
diffusion length is much longer than the transverse spin
diffusion length and that SHE is dominant over SAHE in
Co, both of which are consistent with previous works. Our
research will contribute to a better understanding of theself-induced phenomena in NM/FM bilayer systems
induced by charge-to-spin conversion in the FM layer.
Acknowledgements
M. A. appreciates the support
from the JSPS Research Fellowship (Grant No.
22J21776).
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Manchon, and S. Emori: Phys. Rev. B, 103, 024443(2021).
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Appl., 3, 044001 (2015).

Received Oct. 11, 2023; Accepted Dec. 6, 2023

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Copyright ©2024 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., 48, 34-39 (2024)<Paper>

Domain Wall Displacement Modulation GMR Sensors with Closed-loop
Current-field Feedback
K. Komuro*, D. Oshima*, and T. Kato*, **Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan
Furo-cho, Chikusa-ku, Nagoya, 464-8603, Japan*Department of Electronics, Graduate School of Engineering, Nagoya University,** Institute of Materials and Systems for Sustainability, Nagoya University,

A novel type of giant magneto-resistance (GMR) sensor utilizing domain wall displacement (DWD) modulation
and a closed-loop current-field feedback technique was investigated. In this paper, a Ni 80Fe20 free layer was used for
the GMR sensor since the uniaxial anisotropy of Ni80Fe20 is smaller than that of the (Co90Fe10)92B8 used in the previous
study, resulting in a larger wall displacement with a smaller field. When the domain wall was modulated by amodulation field Hmod = 94 µTrms, the sensitivity of the sensor increased to 2.6 mV/µT in open-loop mode compared witha sensitivity of 0.98 mV/µT for the sensor without Hmod. Moreover, a significant improvement in the linearity of theoutput was obtained by operating the DWD GMR sensor in closed-loop mode, and the sensitivity was also increased
up to 4.2 mV/µT. The improvement in linearity is considered to be due to the suppression of the displacement of theaverage position of the domain walls by the current-field feedback. The noise floor of the output of the DWD GMR
sensor under closed-loop operation was estimated to be 300 pT/Hz1/2 at 10 Hz.
Keywords: magnetic sensors, domain wall displacement modulation, current field feedback, GMR
1. Introduction
Magneto-resistance (MR) sensors have been widely usedin many applications, since they are simple two-terminal
resistance devices and are easily micro-fabricated by low
cost lithography techniques. Major applications of the
MR sensors are hard-disk-drive (HDD) heads1)-3), linearrotary position encoders4),5), and recently they arereported to be applied to bio-magnetic sensors6),7) andautomotive current monitors8) by improving their
sensitivity and linearity, respectively. In order toimprove the sensitivity of the MR sensors, tunnel
magneto-resistance(TMR)
sensorswithhighmagnetoresistance (MR) ratio over 100% are typicallyutilized. For example, sub-pT field9) detection using TMR
sensor was reported for the applications to magnetocardiography (MCG)10) and magneto-encephalography(MEG)11) at room temperature. However, the TMR
sensors consist of magnetic tunnel junctions (MTJ) andbasically have a large resistance, resulting in the larger
shot noise than that of a giant magnetoresistance (GMR)
sensors12). The GMR sensors have a small resistance dueto their metallic nature and high signal-to-noise (S/N)
ratio at low frequencies. Moreover, the fabrication
process of GMR sensors is simple compared to TMR
sensors, which is an apparent advantage in terms ofindustrial applications. Recently, several studies on
GMR sensors report to detect magnetic field as small as
pT. For example, an antiphase modulation bridge
detection technique utilizing GMR elements withsymmetric response was reported in Ref. 13. This
technique reduces 1/f noise significantly which mainly
dominates the noise spectrum of GMR elements at                     Corresponding author: T. Kato(e-mail: kato.takeshi.i6@f.mail.nagoya-u.ac.jp).

34

frequency f < 100 kHz. We have also studied theantiphase modulation GMR sensors and reported thatthe non-linearity due to the hysteresis in the free layers
and the temperature drift are significantly improved14)
by introducing a closed-loop current-field feedback
technique15). However, the sensor output was insufficient
to detect pT-level field.
One of the ways to improve the sensor output is to use
magnetic flux concentrators (MFC) to amplify themagnetic field applied to the GMR elements16). For
instance, Kikitsu et al. reported the detectivity of 13
pT/Hz1/2 at 100 Hz in antiphase modulation GMR sensors
by using MFCs17). Moreover, Tatsuoka et al. utilized the
GMR sensors with MFCs as well as the compensatingcoils wounded around the MFCs, and high detectivity
and wide dynamic range were reported18). Another way is
to detect the field along the easy axis of GMR sensors
since the magnetic susceptibility along the easy axis ismuch higher than that along the hard axis. Conventional
MR sensors detect the fields along the hard axis due tothe small hysteresis. We have previously reported
domain wall displacing (DWD) GMR sensors to detect thefields along the easy axis, which results in several-times
increase of the sensor output and enables to detect nTlevel magnetic fields19)-21). Liao et al. and Huang et al.
also reported that DWD modulation effectively reduces
the hysteresis and increases the sensitivity compared tono modulation22), 23). However, because DWD involves the
motion of the domain walls, the sensor output still has
small hysteresis and contains Barkhausen noise.
In this study, we introduced the closed-loop currentfield feedback technique to DWD modulation GMR
sensors to solve these issues. Here, we discuss the basic
operation and performance of the closed-loop DWD
modulation GMR sensor, and report the detectivity of thepresent closed-loop DWD modulation GMR sensor. MFC

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is expected to be applied to the present sensor for further
improvement of the detectivity which will be studied infuture work.
2. Operating principle
2.1 Domain wall modulation
Figures 1 and 2 show the circuit diagram of DWD GMR
sensor and the schematic of a GMR sensor with an Alwire to apply modulation and feedback fields,
respectively. As shown in Fig. 1, a GMR element wasconnected to the bridge circuit and the modulation field
Hmod was applied along the easy axis by flowing thecurrent through the Al wire placed upon the GMR
element (see Fig. 2). Here we assume the stripe domains
in the free layers as shown in the illustration of Fig. 3
due to the energy balance between induced anisotropy ofthe free layer and the shape anisotropy of the GMR wire.
The DWD modulation field Hmod at the frequency fmod of
100 kHz modulates the position of the domain walls as inFig. 3. fmod is much higher than the frequency of detecting
fields Hext. Since the domain walls are oscillated by Hmod,the center positions of the domain wall shift sensitively
to Hext which is smaller than the wall coercivity. This
technique is considered to be effective to reduce the wellknown Barkhausen effect20) and enhance thesensitivities22), 23).
The bridge circuit output is proportional to the ratio of
the parallel and antiparallel domain areas to thereference layer of the GMR element. Both Hmod and Hext
components appear in the instrumentation amplifier (IA)output, since both fields affect the domain area, and Hmod
component was filtered by the low pass filter (LPF).
2.2 Current field feedback
The output Vout in Fig. 1 is used to flow the current in
Al wire shown in Fig. 2 to produce the feedback field Hf
which cancels Hext. Therefore, the relation between Voutand Hext is expressed as following equation:
𝑉𝑉out =

1
𝐻𝐻ext ,1+ 𝐹𝐹
𝐾𝐾H→V ∙ 𝐺𝐺IA ∙ 𝐺𝐺𝑂𝑂𝑂𝑂(1)

where 𝐾𝐾H→V is the conversion constant from field tovoltage, and 𝐺𝐺IA and 𝐺𝐺OA are the gains of IA and thefollowing operational amplifier (OA) (see Fig. 1). 𝐹𝐹
stands for the feedback constant determined by the widthof the Al wire and the resistance connected in series toFig. 3 Illustration of domain wall displacement (DWD)
modulation. Domain walls in free layer oscillate due tomodulation field Hmod at frequency fmod of 100 kHz. Hmodand detected field Hext are applied along easy axis of freelayer.
Fig. 1 Circuit diagram of the proposed GMR sensor using
domain wall displacement (DWD) modulation withclosed-loop current-field feedback.

Fig. 2 Schematic of GMR sensor device with GMR
element and Al wire. Easy axis of GMR element isparallel to wire width direction. Modulation field Hmodand feedback field Hf are produced by current flowing
through Al wire.

Fig. 4 Illustrations of the operation point under (a) openmode and (b) closed-loop mode of DWD GMR element.
Insets show the time averaged domain structure of thefree and the pinned layers, where red and blue are
domains parallel and antiparallel to the reference layer,
respectively.

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the Al wire. If 1/(𝐾𝐾H→V ∙ 𝐺𝐺IA ∙ 𝐺𝐺𝑂𝑂𝑂𝑂 ) ≪ 𝐹𝐹 , Vout can be
determined only by 𝐹𝐹 . In other words, the feedback
current can be adjusted by tuning the loop gain which isthe product of 𝐺𝐺IA and 𝐺𝐺OA .
Figure 4 shows the schematic of the current-field
feedback operation of the DWD GMR sensor. When no
Hext is applied, the time average of the areal ratio of
domains between antiparallel (red) and parallel (blue) tothe pinned layer is assumed to be 1:1. If Hext is applied to
the GMR element without the feedback circuit, which isreferred to s “open mode”, the center positions of thedomain walls shift due to Hext (see Fig. 4 (a)). On theother hand, closed-loop current-field Hf cancels Hext inthe closed-loop mode (see Fig. 4 (b)), which suppresses
the shift of domain walls under Hext.

Table 1 Parameters of measurement circuit.
Parameter
Voltage of bridge circuit: 𝑉𝑉B
Frequency of 𝐻𝐻mod : 𝑓𝑓mod
Gain of IA: 𝐺𝐺IA
Cut off frequency of LPF
Gain of OA: 𝐺𝐺OA

Value
3V
100 kHz456
159.2 Hz
1 (Open-1, Closed-1)
10 (Closed-10)

3. Experimental setup
3.1 GMR stacks
GMR stacks were fabricated by 8-cathodes RF
magnetron sputtering system. The stacks were substrate/ Ta (5) / Ni80Fe20 or (Co90Fe10)92B8 (10) / Cu (4) / Co90Fe10(3) / Mn80Ir20 (8) / Ta (3) and substrate / Ta (5) /(Co90Fe10)92B8 (10) / Cu (2.2) / Co90Fe10 (3) / Mn80Ir20 (8) /Ta (3), where the numbers in parentheses indicate thethickness in nanometer. The latter is the same stack asstudied in Ref. 19-21. The substrate was Si substratewith the 500 nm-thick thermally oxidized layer. During
the deposition, the external field of 27mT was applied toinduce the exchange bias in the reference layer and theuniaxial anisotropy in the free layer.

Fig. 5 MR loops of GMR elements with Ni80Fe20 (blue) and(Co90Fe10)92B8 (red) free layers with field sweep ranges of(a) –4 mT ≤ Hext ≤ 4 mT and (b) –300 µT ≤ Hext ≤ 300 µT.
produces Hext. Hext was used as an input of the DWD
GMR sensor as well as to measure the MR loops of the
GMR elements. Parameters of the circuit are indicated inTable 1. Hereafter, we call three types of the circuitmodes as “Open-1”,” Closed-1” nd “Closed-10”. “Open-1”
indicates that the sensor is operated under open modeand the OA gain is 𝐺𝐺𝑂𝑂𝑂𝑂 = 1 , corresponding to theconventional DWD GMR sensors19)-21). “Closed-1” and“Closed-10” indicate that the sensor is operated underclosed-loop current-field feedback with the OA gains of
𝐺𝐺OA = 1 and 𝐺𝐺OA = 10, respectively.

3.2 Microfabrication
GMR stacks were microfabricated as shown in Fig. 2.
First, the GMR films were structured with the size of 30µm × 300 µm by maskless lithography followed by Ar+ ion
milling. Ar+ ions were produced by the Kaufman-type Ar+ ion
source and were incident on the sample with an angle of 90˚ fromthe surface. The incident ion energy was set at 700 eV. Then,
Al2O3 insulator with the thickness of 300 nm was deposited.
Finally, Al wires with the size of 60 µm × 360 µm and thethickness of 300 nm were fabricated above the GMR
elements using a lift-off technique.
After the microfabrication, the GMR sensors with
Ni80Fe20 free layer were annealed in v cuum t 270˚C for
10 minutes under the field of 230 mT. The field wasapplied along the short axis of the GMR elements. The
nne ling temper ture w s set t 270˚C, since theblocking temperature of the IrMn is 270℃, and Mn atoms
start to diffuse into the adjacent layers above thistemperature24), 25). The GMR sensors with (Co90Fe10)92B8
free layer were not annealed, since the annealing would
crystallize the free layer, which increases the coercivity.

4.1 MR properties
Figure 5 shows the MR loops of GMR elements with
Ni80Fe20 and (Co90Fe10)92B8 free layers with the fieldsweep ranges of (a)|Hext| ≤ 4 mT and (b) |Hext| ≤ 300 µT.
From Fig. 5 (a), MR ratio and coercivity of the GMR with
Ni80Fe20 are smaller than those with (Co90Fe10)92B8. The
smaller MR ratio in GMR with Ni80Fe20 is owing to thethicker spacer layer between the free and reference
layers. On the other hand, for smaller sweep field of|Hext| ≤ 300 µT shown in Fig.5 (b), the GMR with
Ni80Fe20 free layer exhibited large MR change over 0.6 %while the one with (Co90Fe10)92B8 was only 0.05%. This isdue to the large coercivity of (Co90Fe10)92B8, and thus,
Ni80Fe20 free layer is preferable to obtain higher output
within the small field range.

3.3 Measurement setup
The GMR sensor devices were connected in the bridge
circuit as shown in Fig. 1 and placed into themeasurement system with a pair of coils. The pair of coils

4.2 Domain wall modulation
Since a sinusoidal Hmod with the frequency of 100 kHz
modulates the domain walls in the free layer, themodulated signal can be observed in the output of IA.

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4. Results and Discussions

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Figure 6 shows the IA output when Hmod of 94µTrms at thefrequency of 100 kHz was applied, where no Hext wasapplied. it was slightly distorted due to the hysteresis of
the MR curves. The amplitude of the waveform was notvaried drastically when the external field Hext in therange of ±100µT was applied.
4.2 𝑯𝑯𝐦𝐦𝐦𝐦𝐦𝐦 Dependence of sensitivity and non-linearity
Figure 7 shows Hext-Vout properties of the DWD GMR
sensor with Ni80Fe20 free layer under Open-1 mode,
where Hmod was (a) 0, (b) 37.6, and (c) 94.0 µTrms. Bluesolid curves indicate the measured data. The measured
data were fitted with Rayleigh loops expressed as follows,since the output properties reflect the minor loop of
Ni80Fe20 free layer.
2−𝑎𝑎𝐻𝐻ext+ 𝑏𝑏𝐻𝐻ext + 𝑐𝑐
𝑉𝑉out = {2
𝑎𝑎𝐻𝐻ext + 𝑏𝑏𝐻𝐻ext − 𝑐𝑐(2)

The fitted Rayleigh loops are shown as the red dashedlines in the figure. For the fitting, 𝑏𝑏 was first estimatedfrom two loop ends, then 𝑎𝑎 and 𝑐𝑐 were estimated by theleast square fit. In this paper, we define the non-linearity
of sensor output as 𝑎𝑎 normalized by the full scale of thesensor output Vfull, and the sensitivity of the sensor was
defined as the absolute value of 𝑏𝑏.
Figure 8 show (a) sensitivity |𝑏𝑏| and (b) non-linearity
𝑎𝑎/Vfull of DWD GMR sensor with Ni80Fe20 free layer as afunction of Hmod. Both sensitivity and non-linearity

increased with increasing Hmod as discussed in Fig. 7.
Dependence of sensitivity and non-linearity for Closed-1
and Closed-10 modes will be discussed later.
In order to discuss the reason of the increases ofsensitivity and non-linearity with Hmod, domain
structures of the free layer were observed with the Kerr
microscope. For the measurement, we deposited thesamples with a stack of substrate / NiFe (10) / SiN (40)and microfabricated in the same size as GMR elementsof the sensor devices. Before the observation, the sample
was magnetically saturated with a field of 6 Oe. Figure 9shows the Kerr microscope images of Ni80Fe20 rectangle
at fields of (a) 0 Oe and (b) 1 Oe. At 0 Oe, the flux-closure
domains were observed. The area of domains parallel tothe external field was confirmed to increase at 1 Oe as
shown in Fig. 9 (b), and flux-closure domain structure ispartially collapsed by the large displacement of thedomain walls. The domain structure was completely
different from the stripe domains of (Co90Fe10)92B8 thinfilms reported in Ref. 21 (see Fig. 9 (c)).
From the domain observations, we consider the reasonof enhancement in the hysteresis of the output under thelarge modulation field (see Fig. 7) is due to the variation

Fig. 8 (a) Sensitivity and (b) non-linearity of DWD GMR
sensor with Ni80Fe20 free layer as function of Hmod. Bluecircles are for Open-1 mode, orange circles are for Closed1 mode, and green circles are for Closed-10 mode.
Fig. 6 IA output waveform of DWD GMR sensor with
Ni80Fe20 free layer when Hmod of 94µTrms at the frequencyof 100 kHz and no external field Hext were applied.

cFig. 7 Hext-Vout properties of DWD GMR sensor with
Ni80Fe20 free layer under Open-1 mode applying (a)𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚 = 0 µTrms, (b) 𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚 = 37.6 µTrms, (c) 𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚 = 94.0
µTrms. Solid blue curves indicate measured data, and red
dashed curves are fitted data with Rayleigh loops
expressed in Eq. (2).

Fig. 9 Kerr microscope images of Ni80Fe20 element under
external fields of (a) 0 µT and (b) 100 µT. (c) Domain
structure of CoFeB is also shown as reference21).

es are fitted data with Rayleighloops
expressed
in Eq.
Journalof theMagnetics
Society of Japan Vol.48, No.2, 2024
(2).

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Fig. 10 Hext-Vout properties of DWD GMR sensor with
Ni80Fe20 free layer under (a) Closed-1 and (b) Closed-10
modes. Solid blue curves indicate measured data, anddashed red curves are fitted with Rayleigh loops in Eq.
(2).
of the domain structures under the fields. The increase of
the sensitivity with Hmod is considered to be due to the
reduction of wall coercivity under Hmod as discussed in
the previous paper21).
4.3 Effect of feedback operation
Figure 10 shows Hext-Vout profiles of DWD GMR sensor
under (a) Closed-1 and (b) Closed-10 modes. Hmod was
fixed at 94.0 µTrms. The normalized 𝑎𝑎 was 6.73 mT–2 for
Closed-1, and 0.83 mT–2 in Closed-10 mode. From theseresults, the non-linearity was confirmed to be drastically
improved by applying a current-field feedback techniqueas well as the increase of gain 𝐺𝐺OA . Compared to theOpen-1 mode as shown in Fig. 6 (c), 95% decrease of the
non-linearity was confirmed in Closed-10 mode.
4.4 Summary of sensitivity and non-linearity
Figures 8 (a) and (b) summarize the sensitivity and thenon-linearity as a function of Hmod under three operation
modes, Open-1, Closed-1, and Closed-10. As shown in Fig.
8 (a), sensitivity increased with increasing Hmod becauseof the reduction of wall coercivity by Hmod. Moreover, thesensitivity for Closed-10 mode was much larger than thatfor Closed-1 mode. This is due to the increase of
𝐾𝐾H→V ∙ 𝐺𝐺IA ∙ 𝐺𝐺𝑂𝑂𝑂𝑂 in equation (1).
As shown in Fig. 8 (b), non-linearity decreased in orderof Open-1, Closed-1, Closed-10 at any Hmod. Therefore, we
can conclude that closed-loop feedback operation iseffective to improve the linearity of the DWD GMR
sensors.
In order to discuss the improvement of linearity, theeffective field applied to the GMR elements were
estimated in each mode. Effective input field Heff isexpressed as follows:
1
𝐻𝐻
𝐾𝐾H→V ∙ 𝐺𝐺IA ∙ 𝐺𝐺𝑂𝑂𝑂𝑂 ext
1+𝐹𝐹= 𝜂𝜂𝐻𝐻ext

𝐻𝐻eff = 𝐻𝐻𝑒𝑒𝑒𝑒𝑒𝑒 − 𝐹𝐹𝑉𝑉out =(3)

Fig. 11 Relations of derived 𝜂𝜂 and non-linearity(normalized 𝑎𝑎). Red circles are for 𝐻𝐻𝑚𝑚𝑚𝑚𝑚𝑚 = 94.0 µTrms,
blue circles are for Hmod = 37.6 µTrms, and black circles
are for Hmod = 0. Circuit modes are also indicated infigure.
and the relation between 𝜂𝜂 and the normalized 𝑎𝑎 were
evaluated for every Hmod. Note that 𝜂𝜂 means theattenuation constant of the field applied to the GMR
elements. The smaller 𝜂𝜂 means the larger Hf to cancel
Hext. Figure 11 shows 𝜂𝜂 dependence of the normalized 𝑎𝑎
of DWD GMR sensors under different operation modes.
Open-1 mode has 𝜂𝜂 of 1 independent of Hmod, since 𝐹𝐹 =∞ in Eq. (3). According to the results, the normalized 𝑎𝑎
decreased with decreasing 𝜂𝜂 . The reduction of 𝜂𝜂 will
impedes the displacement of the average positions of thedomain walls under DWD modulation, which isconsidered to be effective to reduce non-linearity of thesensor output. In Closed-10 mode, the displacement of
the average position of the domain wall is negligibly
small in the range of the total applied field ±100 µT.,
resulting in the significant improvement of output
linearity.
4.5 Noise spectrum
Noise spectrum of Vout of DWD GMR sensor with
Ni80Fe20 free layer under Closed-10 mode was measured.
Hmod was 94.0 µTrms. The whole sensor circuit was placed
inside the NiFe magnetic shield box (Ohtama) with ashielding factor of 66 dB, and the terminal of Vout wasconnected to the high pass filter with cut-off frequency of
0.1 Hz (NF Dual Programmable Filter 3624). The noise
spectrum was measured by the FFT analyzer(ONOSOKKI FFT Analyzer CF-9200).
Figure 12 shows the FFT spectrum of Vout, where thevertical axis was converted to the input referredmagnetic field. From the spectrum, the noise floor at 10
Hz was estimated to be 300 pT/Hz1/2 as shown in the redline in the figure. Further reduction of the noise floor is
expected by applying MFC which will be studied in future
work.

Here, 𝐾𝐾H→V were calculated from |𝑏𝑏| for Open-1 mode,

38

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conducted at the Next-generation biomaterials Hub,
Nagoya University, supported by Advanced Research
Infrastructure for Materials and Nanotechnology inJapan of MEXT, Japan.
References

Fig. 12 FFT spectrum of output of DWD GMR sensor
under closed-loop operation with OA gain GOA of 10. Hmodof 94 µTrms was applied during measurement, and no
external field Hext was applied.
5. Conclusion
In this paper, the closed-loop current-field feedback
operation was implemented to the DWD GMR sensors.
Ni80Fe20 were used for the free layer since the uniaxial
anisotropy is smaller than that of (Co90Fe10)92B8 used in
the previous study, resulting in larger wall displacementin smaller applied field. By applying Hmod to DWD GMR
sensor under open mode operation, the sensitivity wasincreased roughly twice compared to GMR sensor
without Hmod. Hysteresis (non-linearity) of the output
also increased with increasing Hmod due to thedisplacement of the average positions of the domain walls.
However, the large hysteresis of DWD GMR sensor with
Ni80Fe20 free layer under open mode operation
significantly reduced by applying closed-loop currentfield feedback operation. The feedback operation withlarge loop gain effectively impedes the displacement of
the average positions of the domain walls, resulting in
the reduction of non-linearity of Vout. Finally, the noise
floor of 300 pT/Hz1/2 was obtained for DWD GMR sensor
under the closed-loop mode. Further increase of thesensitivity is expected by applying MFCs, and from theseresults, the proposed sensor was confirmed to be one ofthe potential candidates of high sensitivity GMR sensors.
Acknowledgments We would like to thank Prof. T.
Uchiyama, Nagoya University for helping to measure thenoise spectrum of the sensor output. This work is
supported in part by JSPS KAKENHI Grant Number
20H02182. This work was also supported in part by the
Project of Creation of Life Innovation Materials forInterdisciplinary
andInternational
Researcher
Development of the Ministry of Education, Culture,
Sports, Science and Technology (MEXT), Japan. A part ofthis work was performed under the Research Program of“Dyn mic Alli nce for Open Innov tion Bridging Hum n,Environment nd M teri ls” in Network Joint Rese rch
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Appl. Phys., 43, 455001 (2010).
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Phys., 109, 07E523 (2011).
22) S. -H. Liao et. al.: IEEE Trans. Magn., 57, 4000204 (2021).
23) H. -S. Huang et. al.: IEEE Trans. Magn., 58, 4001004 (2022).
24) L. Wang et. al., IEEE Sens. J., 21, 27393 (2021).
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Chapman: J. Appl. Phys., 89, 6904 (2001).
Received Oct. 26, 2023; Accepted Dec. 28, 2023

Journal of the Magnetics Society of Japan Vol.48, No.2, 2024

39

INDEX

Editorial Committee Members・Paper Committee Members
S. Yabukami and T. Taniyama (Chairperson), N. H. Pham, D. Oyama and M. Ohtake (Secretary)
H. Aoki
M. GotoT. GotoK. Hioki
S. Inui
M. Iwai
Y. Kamihara
H. Kikuchi
T. Kojima
H. KuraK. Masuda
Y. Nakamura
K. Nishijima
T. Nozaki
T. SatoT. Suetsuna
K. Suzuki
Y. Takamura
K. ThamT. Tanaka
N. Wakiya
S. Yakata
A. YaoS. Yamada
M. Yoshida
N. Adachi
S. HakuT. Maki
M. Sekino
T. Takura

K. Bessho
S. Honda
S. Muroga
Y. Shiota
S. Tamaru

M. DoiS. Isogami
M. NaoeS. Sugahara
S. Yoshimura

T. DoiT. Kawaguchi
T. Narita
I. Tagawa

T. Hasegawa
N. Kikuchi
Y. SatoK. Tajima

K. ItoA. Kuwahata
E. Shikoh
M. Toko
R. Hashimoto
K. Kobayashi
S. Seino
M. Takezawa

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編 集 委 員・論 文 委 員
薮上 信（理事） 谷山智康（理事） Pham NamHai（幹事）
青木英恵
伊藤啓太
乾
成里
岩井守生
後藤太一
後藤
穣
佐藤
拓
仕幸英治
Kim Kong Tham
仲村泰明
西島健一
山田晋也
吉田征弘
脇谷尚樹

大竹 充（幹事） 小山大介（幹事）
神原陽一
菊池弘昭
藏
裕彰
末綱倫浩
鈴木和也
高村陽太
野崎友大
日置敬子
増田啓介

桑波田晃弘
田中哲郎
八尾
惇

小嶋隆幸
都甲
大
家形
諭

安達信泰
関野正樹
成田正敬

小林宏一郎
田島克文
別所和宏

菅原
聡
土井正晶
室賀
翔

清野智史
直江正幸
吉村
哲

磯上慎二
田倉哲也
白
怜士

川口昂彦
田河育也
橋本良介

菊池伸明
竹澤昌晃
長谷川 崇

佐藤佑樹
田丸慎吾
本多周太

塩田陽一
土井達也
槙
智仁

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