CMD Workshop 37 : Spintronics course
in Center for Spintronics Research Network (CSRN),
Graduate School of Engineering Science, Osaka University.

September 1, 2020

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. Spin-dependent transport in magnetic tunnel junctions withhalf-metallic Heusler alloys
Y. Miura, et al., PRB 83, 214411 (2011).

2. Magneto-crystalline anisotropy at interfaces of Fe(001) with
MgO and MgAl2O4
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

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

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

HDD read-out-headCorresponding to SQUID

Magnetization reversal in MTJs
１．Magnetic field by current

current

current

problem：・complicate circuit.
・current∝1/device-size

FMInsulator
FM

Effects of demagnetizing field increase the criticalcurrent for writing with decreasing size of device

MTJ antiparallel

MTJ parallel

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

STT MRAM

conventional
MRAM


e 
2

e 
2

current

H

H

Writing current

STT type

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

Tohoku Univ. Ando lab. HP

current

Conventi
onal typetargetMemory cell size (μm)

・simple circuit・current∝device-size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．Perpendicular magnetic anisotropy(PMA)

3. Low damping constant(α)

Hanti-4πMs

Topics
0. Introduction on spintronics

1. Spin-dependent transport in magnetic tunnel junctions withhalf-metallic Heusler alloys
Y. Miura, et al., PRB 83, 214411 (2011).

2. Magneto-crystalline anisotropy at interfaces of Fe(001) with
MgO and MgAl2O4
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

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

Introduction: Half-metallic ferromagnetic
The Half-metallic ferromagnets

Julliere modelGP  GAP
2 PL  PRGP
1  PL  PR

Spin-polarization at EF

PL ( R ) DL( R )  DL( R )DL( R )  DL( R )Co-based full Heusler alloys

Up spinenergyDown spin

Co2YZ (Y=Fe,Mn,Cr : Z=Si,Ge,Al,Ga)(1) B2-type disorderZ
L21-structure

DOS

TMR 

EF

High Curie temperature (900K)
Simple fabrication process

Y
Co

Co2MnSi(2) D03-type disorder

Y. Miura, et al., PRB, 69 (2004) 144413.

Problem in MTJs with half-metallic Heusler alloys

Problem in MTJs with half-metallic Heusler alloys
TMR ratio of MTJs with Co2MnSi(CMS)

CMS/MgO/CMS(001)
B. Hu, et al., PRB 94 (2016) 094428.

S. Tsunegi, et al., APL 93 (2008) 112506.

Present top data

Problem: Reduction of the TMR ratio at room temperaturein spite of high curie temperature of Co2MnSi: 985K

Introduction (theory)
1. Temperature dependence of bulk density of states owing to non-quasiparticle
M. I. Katsnelson, et al., Rev. Mod. Phys. 80, 315 (2008).

X-ray photoelectron spectroscopy of bulk CMS
Temperature dependence of total DOS
of bulk CMS calculated from DMFT

K. Miyamoto, et al., PRB. 79, 100405(R) (2009).

30K

GGA

Valence band electronic
structures of bulk CMSIntroduction (theory)
2. Effects of the spin-flip scattering through the interface states promoted bymagnetic excitation.
Anti-parallel magnetization
P. Mavropoulos, et al., PRB, 72 (2005) 174428.

Co2MnSi/MgO(001)
Y. Miura, et al., PRB 78, 064416 (2008).

Y. Miura, et al., JPCM 19, 365228 (2007).

Purpose of this work
・To clarify a possible origin of reduction of TMR ratio at RT
in MTJ with half-metallic Heusler alloys,
・We investigate effects of spin-flip scattering through the interface states
at CMS/MgO junctions originating from non-collinear magnetic structures.
Thermal fluctuation of local spin-moments ⇒ Non-collinear magnetic structures

Calculation Method

PWSCF http://www.pwscf.org/

Transport calculations

e2 N
G 
Ti

h i

Plane-wave basis set
 Ultra-soft pseudopotential method
 GGA for Exchange-Correlation termElectronic structures

Landauer formula Zero bias limet Ballistic Conductance

H. J. Choi and J. Ihm, PRB 59 (1999) 2267.
A. Smogunov, A. Dal Corso and E. Tosatti, PRB 70 (2004) 045417.

Conductance calculation in Non-collinear spin system
First, we perform electronic structure
calculations in collinear spin system
Then, we artificially rotate spin-quantum
axis of local spin-moments to obtain
density-matrix in non-collinear spin system.

The rotation of spin-quantum axis in NC spin system
The density matrix in non-collinear spin system is obtained from theinverse unitary transformation of spin-density in collinear spin system.
Collinear spin system(ni)Non-collinear spin system(nαβ)θ,φ

n r    U ni r U i
i   , i

 exp  12 i  cos  12   exp  12 i sin  12   U  
1
1
1
1








exp
i

sin

exp
i

cos



2
2
2
2



Local potential in Collinear spin system

J. Kubler et al., J. Phys. F: Met. Phys. 18, 469 (1988).

VL r   VH r   1  E XC  1  E XC  E XC 

0




2   (  , ) n
2  n
n 





E

E

E
1
1

XC
  XC  XC  0
VL r   VH r  
2  (  , ) n
2  nn  


Local potential in Non-Collinear spin system VL r   VH r   1  E XC  1  E XC  E XC  cos 
2  (  , ) n
2  nn 
 1  E XC  E XC  sin  cos   i  E XC  E XC  sin  sin  2  nn 
2  nn   


1  E XC E XC 
i  E XC E XC 

sin

cos

sin

sin









2  nn 
2  nn E XC 1  E XC E XC 
1

cos

VL r   VH r  
 



2  (  , ) n
2  nn 


Y. Miura, et al., Phys. Rev. B 83, 214411 (2011).

Transport in non-collinear spin MTJsθ

MgO(2nm)

Local Potential
[eV]

θ
0.01
0.005
0
-0.005-0.01-0.015-0.02-0.025

Local Potential
Off-diagonal part
diagonal part

0

5

10

15
20
distance [angstrom]

25

30

35

40
107
106

tpara(θ)

105
104
103
102

tanti(θ)

101
100
10-1

Angle of Local Moment θ [degree]
Y. Miura, et al., Phys. Rev. B 83, 214411 (2011).

Angle of Local Moment θ [degree]Effects of sub-interfacial non-collinear spin to TMRθCase 1θCase 2

2rd-layer of interfacial Co spin-moments are cantedθ
Case 3

1st-layer of interfacial Co spin-moments are canted(Co termination)(MnSi termination)
3rd-layer of interfacial Co spin-moments are canted(Co termination)θθθ

Noncollinear magnetic structures of the first and the second interfacial layer strongly reduce TMR.
Noncollinear magnetic structure of the third and forth interfacial layer show relatively small reduction of TMR.

Exchange stiffness constant at CMS/MgO(001)
Increase of band energy of Non-collinear Spin ⇒ Strength of exchange couplingE(θ)=A(1-cosθ)A∝JM2

CMS/MgO(001)
Co-term.

Fe/MgO(001)

MnSi-term.

E(θ)

Exchange stiffness of interfacial atoms
A [meV/u.c.a.]A. Sakuma, et al., JAP 105, 07C910 (2009).

Off-diagonal part of local potential E XC E XC  sin V (   ) r   


n
n


 
 

Bulk (CMS or Fe)
MgO interface
ΔA [meV/u.c.a.]

Co1
414
145
-269

Mn1
529
565
＋34

Interfacial local spin-moment
M [μB]Co1
Mn1
Bulk (CMS or Fe)
MgO interface
ΔM [μB]

0.93
0.54
-0.39

Fe1
600
753
＋153

Fe1
3.31
2.35
4.06
2.98
＋0.75 ＋0.63

Co2
414
347
-67

TMR ratio at finite temperature
Boltzmann average of tunneling conductance  exp  2 E   k T sin dtT  t exp  2 E   k T sin d( para, anti )B( para, anti)

B

Calculations
Fe/MgO/Fe
CMS/MgO/CMS(MnSi-term.)
CMS/MgO/CMS(Co-term.)

MgO thickness ～2nm

Temperature [K]S. Tsunegi, et al., APL 93 (2008) 112506.

Reduction TMR ratio at RT in CMS/MgO/CMS MTJ can be attributed toa spin-flip scattering at interfacial region caused by thermal fluctuation.

Exchange coupling for other Heusler alloys
Pwscf with GGA

Increase of band energy E(θ) [meV]

500
450

bcc-Fe/MgO(001)400

B2-CoFe/MgO(001)
Co2FeSi/MgO(001)
Co2FeAl/MgO(001)
Co2MnSi/MgO(001)
Co2MnAl/MgO(001)

350
300
250

E(θ)

200

B2-CoFe/MgO(001)

Co termination

E    A1 cos  bcc-Fe/MgO(001)

Co2FeSi/MgO(001)
Co2FeAl/MgO(001)

150
100

Co2MnSi/MgO(001)50
0Co2MnAl/MgO(001)

0

10
20
30
40
50
Angle of interfacial Co spin-moment θ [degree]60

Exchange stiffness constant[meV per unit-cell-area]

Exchange stiffness constant at Co termination
Inter-atomic layer exchange stiffness constant A [meV/cell area]
E    A1 cos  
900
800
700
600
500
400
300
200
100
0

Local spin-moment [μB]

Co2MnSi/MgO

Co2MnAl/MgO

Co2FeSi/MgO

Co2FeAl/MgO

B2-CoFe/MgO

Interfacial Co spin-moment at Co termination [μB]

A∝JM2

1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
Co2MnSi/MgO

Co2MnAl/MgO

Co2FeSi/MgO

Co2FeAl/MgO

B2-CoFe/MgO

Enhancement of interfacial Co spin-moment is effective to obtain large exchange coupling.

Comparison with Experimental results on TMR at LT and RT
Co2MnSi/MgO(001)
S. Tsunegi, et al., APL 93 (2008) 112506.

Co2Fe(Al,Si)/MgO(001)
W. Wang, et al., APL 95 (2009) 182502.

TMR RT  217%
 0.29
TMR 2K  753%

T. Ishikawa, et al., APL 94 (2009) 092503.

TMR RT  180%
 0.26
TMR 5K  700%

TMR RT  330 % 0 .47
TMR 10K  700 %N. Tezuka, et al., APL 94 (2009) 162504.
TMRRT 386%

 0.46
TMR9K 832%

Summary of the first topic◇ Spin-flip scattering at 1ML of interfacial non-collinear magnetic structuresstrongly affect the spin-dependent conductance and TMR ratio.
◇ Interfacial Co-layer is easy to fluctuate at RT due to the small exchange
stiffness at CMS/MgO(001) junctions.
◇ The reduction of the TMR ratio at RT can be attributed to spin-flip scattering
at interfacial region caused by thermal fluctuation of interfacial Co-layers.
To raise the TMR ratio at RT, we have to insert CoFe-layer to enhance the interfacialexchange stiffness of CMS/MgO junction.

Topics
0. Introduction on spintronics

1. Spin-dependent transport in magnetic tunnel junctions withhalf-metallic Heusler alloys
Y. Miura, et al., PRB 83, 214411 (2011).

2. Magneto-crystalline anisotropy at interfaces of Fe(001) with
MgO and MgAl2O4
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

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

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 Perpendicular Magnetic Anisotropy(PMA) for MgAl2O4(MAO)
Multilayer structure
Annealed @350‐450℃

Lattice mismatch between
bcc-Fe and MgAl2O4 is 0.2%.

MgAl2O4(mono‐, poly‐, a‐)Fe(0.7)Cr(30)
MgO Sub.

J. Koo, et.al., Phys. status solidi RRL 8, 841 (2014).
Ki of Fe/MgO(001) is 1.4mJ/m2,
J. W. Koo, et al., Appl. Phys. Lett. 103, 192401 (2013).

Purpose of this work
We study interfacial magnetocrystalline anisotropy (MAE) in Fe/MgAl2O4 andFe/MgO by means of first-principles calculations based on density functional theory.

Fe/MgAl2O4(2aFe)

Fe/MgO (aFe,aMgO)・origin of interfacial perpendicularmagnetocrystalline anisotropy (PMA)

Al
Mg
O
Fe

O

Mg

Fe

・XMCD Measurement(orbital and spin moment, quadrupole moment)

・First-principles calculations
・2nd order perturbation of SOI

Second order perturbation of spin-orbit interaction (SOI)
Bruno, PRB 39, 865 (1989).
Wang, Wu, Freeman, PRB 47, 14932 (1993).
van der Laan, JPCM 10, 3239 (1998).

𝛿𝐸

𝜉𝐿 ⋅ 𝑆⃗𝐻

exc 𝐻 gr𝜀exc 𝜀grexc

gr exc𝑐, ,𝑖, 𝜇

μ：local atomic orbital index
i,j：index of atomic position,

Magneto-crystalline anisotropy (MCA) energy
Δ𝐸
Δ𝐸

𝑖

δ𝐸 in-plane1𝜉,Δ𝐸↑⇒↑ 𝑖,

Δ𝐸↓⇒↓ 𝑖δ𝐸 perpendicuar𝑜, 𝜎 𝐿 𝑢, 𝜎, 𝑖𝜀 ,Δ𝐸↑⇒↓ 𝑖𝑜, 𝜎 𝐿 𝑢, 𝜎, 𝑖EF

up-spin𝜀 ,Δ𝐸↓⇒↑ 𝑖E
down-spin

Orbital moment

𝐿

4𝜉
,

𝑜, ↑ 𝐿 𝑢, ↑, 𝑖𝜀 ,𝑜, ↓ 𝐿 𝑢, 𝜎, 𝑖𝜀 ,Spin conserving term and spin flip term in magnetic anisotropy
Spin conserving term

Δ𝐸↓⇒↓ 𝑖𝜉,zperpendicular𝑢, ↓ 𝐿 𝑜, ↓, 𝑖𝜀 ,↓ 𝜀 ,↓,𝑢, ↓ 𝐿 𝑜, ↓, 𝑖𝜀 ,↓ 𝜀 ,↓In-plane

𝐿 𝑌
xContributed to PMA energy, if
there are d orbitals with thesame magnetic quantum
number m exist around EF.

𝑥

Spin flip term

𝐿 𝑌

𝑚𝑌

𝑧𝑥, ↓ 𝐿 𝑦𝑧, ↓Δ𝐸↓⇒↑ 𝑖𝜉

𝑥𝑦, ↓ 𝐿 𝑧𝑥, ↓2𝑢, ↑ 𝐿 𝑜, ↓, 𝑖𝜀 ,↑ 𝜀 ,↓2nd order perturbation energyΔ𝑚Orbital moment anisotropy term
⇒Spin-conserving term∆

∝𝑌

Contributed to PMA energy, if
there are d orbitals with m
and m±1 exist around EF.

1𝑦 , ↓ 𝐿 𝑥𝑦, ↓

,

Δ𝐸

𝜉

𝑚

𝜉
,

1

𝑥

𝑦 , ↓ 𝐿 𝑧𝑥, ↓3𝑧

𝑟 , ↓ 𝐿 𝑦𝑧, ↓1
3𝑢, ↑ 𝐿 𝑜, ↓, 𝑖𝜀 ,↑ 𝜀 ,↓Bruno, PRB 39, 865 (1989).
Wang, Wu, Freeman, PRB 47, 14932 (1993).
van der Laan, JPCM 10, 3239 (1998).

Magnetic dipole (Quadupole moment) term
⇒Spin-flip term

Intuitive understanding of magneto-crystalline anisotropy (MCA)
P. Bruno, PRB 39, 865 (1989).
G. Laan, JPCM 10, 3239 (1998).

Orbital moment term𝜉𝐿 ⋅ 𝑆⃗

𝐻

Δ𝐸

Δ𝑚Orbitalmoment term

<Lz>

z

𝑚

∆

Magnetic 𝑚
dipole term
<Lx>

𝑇

𝑇

𝐿
Q S

<S> In-planemagnetic
anisotropy

𝑦 , 𝑑 𝑥𝑦

Magnetic dipole term T ⇒Quadrupole moment of spin density

2
𝑸𝑆
7

𝐿

z

<S>
Perpendicularmagnetic
anisotropy

𝑑 𝑥

Δ𝑚

𝑇

2
7

𝑄 𝑆

𝑟 , 𝑑 𝑦𝑧 , 𝑑 𝑧𝑥

Q: Quadrupole moment of spin density
Q z > 0 (T z <0) ⇒ Oblate distribution

Q z < 0 (T z >0)⇒ Prolate distribution
Qz=0
z

𝑑 3𝑧

z

z

isotropic
Perpendicular magnetic anisotropy

In-plane magnetic anisotropy

MCA energy for Fe/MgAl2O4(MAO) and Fe/MgOOFe

Fe/MgO(001)(a||=aFe)

K. Masuda and Y. Miura,
PRB 98, 224421 (2018).

Mg
Mg
Fe O

Fe/MgAl2O4(MAO)(001)(a||=2aFe)

Al

Orbital moment anisotropy, Δmorb

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0

●exp.
[1]
●exp.
[2]

Fe/MgAl2O4

Orbital moment anisotropy Δmorb[μB]

Magnetic anisotropy energy,
ΔEMCA [mJ/m2]

Magneto-crystalline anisotropy, ΔEMCA

Fe/MgO

0.03
0.025
0.02
0.015
0.01
0.005
0
Fe/MgAl2O4

Fe/MgO

Δ𝑚

21 𝜉
2𝜇 ∆𝐸

[1] J. W. Koo, et al., Appl. Phys. Lett. 103, 192401 (2013).
[2] J. W. Koo, et.al., Phys. status solidi RRL 8, 841 (2014).

Δ𝐸

𝑚Spin-decomposed PMA energy of Fe/MgAl2O4(MAO) and Fe/MgO
Fe/MgAl2O4(MAO) a=aFe

ΔEMCA=1.6[mJ/m2]

ΔEMCA=1.2[mJ/m2]

Al

O
Mg

Fe/MgO a=aFe

Fe2

・Interfacial Fe mainly contributes to Perpendicular (Positive) MCA
・Spin conservation term Δ𝐸↓⇒↓ 𝑖 mainly contributes to Perpendicular MCA.
・For Fe/MgO, the spin flip term Δ𝐸↑⇒↓ 𝑖 also contributes to Perpendicular MCA.

Magnetic dipole term of Fe/MgAl2O4 and Fe/MgO
𝑇

J. Stöhr and H. König, PRL 75, 3748 (1995).

Quadrupole distributionof d orbitals

16𝑚

8𝑚

8𝑚

16𝑚

Spin moment of each dorbital for interfacial Fe
Fe/MgOd(zx)d(3z2-r2)
d(xy)

𝑇

𝑄 𝑆

Magnetic dipole term, mT

Fe/MgAl2O4

d(yz)

16𝑚
𝑚

Magnetic dipole mT [μB]

𝑚

2
7

0.140
0.120
0.100
0.080
0.060
0.040
0.020
0.000

Fe/MgAl2O4d(x2-y2)
0

0.2

0.4

0.6

spin moment md

0.8

Fe/MgO

Magnetic dipole term of Fe/MgAl2O4 and Fe/MgO
2

𝑇
𝑚

7

𝑇

𝑄 𝑆

2
7

16𝑚

8𝑚

16𝑚

16𝑚

/16

J. Stöhr and H. König, PRL 75, 3748 (1995).

𝑄 𝑆

Fe/MgAl2O4(aFe)

Magnetic dipole term, ΔmT

Magnetic dipole mT [μB]8𝑚

Fe/MgO (aFe)

0.140
0.120
0.100

Al

0.080
0.060

Mg

0.040

O

O

Mg

0.020
0.000

Fe/MgAl2O4

Fe/MgO

Qz≂0 (Tz≂0) (isotropic)
Qz<0 (Tz>0) (Cigar-type)Fe

Fe

Summary of the second topic
・Fe/MgAl2O4(001) show Perpendicular MCA, whichis 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 Perpendicular MCA,
resulting in larger MCA energy than that of Fe/MgAl2O4.
・Cigar type quadrupole moment additionally increases thePerpendicular MCA of Fe/MgO, but not for Fe/MgAl2O4(MAO).

The quadrupole moment of spin-density is essential tounderstand the magneto-crystalline anisotropy (MCA)
especially for ferromagnetic interfaces.

Topics
0. Introduction on spintronics

1. Spin-dependent transport in magnetic tunnel junctions withhalf-metallic Heusler alloys
Y. Miura, et al., PRB 83, 214411 (2011).

2. Magneto-crystalline anisotropy at interfaces of Fe(001) with
MgO and MgAl2O4
K. Masuda and Y. Miura, PRB 98, 224421 (2018).

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

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

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

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

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

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

Potential and charge for model system
Vloc(E)

Charge density difference
ρ(E)-ρ(E=0)

Local potential [eV]

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

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 MCA and damping α of Fe surface and Fe/MgO interface
Fe(001)surface

Fe

Fe

Cu

Fe

Cu

Cu

Cu

7% changefor 1V/nm
MCA change-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
MCA change-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 third 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 Perpendicular MCA.
・The voltage dependence of magnetic damping of Fe/MgO(001) can be
attributed to the spin conservation term.

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