CMD Workshop 35 : Spintronics course
in Center for Spintronics Research Network (CSRN),
Graduate School of Engineering Science, Osaka University.

September 3, 2019

Spintronic Interface design(スピントロニクス・インターフェース・デザイン)
Yoshio Miura
National Institute for Materials Science (NIMS)
Research Center for Magnetic and Spintronic Materials (CMSM)
Spin Theory GroupTopics
0. Introduction on spintronics

1. First-Principles Study on magneto-crystalline anisotropy ofFe/MgO(001) and Fe/MgAl2O4(001)
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

2. First-Principles Study on magnetic damping of Fe/MgO(001)
Y. Miura, in preparation

3. First-Principles Study on Anisotropic Magneto-Peltier Effect
K. Masuda, K.-i. Uchida, R. Iguchi, Y. Miura

PRB 99, 104406 (2019)

Instroduction
Magnetic tunnel junction (MTJs)

Tunneling magnetoresistance(TMR)

TMR ratio 

RAP  RP
RAP

Magnetoresistive Random Access Memory (MRAM)
・Non volatile memory
・Fast writing speed (10～50ns)
・Low electricity consumption (～30μW)
・Long endurance (10 years)

Everspin
64Mbit MRAM

TMR
deviceTransistor

Magnetic censer
Earth’s magnetic field censer・current censer for car・biomagnetic censer

HDD read-out-headCorresponding to SQUID

Magnetization reversal in MTJs
１．Magnetic field by current
problem：・complicate circuit.
・current∝1/device-size
Effects of demagnetizing field increase the criticalcurrent for writing with decreasing size of device

２．Spin transfer torque （STT）
The spin flip of conductive electron givethe torque to the local spin moment due
to the angular momentum conservation


e 
2



e 
2

Spin injection type

Writing current

J.C. Slonczewski,
JMMM 159 (1996) L1.

Tohoku Univ. Ando lab. HP

Memory cell size (μm)

・simple circuit・current∝device-sizeMagnetization reversal in MTJs
３．Domain wall motion type
Magnetic
domain

Domainwall

Magnetic
domainMagnetic structures
around domain wall

http://www.jst.go.jp/pr/announce/20060301/index.html

M. Hayashi,et.al. PRL92,077205 (2007)

・Fast and stable magnetization reversal was realized in experiments
Parallel magnetization
H. Tanigawa, et al., Appl. Phys. Exp. 4, 013007 (2011).

（3-terminal device）
Current
Anti-Parallel magnetization⇒Faster magnetization
reversal with low energy
consumption

Voltage-driven dynamic switching in MTJ

Write Error Rate (WER)

From website of Sahashi’s ImPACT project in JST

Pulsed bias voltage changes PMA of interface ofFM layer and promote the precession motion of
the magnetization.
By removing the voltage with a proper pulse
duration, such as a half precession period,
magnetization switching can be achieved.
Basically, no current flow

Thermal stability factor

Large Ku and Small damping α can reduce the WER

Magnetization reversal by spin transfer torque (STT)
Damping torque(magnetic friction)
Spin transfer torque

Reduction of critical current density (Jc0) α：Magnetic damping constant(107A/cm2⇒105A/cm2)
MS：Saturation Magnetization
J.C. Slonczewski, JMMM 159 (1996) L1.

Hanti±4πMS: Effective anisotropy field
P：Spin polarization
t：Thickness of FM layer

１. High spin polarization (P)2. Low damping constant(α)
３．Perpendicular magnetic anisotropy(PMA)

Hanti-4πMs

Topics
0. Introduction on spintronics

1. First-Principles Study on magneto-crystalline anisotropy ofFe/MgO(001) and Fe/MgAl2O4(001)
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

2. First-Principles Study on magnetic damping of Fe/MgO(001)
Y. Miura, in preparation

3. First-Principles Study on Anisotropic Magneto-Peltier Effect
K. Masuda, K.-i. Uchida, R. Iguchi, Y. Miura

PRB 99, 104406 (2019)

Thermal stability of magnetization in MTJs
To achieve ultra high density MRAM
Perpendicular MTJ

In-plane MTJ
Side view

Side view

Top view

Top view

Aspect ratio >2

For 10 year’s
write endurance

K uV
 60
Thermal stability factor
k BT
Ku : uniaxial magnetic anisotropy
V : Volume, T : Room Temperature (300K)

Large Ku is required with decreasing volume
towards scaling down of device dimensions

Examples of Perpendicular MTJ
Using L10-type FePt, CoPt, CoFePd alloys and its multilayered structures[1] M. Yoshikawa, et al., IEEE Trans. Magn. vol.44 2573 (2008). (Toshiba)[2] K. Yakushiji, et al., APEX vol. 3 053003 (2010). (AIST)[3] K. Mizunuma et al., APEX vol. 4 023002 (2011). (Tohoku)

Interfacial Perpendicular Magnetic Anisotropy (PMA) for MgO
S. Ikeda, et al., Nature Materials 9, 721(2010).

In-plane magnetization (tCoFeB=2.0nm)

・CoFeB/MgO/CoFeB(001)

Perpendicular magnetization (tCoFeB<1.3nm )TMR ratio of 120% at 300K

Interfacial perpendicular MCA of
Fe/MgO(001), which is Ki=1.30 mJ/m2

Interfacial PMA for MgAl2O4

Q. Xiang, et al., APEX 11, 063008 (2018).

Calculation results
Calculation: VASP-PAW-PBE, 37x37x1 (19x19x1) k-points for Fe/MgO (Fe/MgAl2O4)
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

Ki(mJ/m2)

Edemagt(mJ/m2)

Kefft=Ki-Edemagt(mJ/m2)ΔMorb,i(μB/atom)Ki (mJ/m2)
Experiments

Fe/MgAl2O4(a=aFe)

1.192-0.895

0.296

0.026

-

Fe/MgO(a=aMgO/√2)

1.617-0.828

0.788

0.030

1.30 [1]Fe/MgO(a=aFe)

1.552-0.908

0.643

0.020

0.98 [2]・Bruno’s relation holds for all cases
・PMA of Fe/MgAl2O4 is slightly smaller than that of Fe/MgO,
which is consistent with experimental results.
[1] S. Ikeda, et al., Nature Materials 9, 721 (2010).
[2] Q. Xiang, et al., APEX 11, 063008 (2018).

Second order perturbation of spin-orbit interaction (SOI)
P. Bruno, PRB 39, 865 (1989). G. Laan, JPCM 10, 3239 (1998).

exc H SO gr

E 2     H SO   L  S

2

 exc   gr

exc

E

i    i1 , 2 ,1 , 2



 ,

 
1  L  S  2 grgr (exc)   ci , , i, η:direction of spin (x or z)
(2)

exc





 
 2  L  S 1 μ：local atomic orbital index
i,j：index of atomic position








   j G  12,  12  ,  ; i , j  G  12,  12  ,  ; i , j  G  12,  12  ,  ; i , j  G  12,  12  ,  ; i , j
 ,

 ,

 ,

 ,

j

Joint Local DOS

G  12, 1 2  1 ,  2 ; i , j   ,d  1d  2
i, j
i, j


k ,  2 
n
k
,

n





,
,
1

1
1
1
2 ,  2 , 2
1  E F  2  2   1 k

Magneto-crystalline anisotropy energy(MAE)

E

(2)
MCA

i   E i   E i 
(2)
z

(2)
x

We directly estimated the second-order perturbative contribution of MCA
energy depending on each atomic site and spin-transition process.
ξFe=50meVSecond order perturbation for MAE analysis
Magneto-crystalline anisotropy energy(MAE)E 2   
o, u

  2
o L  S u  E 2 

2 
2 
2 


E


E


E
up  upup down
down  up
down downu  o2 
 E up up  0

For more than half 3d-TM, up-spind states are fully occupied.

2 

 E up  down  02
2 Edownup   


o ,u



o  Lx u u  o2 2 E down down   2

 2 o ,uo  Lz u u  oo  Lz u o , uu  oEF

up-spinE
down-spin

2≂0, in case of large exchange coupling2 2 o , uL z Yl m  mY l mContributed to perpendicular MAE, if there
are d orbitals with same magnetic quantum
number (m) around EF

L x Yl m  Yl m  1
Contributed to in-plane MAE, if there are dorbitals with m and m±1 exist around EF.

o  Lx u u  o2

MAE vs. orbital magnetic moment (Bruno’s relation)
First-order perturbative wavefunction correction by SOI 
exc   I L  S gr
I gr (1)   exc
 exc   gr
exc
Orbital moment 
exc  L  S grL   gr L   gr (1)  c.c.    gr L exc
gr exc   gr

gr, exc


Li 











 c.c.

   L  S     L  S    j Gi, ,j ,    Gi, ,j ,   eo ,u ,o ,ujOrbital moment operator include only spin-conservation term, because it does not include spin operator,E ( 2 )    ii

2nd perturbation energy   ,  Gi, ,j  ,   

Large exchange coupling

 





   j G i, ,j   ,     G i, ,j   ,     G i, ,j   ,     G i, ,j   ,   jGi, ,j  ,     Gi, ,j  ,     0More than half   L S     L S  

Bruno’s relation PRB 39, 865 (1989).
[ 001 ]
[ 100 ]
 E MCA 


m
4

orb

 m orb

MAE of Fe/MgAl2O4(001) by controlling lattice constant

O
Al

Fe2

Mg

・Interfacial Fe mainly contributes to PMA・Spin conservation term ΔE↓⇒↓ mainly contributes to PMA.

LDOS and band contribution to MAE of Fe/MgAl2O4(001)MAE of Fe/MgO(001) with changing lattice distortion

a=aFe

a=aMgO・Not only spin conservation term ΔE↓⇒↓ but also spin-flip term ΔE↑⇒↓ contributes to PMA,
resulting in larger PMA than that of Fe/MgAl2O4.
・PMA of Fe/MgO(001) interfaces increases with increasing in-plane lattice constant.

Difference between Fe/MgAl2O4(001) and Fe/MgO(001) interfaces

Fe/MgAl2O4(aFe)

Fe/MgO (aFe)

Fe/MgAl2O4(aFe)Al
on top of Fe

Mg
not on top of Fe

O
Fe

O

Mg

Fe

Interfacial hybridization between Fe d3z^2 and O pz is different

Fe/MgO (aFe)Modification of PMA of W/Fe(001) by controlling lattice constantExperiments
MgO sub./Cr (30nm)/W(tW)/[Fe(2)/W(tW)]4/Cr(3 nm)

Collaboration with Prof. Okamoto in Tohoku
Appl. Phys. Express 10, 063005 (2017)

Calculation

W contribution to PMA

Fe contribution to PMA

W insertion between Fe/MAO and Fe/MgO interfaces
a=aFe
a=aFe
a=aMgO

MAE contribution for each atom of Fe/W(3ML)/MgO(001) in a=aFe

MgO
side

-0.013μB -0.066μB -0.151μB

・Each W atom at
W/Fe interface
contribute to PMA.
・spin-flip term

SummaryKi(mJ/m2)

Edemagt(mJ/m2)

Kefft=Ki-Edemagt(mJ/m2)ΔMorb,i(μB/atom)Ki (mJ/m2)
Experiments

Fe/MgAl2O4(a=aFe)

1.192-0.895

0.296

0.026

-

Fe/MgO(a=aMgO/√2)

1.617-0.828

0.788

0.030

1.30 [1]Fe/MgO(a=aFe)

1.552-0.908

0.643

0.020

0.98 [2]・Fe/MgAl2O4(001) show PMA, which is slightly smaller than that of
Fe/MgO(001).
・ For Fe/MgO(001), not only spin conservation term ΔE↓⇒↓ but also
spin-flip term ΔE↑⇒↓ contributes to PMA, resulting in larger PMA thanthat of Fe/MgAl2O4.
・3ML W insertion between Fe and MgAl2O4 interfaces,
Fe/W(3ML)/MgAl2O4(001), is promising to obtain large PMA more than2mJ/m2

Topics
0. Introduction on spintronics

1. First-Principles Study on magneto-crystalline anisotropy ofFe/MgO(001) and Fe/MgAl2O4(001)
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

2. First-Principles Study on magnetic damping of Fe/MgO(001)
Y. Miura, in preparation

3. First-Principles Study on Anisotropic Magneto-Peltier Effect
K. Masuda, K.-i. Uchida, R. Iguchi, Y. Miura

PRB 99, 104406 (2019)

Experiments electric field effects of PMA and magnetic damping-21% of magnetic damping α is changed by 1V/nm EF for t=1.4nm
Magnetic anisotropy change by EF

EF dependence is insensitive tothickness of FM layer

Magnetic damping change by EF

Large thickness dependence of FM layer

Kambersky’s torque correlation model
V. Kambersky, Czechoslovak Journal of Physics B 26, 1366 (1976).
Damping TorqueSpin orbit torque

Generalized Langevin equation for magnetization dynamics

dS  t  iS  t   i  t  
dtPrecession-tem0Spin-torqueterm from SOI S t dt 0Damping-term

Magnetic susceptibility      Green function of Torque operator



1





P

t
,


t

0 g B 2
VP
  i 0       P 1 F   i 0

F   i 0   i  t ,   t e Magnetic susceptibility from LLG equation      Magnetic damping constant(comparing macroscopic formula)i   i 0 t



0

dt

 Ms

  H eff  i

1



   lim
Im  F   i 0  0  VM


0
S

Purpose of this work
If PMA and magnetic damping can be simultaneously reduced by applied voltage,
we can drastically reduce power consumption and write error rate in magnetization
reversal of MRAM.

Voltage dependence of magnetic damping is hardly investigated.

This work investigates the voltage dependence of magnetic
damping and magnetic anisotropy of Fe/MgO interface based on
the first-principles calculation.
Origin of Magnetic Damping α・Electronic system
・Phonon・Atomic disorder・Other extrinsic factors

First-principles calculation of damping constant
V. Kambersky, Czechoslovak Journal of Physics B 26, 1366 (1976).

 2
g 2 0 B2




Γ
k

VM S k nm nm
EF  Enk 2   2 EF  Emk 2   2
Matrix elements of torque operator

Γ


nm







SO
k  n, k  S , H m, k







k m
m, k   ci i

Bulk-Fe

y
Fe

Fe

Fe

Fe

Fe

Fe

Spin-orbit interaction
VASP code

0.0012x0.0010FeFe 
H SO   L  S

matrix elements of torque operator
based on the local atomic orbital

i , ,

z

Eigenstates at eachk-point and band   0 g B / 

Fe

α

⇒For
Fe/MgO(001)interface, I
considered
50x50 k-points.

0.00080.0006

α=0.0011 (this work)
α=0.0013 (by Gilmore)
K. Gilmore, PRL 99, 027204 (2007)

0.00040.00020.0000Converge for503 k-points

2 atoms/cell
15

20

25

30

35

40

45

k points 3 N k

50

55

60

Vloc(E)

Dipole correction⇒ G. Makov and M. C. Payne, PRB 51, 4014 (1995).

Charge density difference
ρ(E)-ρ(E=0)

Local potential [eV]

Potential and charge for model system
10
8
6
4
2
0
-2
-4
-6
-8
-10

－

＋

Vacuum(7.5Å)

Vacuum(7.5Å)

0.00040.00030.00020.00010.0000-0.0001

E=+0.10V/nm-0.0002

E=+0.05V/nm-0.0003-0.0004

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Distance [nm]

3.5

4.0

E>0 :Increase of electron accumulation at Fe/MgO interface
E<0 :Decrease of electron accumulation at Fe/MgO interface

4.5

5.0

Voltage dependence of PMA and damping α of Fe surface and Fe/MgO interface
Fe(001)surface

Fe

Fe

Cu

Fe

Cu

Cu

Cu

7% changefor 1V/nm
PMA-9.7fJ/Vm

C. G. Duan, et al., PRL 101, 137201 (2008).

Fe/MgO(001)interface

Increase of electron
at Fe surface

O Mg O Mg O Mg O

Fe

～2% change
for 1V/nm
PMA-110.9fJ/Vm

Increase of electron
at Fe/MgO interface

Fe

Increase ofelectron at
Fe surface

Fe

Cu

Cu

Cu

Cu

20.2% change
for 1V/nm

Increase of electron
at Fe/MgO interface

Decomposition of magnetic damping α   S  , H SO   S z L  S  Lz 

Torque operator

Spin conservation (Orbital deexcitation) term




u L o

Spin flip (Orbital conservation) termu  LZ o

The matrix elements are non-zero foratomic orbitals between different
magnetic quantum number, such asd(yz,zx)-d(z2), d(yz,zx)-d(x2-y2),d(yz,zx)-d(xy)The matrix elements are non-zerofor atomic orbitals between samemagnetic quantum number, suchas d(yz)-d(zx),d(x2-y2)-d(xy)Cu/Fe(5ML)/MgO

Cu/Fe(5ML)/MgO

Increase of electron
at Fe/MgO interface

Local Density of States [states/eV/atom]

Origin of electric filed dependence
3

Fe/MgO(001) interface

2

Majority-spin

1
0
-1
-2

Minority-spin

-3
-4

-3

-2

-1

0

1

2

E-EF [eV]Second order perturbation of SOI
D. Wang, et al., PRB 47, 14932 (1993).

EPMA  ( ) 2o ,u ,ko, k ,  Lz u, k , 

2

3

4

Large matrix element of

d x y2 o, k ,  Lx u, k ,  u,k   o,k22

 L d  yz, zx Increase damping withincreasing EF

Lx  12 L  L 

The <d(x2-y2)|L-|d(yz)> increase the damping, but decrease the PMA.⇒opposite EF dependenceSummary of the second topic

First principles study on voltage control of magnetic anisotropy(VCMA) and magnetic damping in Fe/MgO interface

・For Fe/MgO(001) surface, the magnetic damping increases with increasing
the electron accumulation at interface (positive EF).
(20% of damping constant α can be changed by EF=1[V/nm] for Fe/MgO(001))

・It is opposite to that of PMA (perpendicular magnetic anisotropy).
・The voltage dependence of magnetic damping of Fe/MgO(001) can be
attributed to the spin conservation term.

Topics
0. Introduction on spintronics

1. First-Principles Study on magneto-crystalline anisotropy ofFe/MgO(001) and Fe/MgAl2O4(001)
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

2. First-Principles Study on magnetic damping of Fe/MgO(001)
Y. Miura, in preparation

3. First-Principles Study on Anisotropic Magneto-Peltier Effect
K. Masuda, K.-i. Uchida, R. Iguchi, Y. Miura

PRB 99, 104406 (2019)

Introduction
Magnetoresistance devices

Magnetoresistance (MR)

RAP  RP
MR ratio 
RAP

Thermalgradient

Thermal management of spintronics devices

Ferro

・Thermal spin torque transfer

barrier(insulator)

X. Jia et al., PRL. 107, 176603 (2011).

・Thermal readout of MRAM
B. Geisler, P. Kratzer PRB. 92, 144418 (2015).

V

Ferro
Transistor

or

ΔTThermal managements in MTJs
TMR ratio of MTJs with Co2MnSi(CMS)-MgO
S. Tsunegi, et al., APL 93 (2008) 112506.

Problem: Reduction of the TMR
ratio at room temperaturein spite of high curie temperature～1000K

Thermalgradient

Ferro・Self-cooling of MTJs bymagneto-Peltier effectbarrier(insulator)
V

Ferro

or

ΔT

Observation of Anisotropic Magneto-Peltier Effects (AMPE)
K. Uchida, et al., Nature, 558 (2018) 95.

Large AMPE wasobserved for Ni,
but not for Fe.

First-principles calculations of Seebeck and Peltier coefficientGroup velocity

 



1  n , kv n , k   k （k-vector derivative of band dispersion ） f 
e 2 K 0  e 2  D    0     vd   
 f 
e 2 K 1  e 2  D    0     v 2 d   

（WIEN2k+BoltzTraP code）

Seebeck CoefficientK1
 
eK 0 T

Peltier coefficient

 

K1
 T
eK 0

Spin-orbit interaction (SOI) and anisotropic magneto-Peltier effect (AMPE)
Spin-orbit interaction

NuclearMagnetic field by electron motion
Electron
spin

Nuclearspin

Interaction between electron spin andmagnetic field by the orbital motion
Spin-orbit constantCoupling between spin (magnetization direction) and orbital (crystal axis)
Anisotropic band dispersion

Π⊥Without SOI

Current
perpendicular tomagnetization
Direction ofMagnetization

Peltier coefficient：Π⊥＝Π//With SOI
Current parallel tomagnetization

Π// Peltier coefficient：Π⊥≠Π//

Anisotropic magneto-Peltier effects (AMPE) of Fe,Co,Ni
bcc-Fe (2atoms/u.c.)Definition of AMPE
磁気モーメント//[010]fcc-Ni (4atoms/u.c.)Comparison of band dispersion of Fe, Ni

Ni: Large d(xz,xy)-band hybridization between Majority- and Minority-spin states due to spinorbit⇒Large AMPE(ΔΠ)

Mechanism of AMPE in Fe, Ni

Spin-flip term

Spin-conserving termBand dispersion parallel to magnetization

W/o SOIWith SOI 
H SO  L  S←anisotropic band
dispersion→

Bcc-FeFcc-NiDOS

DOS

Large exchange splitting

Small exchange
splittingEFd bandBand dispersion perpendicular to magnetizationεEFd bandεd-Band hybridization between majority- and minority-spin states due to SOI is important for large AMPE.
To this end, ferromagnetic materials with small exchange splitting such as Ni is more favorable for large AMPE.

Prediction of new materials with huge AMPE

Tc～200K

Tc～300K

FePt 3.30μB/cell

NiPt

1.06μB/cell

Smaller exchange splitting of NiPt than FePt★：exp. (from AMSE)

Total Density of States [states/eV/cell]☆：exp. (from AMPE)

3

Majorityspin

2
1
0
-1
-2
-3

Mnjorityspin

FePt
NiPt
-6

-5

-4

-3

-2

Energy E-EF [eV]

-1

0

1

2

Summary of the third topic

・In first-principles calculations, AMPE
is Fe<Co<Ni, and FePt<<NiPt<Ni3Pt.
・Hybridization of Majority-spin and Minority-spind-band around the Fermi level is more important
for large AMPE.

Summary of this talk
MRAM

Magnetic censer

HDD read-out-head

Earth’s magnetic field censer・current censer for car・biomagnetic censer

Required performance for pMTJs

High TMR ratio
over 200% at
300K

Large thermal
stability factor
KuV/kBT > 60 at
300K

Low magnetization
switching current
density Jc0 less than
0.5MA/cm2

Corresponding to SQUID

Required properties for
spintronic materials
High spinpolarization
with low
resistance

Strongperpendicul
ar magnetic
anisotropy

Small magnetic damping
and large VCMA effects