CMD Workshop 31 : Spintronics course
in Center for Spintronics Research Network (CSRN),
Graduate School of Engineering Science, Osaka University.

September 12, 2017

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
Kyoto Institute of Technology (KIT)Instroduction
Magnetic tunnel junction (MTJs)

Tunneling magnetoresistance(TMR)

TMR ratio 

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

Very Large-Scale Integrated (VLSI) circuit

TMR
deviceRAP  RP
RAP

Everspin
64Mbit MRAM

Transistor

Drastically reduce power consumption due to static powerby replacing volatile DRAM and SRAM
H. Ohno, et al., IEDM pp. 218-221 (2010).

Magnetization reversal by spin transfer torque (STT)
e
e



2

Damping torque(magnetic friction)Spin transfer torque
2Reduction of critical current density (Jc0) α：Magnetic damping constant(107A/cm2⇒105A/cm2)
MS：Saturation Magnetization

J c 0   M S H anti  2M S  t / P
J.C. Slonczewski, JMMM 159 (1996) L1.

Hanti±2πMS: Effective anisotropy field
P：Spin polarization
t：Thickness of FM layer

１. High spin polarization (P) with low resistance
2. Low damping constant(α) with perpendicular magnetic anisotropy(PMA)
Usually strong perpendicular magnetic anisotropy (PMA) is originatedto the large spin orbit interaction leading to large damping α

３．Small magnetization (Ms) with high Curie temperature
Ferrimagnetic materials

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

2. Spin-dependent tunneling conductance in magnetic tunnel
junctions with spinel-type MgAl2O4 barrier
Y. Miura, et al, PRB, 86, 024426 (2012).
K. Masuda and Y. Miura, PRB 96, 054428 (2017)

3. Electric field dependence of magnetic damping constantof Fe(001) surface
YM, M. Tsujikawa, M. Shirai, in preparation.
4. Magneto-crystalline anisotropy at interfaces of Fe(001)with various non-magnetic metals
Y. Miura, M. Tsujikawa, M. Shirai, J. Appl. Physics, 113, 233908/1-6 (2013).

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

2. Spin-dependent tunneling conductance in magnetic tunnel
junctions with spinel-type MgAl2O4 barrier
Y. Miura, et al, PRB, 86, 024426 (2012).
K. Masuda and Y. Miura, PRB 96, 054428 (2017)

3. Electric field dependence of magnetic damping constantof Fe(001) surface
YM, M. Tsujikawa, M. Shirai, in preparation.
4. Magneto-crystalline anisotropy at interfaces of Fe(001)with various non-magnetic metals
Y. Miura, M. Tsujikawa, M. Shirai, J. Appl. Physics, 113, 233908/1-6 (2013).

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

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

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]In-plane wave vector (k//) dependence of tunneling conductance
Majority-spin states

Energy E-EF[eV]

3
2
1
0

Δ1 band

-1
-2
-3

Γ

Parallel magnetization
1.8x10-7 (θ=5°,φ=0°)

Anti-parallel magnetization(θ=5°,φ=0°)

Conductance [e2/h]

Co2MnSi(Zv=29)

MgO (2nm)kz along [001]

kx

ky

kx

Broad peak at k//=0
The spin-flip conductance is dominated by the
conducting electrons with Δ1 symmetry.

kyElectronic states contributing to spin flip scattering
Non-collinear magnetic structure make a mixingof the majority- and minority-spin states.

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

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 Fe-layer to enhance the interfacialexchange stiffness of CMS/MgO junction.

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

2. Spin-dependent tunneling conductance in magnetic tunnel
junctions with spinel-type MgAl2O4 barrier
Y. Miura, et al, PRB, 86, 024426 (2012).
K. Masuda and Y. Miura, PRB 96, 054428 (2017)

3. Electric field dependence of magnetic damping constantof Fe(001) surface
YM, M. Tsujikawa, M. Shirai, in preparation.
4. Magneto-crystalline anisotropy at interfaces of Fe(001)with various non-magnetic metals
Y. Miura, M. Tsujikawa, M. Shirai, J. Appl. Physics, 113, 233908/1-6 (2013).

Complex band structure of MgO and tunneling effects
・Transmission of 1D potential

MgO band at (kx,ky)=(0,0)V(z)=VB (0≤z≤d)V(z)=0 (z<0, z>d)eik z ZVBe  z

EF
z=0



z=d

Imaginary part of complex band structure
determines the decay rate of evanescent statein barrier
2mVB  EF    V r   E   r   02kComplex band calculation
for given E

Coherent tunneling in Fe/MgO/Fe(001)
W. H. Butler, et al., PRB, 63 054416 (2001).

C4v

[001]

Crystalline-MgO
barrier MTJ

Amorphous Al-O
barrier MTJ

Δ1

Δ1

Δ2

Δ5

bcc-Fe(001)

bcc-Fe
(001)

MgO(
001)

a-AlO

Symmetry dependenttransmission
Projection to
Z direction

Δ1

s

Δ5

Band dispersion of bcc-Fe(kx,ky)=(0,0)

bcc-Fe(001) Incoherent tunnelingbcc-Fe Coherent(001) tunneling

z

Δ2

C4v

Density of states
dependent transmission

pz d 3z 2  r 2

px
Δ5

py

d yz

Half-metallic on Δ1 stated zx

d x 2  y2
Δ2

d xy

Giant TMR in Fe/MgO/Fe(001)
Fe majority-spin

Fe minority-spin

3

3

Δ1

2

Δ5

1

E-EF（eV）

E-EF（eV）

Δ1

2

1
0

Δ5

-1
-2
-3

-1

Δ2

-2

Δ2

Fe

-4

-4
-5
Γ

Δ1

0

-3

Δ2
H

kz along [001]

Up spin electron
Down spin electron

-5

Γ

H

kz along [001]Half-metallic on Δ1 state inbcc-Fe (P=1)

Δ5

MgO

Fe

Highly spin-polarized current
Theoretical TMR ratio⇒1500%(MgO thickness～1nm)

Experiment
S. Yuasa, et al., JJAP, 43 L588 (2004).
S. Parkin, et al., Nature Material, 3 862 (2004).
S. Yuasa, et al., Nature Material, 3 868 (2004).
S.Ikeda,et al Appl.Phys. Lett. 93, 082508 (2008).
Co20Fe60B20/MgO/Co20Fe60B20 (TMR ～604% @300K)

TMR for Fe/MgO/Fe(001)Spinel Barrier
MgAl2O4

Normal spinel structure

Fd3m(No. 227)

Tetrahedral A-site・・・Mg2+

fcc-sublattice ・・・O2-

Octahedral B-site・・・Al3+(u-parameter)

Advantage:
1. Very small lattice mismatch with bcc-Fe (<0.5%)
Lattice constant : (8.09Å)/√2=5.72Å
2. Modulation of lattice constant by choosing cation atoms.
MgAl2O4, ZnAl2O4, SiMg2O4, TiZn2O4, SiZn2O4, Al3O4, etc.

Experiments：MTJs with normal spinel MgAl2O4 barrier on Fe(CoFe)
TMR=160%@15K (120%@RT)
H. Sukegawa, et al., APL 96, (2010) 212505.

TMR=328%@15K (188%@RT)
TMR=478%@15K (303%@RT)
H. Sukegawa, et al., PRB 86, 184401 (2012).
Y. Nian, et al., PRB, 43 (1991) 4461.
Calculation：bulk MgAl2O4 R. Khenata, et al., Physics Letters A, 344 (2005) 271.

Purpose of this work
Coherent tunneling properties of spinel MgAl2O4–based MTJs
Origin of the TMR effect in Fe/MgAl2O4/Fe(001) MTJs.

Electronic and transport calculations of Fe/MgAl2O4-based MTJs
together with Fe/MgO-based MTJs on the basis of the firstprinciples density functional method.

Calculation method
Electronic structure calculation
PWSCF http://www.pwscf.org/
Conductance calculation

Ultra-soft pseudopotential
 GGA for exchange-correlation term

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

electrode region L   k   rk  k k k  L

FeScattering region

electrode regionS R   t k  k k 

MgAl2O4k  RFe~I   Vloc (r )  k (r )   Dmn  nI  k  mI (r )  E k (r )2

I , mn・Fixed k//
・Fixed spin index
・Zero bias limit conductanceLandauer formula

e2 N
G 
Ti

h i

Complex band structures of MgAl2O4
k//=(0,0)

MgAl2O4

MgO

kz=kz’+ikz’’

MgAl2O4 has the smallest imaginary partwith the Δ1 symmetry in the energy gap.

Structures of Fe/MgAl2O4(001) interface
aMgAl2O4=8.09[Å]aMgAl2O4/√2=5.72[Å]0.5% lattice mismatch
aFe=2.866[Å]aFe×2=
5.732[Å]aMgO/√2=2.979[Å]Possible interfacial structures(B-site termination）① Al-top② Al-O hollow ③ Al-Al hollow④ O-topaMgO=4.213[Å]Energy [eV/ucv]① Al-top0(基準)② Al-O hollow-0.1③ Al-Al hollow

2.5④ O-top-3.2 Stable※ucv=unit cell volume

O-top configuration with
B-site termination

TMR effect of Fe/MgAl2O4/Fe(001) MTJ

YM, et al, PRB, 86, 024426 (2012).

Fe/MgAl2O4/Fe

Fe/MgO/Fe

9.56Å

9.32Å

G P  G AP
TMR 
G AP

Fe/MgAl2O4/Fe

Fe/MgO/Fe

160%

1600%

Conductance

Fe/MgAl2O4/Fe

Fe/MgO/Fe

GP

0.52

0.103

(parallelmagnetization)

↑0.5
↓0.02

↑0.1
↓0.003

※unit

GAP

0.2

0.006

[S  m 2 ]

↑0.1
↓0.1

↑0.003↓0.003(Anti-parallel
magnetization)

The large conductance in the anti-parallel magnetization, indicating
appearance of new conductive channel in the Fe/MgAl2O4/Fe MTJs.

Band dispersion of bcc-Fe at k//=(0,0)

s,pz,dz2

Primitive unit cell (aFe=2.87Å)

Δ1

Δ1
0

ky

π
a

With Δ1 state

π
a

kx
Γ

π
a

k//=(0,0)-2 kZ along [001]

ky

ky

kx
Γ

0 Δ1

-2 kZ along [001]-2 kZ along [001]

π
a

Δ1

k//=(0,0)k//=(0,0)-2 kZ along [001]Minority spin
2

2

0

0

k//=(0,0)

Majority spin

E-EF (eV)

E-EF (eV)Majority spin
Minority spin
2
2

Doubled unit cell (a’Fe=2×aFe=5.73Å)

ky

π
a'

Γ

kx
π
a'

Without Δ1 stateWith Δ1 state

π
a'

Γ

kx
π
a'

With Δ1 state

The minority-spin states with the Δ1 symmetry appear
along Δ line due to the band folding effect.

Projection of the tunneling wavefunction
Projection of tunneling wavefunction at EF

s (r' ) ：Tunneling wave function

Wlm ：Local orbital

Ψs
Parallel magnetization

Choi and Ihm, Phys. Rev. B.,59(1998) 3.

Fe/MgAl2O4/Fe
Majority-spin ：Atom index

Minority-spinl,m: atomic orbital index

Fe/MgO/Fe
Majority-spin

Minority-spin

In minority-spin states, the Fe/spinel-based MTJ has the slow decay
Δ1 evanescent states due to the folded Fe-s channels.
YM, et al, PRB, 86, 024426 (2012).

Comparison with experimental TMR of Fe/MgAl2O4/Fe
Experiments：
Calculation：
160% at 0K,
Fe/Mg-Al-O(1.1nm)/Fe 165% at 15K APL 96, (2010)
Fe/MgAl2O4(1.2nm)/Fe
CoFe/MgAl2O4(1.2nm)/CoFe

Fe/Mg-Al-O(1.2nm)/Fe 328% at 15K
PRB 86, (2012).
CoFe/Mg-Al-O(1.2nm) 479% at 15K

H. Sukegawa, et al.,
A:TMR≈165%
APL 96, (2010) 212505.

Oxidation of
Al on Mg

Presence of {022}spot indicatingordered spinel
structure

abarrier≈8.0Å

Sukegawa, et al., PRB
B:TMR≥300% H.
86, 184401 (2012).
abarrier≈4.0Å Oxidation ofmagnalium (Mg-Al)

abarrier=aspinel

abarrier=aspinel/2

Absence of {022}spot indicatingordered spinel
structure

Due to the reduction of the lattice constant, the band folding and appearance of
new conductive channel in minority-spin states were suppressed in the MTJs.

Why unit-cell size of Mg-Al-O barrier reduces?
The Mg2+ - Al3+ swapping in two different cation sites just transforms the normal
spinel to the inverse spinel, and it does not affect the unit-cell size and its space group.
Cations must randomly occupy octahedral and tetrahedral sites including vacant sites.
Fd3m(No.227)
Normal Spinel MgAl2O4

All cation-sites areoccupied by cation atoms(Mg2+,Al3+)
O2-

abarrier=aspinel≈8.0Å
Cation-site disordered spinel

abarrier=aspinel/2≈4.0Å
Fm3m(No.225)
F43m(No.216)

Cation-site disordered Mg-Al-O barrier
H. Sukegawa, et al., PRB 86, 184401 (2012).

Possible structure of cation-site disordered structure
Fm3m(No. 225)

F43m(No. 216)

O

abarrier=aspinel/2≈4.0Å

Cation-site(Mg2+,Al3+)

By H. Sukegawa and S. Mitani, et al., NIMS

Key
The anion-site does not changes from the spinel structure by thedisordering, and it is always occupied by oxygen atoms making
the fcc-sublattice.

Coherent tunneling in cation-site disordered spinel?
H. Sukegawa Y. Miura, et al.,
PRB 86, 184401 (2012).

Δ1

The projection of Δ1 WF on O is one order magnitude larger than that of Mg and Al.
Coherent tunneling through Δ1 state is dominated by Oxygen,cation-site disorder has little effect on coherent tunnelingBias voltage dependence of TMR
Vc

Vc

K. Masuda and Y. Miura, PRB 96, 054428 (2017)

The critical bias voltage Vc of the MgAl O -based MTJ
is clearly larger than that of the MgO-based MTJ
2

4

Summary of the second topic
Band folding effects reduce TMR ratio of Fe/MgAl2O4/Fe(001) MTJs.
Suppression of band folding by cation-site disordered Mg-Al-O MTJs.

Giant TMR in Fe/MgAlO/Fe in experiments (479% at 15K)

Disorder-induced TMR enhancement in Fe/Mg-Al-O/Fe
H. Sukegawa and YM, et al., PRB 86, 184401 (2012).

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

2. Spin-dependent tunneling conductance in magnetic tunnel
junctions with spinel-type MgAl2O4 barrier
Y. Miura, et al, PRB, 86, 024426 (2012).
K. Masuda and Y. Miura, PRB 96, 054428 (2017)

3. Electric field dependence of magnetic damping constantof Fe(001) surface
YM, M. Tsujikawa, M. Shirai, in preparation.
4. Magneto-crystalline anisotropy at interfaces of Fe(001)with various non-magnetic metals
Y. Miura, M. Tsujikawa, M. Shirai, J. Appl. Physics, 113, 233908/1-6 (2013).

Magnetization reversal by spin transfer torque (STT)
e
e



2

Damping torque(magnetic friction)Spin transfer torque
2Reduction of critical current density (Jc0) α：Magnetic damping constant(107A/cm2⇒105A/cm2)
MS：Saturation Magnetization

J c 0   M S H anti  2M S  t / P
J.C. Slonczewski, JMMM 159 (1996) L1.

Hanti±2πMS: Effective anisotropy field
P：Spin polarization
t：Thickness of FM layer

１. High spin polarization (P) with low resistance
2. Low damping constant(α) with perpendicular magnetic anisotropy(PMA)
Usually strong perpendicular magnetic anisotropy (PMA) is originatedto the large spin orbit interaction leading to large damping α

３．Small magnetization (Ms) with high Curie temperature
Ferrimagnetic materials

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

Voltage control of PMA and magnetic damping
Reduction of PMA and magnetic damping simultaneously
Voltage Control of Magnetic damping

Voltage Control of PMA
E≠0

E=0Large Ku

Small Ku

E=0
Large αE≠0Small αSimultaneous control of PMA and magnetic damping by applied voltage
E=0Large Ku,
Large αImprovement of control ofmagnetization dynamics ⇒E≠0
Small Ku,
Small αReduction of Writing Error

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
Theoretical studies of electric field dependence of PMA[Theory]
K. Nakamura, et al., PRL 102, 187201 (2009). Vac/Fe/Vac
M. Tsujikawa, and T. Oda, PRL 102, 247203 (2009). Vac/Pt/Fe/Pt/Vac
M. K. Niranjan, et al., APL 96, 222504 (2010). Vac/Fe/Vac
D. Yoshikawa et al., APL 7, 113005 (2014). MgO/Fe/MgO
M. Tsujikawa, et al., JAP 109, 07C107 (2011). Vac/Pt/(Au)Fe/MgO

Electric field dependence of magnetic damping is hardly investigated.

This work investigates the electric field effects of magnetic damping
constant of FM layer on the basis of the first-principles calculation.

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

Spin 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 is
calculated by the local atomic orbital.

i , ,

z

Eigenstates at eachk-point and band   0 g B / Feα⇒For Fesurface,50x50 isadopted.

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

Magnetic damping of 3d transition metal 2g 2 0 B2




Γ
k

VM S k nm nm
EF  Enk 2   2 EF  Enk 2   2

Scattering rate = (electron lifetime)-1

eV   

Intraband term
（conductivity term）

Damping α

0.01Interband term
（resistivity term）

Fe
0.001

0.001

0.01

0.1

1.0

 

Scattering rate  eV

We adopted the scattering rate of δ=1[mRyd]which reproduces the conductivity of bcc Fe at 100K.
J. Kunes and V. Kamversky, PRB 65, 212411 (2002).
A. Sakuma, JPSJ 81, 084701 (20012).

Damping α

0.01

Co
0.001

0.001

0.01

0.1

Scattering rate

1.0

 eV 

Local potential [eV]
Vloc(E)

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

－

O Mg O Mg O Mg O

a=2.833[Å]Charge density difference
ρ(E)-ρ(E=0)

E=+0.10V/nm＋ E=+0.05V/nm

Fe

Fe

Fe

Cu

Cu

Cu

Cu

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

E>0 :Increase of electron accumulation at Fe surface
E<0 :Decrease of electron accumulation at Fe surface

4.0

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

After T. Oda, et al., APEX 7, 113005 (2014)

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 for
occupied and unoccupied atomic
orbitals between different magnetic
quantum number, such as d(yz,zx)d(z2), d(yz,zx)-d(x2-y2), d(yz,zx)-d(xy)The matrix elements are non-zerofor occupied and unoccupied
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

E-EF [eV]234Large matrix element ofSecond order perturbation of SOI

d x y22

EPMA  ( ) 2o ,u ,ko, k ,  Lz u, k , 2 o, k ,  Lx u, k ,  u,k   o,k2

 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
Voltage dependence of PMA and magnetic damping constant of
Fe(001) surface and Fe/MgO(001) interface

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

2. It is opposite to that of PMA (perpendicular magnetic anisotropy).
3. Voltage dependence of magnetic damping can be attributed to spinconservation term between d(yz,zx) and d(x2-y2) of interfacial Fe atom .

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

2. Spin-dependent tunneling conductance in magnetic tunnel
junctions with spinel-type MgAl2O4 barrier
Y. Miura, et al, PRB, 86, 024426 (2012).
K. Masuda and Y. Miura, PRB 96, 054428 (2017)

3. Electric field dependence of magnetic damping constantof Fe(001) surface
YM, M. Tsujikawa, M. Shirai, in preparation.
4. Magneto-crystalline anisotropy at interfaces of Fe(001)with various non-magnetic metals
Y. Miura, M. Tsujikawa, M. Shirai, J. Appl. Physics, 113, 233908/1-6 (2013).

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

MTJs with perpendicular magnetization
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)

MTJs with interfacial perpendicular MCA
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

Purpose of this work
In order to achieve ultra high-density MRAM, we need further
enhancement of the thermal stability of the ferromagnetic layer of MTJs.
Perpendicular Perpendicular MTJ
or In-plane?

Cap(X)
Perpendicular
MCA

CoFeB

X: Nonmagnetic metal elements

X=Hf, Ti, V, Nb,Ta, Cr, W, Ru, Rh, Ir, Pd,
Pt, Cu, Ag, Au, Zn, Cd, Al, Mg

MgO
CoFeB
Buffer layer

We investigate MCA energy at the (001) interface between bcc-Fe and various
non-magnetic metal elements (X) on the basis of the first principles calculations.
・To find nonmagnetic-metals showing the perpendicular MCA at interfaces with Fe
・To obtain the fundamental understanding of the interfacial MCA

Calculation system
・VASP-PAW with plane wave basis set
・GGA for the exchange correlation term
・The Brillouin zone sampling with 24×24×2.

1) G. Kresse and J. Hafner, Phy. Rev. B 47, RC558 (1993).
2) P. E. Blöchl, Phy. Rev. B 50, 17953 (1994).
3) J. P. Perdew, et al., Phy. Rev. Lett. 77, 3865 (1996).

1. For non-magnetic metals elements (X), we assumed fct or bct structures
2. Construct super-cell of Fe/X(001) includimg 9 atomic layers of Fe and X.
3. The in-plane lattice constant is fixed to that of MgO.(a//=4.23/√2Å) aFe/X(001)=aMgO
4. X/Fe(001) interfacial structures are fully optimized along the perpendicular direction.
5．The MCA energy EMCA is defined to be positive for out-of-plane easy axis.
EMCA>0

EMCA<0MCA energy of Fe/X(001) interfaces (a//=aMgO)
2.0

1.49mJ/m2

1.61mJ/m2

MCA energy [mJ/m2]

1.0
0.0

Al

Ti V Nb Ta Cr W Os Rh Ir Pt Pd
HfRu

Cu Ag Au Zn Cd

Mg

-1.0

Fe/ FeMgOsurf.

-2.0
-3.0
-4.0

Elements having partiallyfilled d states

Elements without
partially filled d states-5.0
Chemical Trends
Experiments
Y. Miura, et al., JAP 113, 233908 (2013).
2
Fe/Cu=+0.32 mJ/m
M. metals
J. Pechan,
et al., PRB
52,elements
3045 (1995).
1. Fe(001)Kiinterfaceswith(RT)noble
or typicalmetal
2 (RT), R. Cabanel, el al., JAP 67, 5409 (1990).
Fe/Ag(001)Ki=+0.80mJ/m
tends to show
perpendicular
MCA except for X=Al.
2 (RT), B. Heinrich, et al., JAP 70, 5769 (1991).
Fe/Au(001)
2. Fe(001)Kinterfaces
withtransition elements having partially filled di=+0.47mJ/m/V4)(001)
Ki=-4μeV/atom(250K)
M. Farle,el al.,
Lett., 49, 658 (2000)(Fe4bands
tends
to show in-plane MCA
exceptfor Europhys.
X=Hf.

Second order perturbation of spin-orbit interaction
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 LDOSG  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(2)
i   E z( 2 ) i   E x( 2 ) i 
 E MCAWe directly estimated the second-order perturbative contribution of MCA
energy depending on each atomic site and spin-transition process.
ξFe=50meVξAg=200meV ξPd=200meV ξHf=350meVMCA energy of Fe(001) surface(a//=aMgO)
Second-order contribution to MCA energy

Y. Miura, et al., JAP, 113, 233908 (2013)

1.00
0.75
0.50
0.25
0.00
-0.25
-0.50
-0.75
-1.00



 L
2

Z

1

Surface Fe-d orbital
contributionμ1/μ2

x2-y2/xy zx/yz

yz/zx

xy/x2-y2

PRB 39, 865 (1989).

Bruno’s relation
2

 E MCA 

LDOS [states/eV/atom]

 ,G  12,  12  ,  ; i , i

Lz  Lx

E-EF [eV]

4

L

z

 Lx 

Ag/Fe(001) interfaces (EMCA=+0.768 [mJ/m2])
Second-order contribution to MCA energy

Y. Miura, et al., JAP 113, 233908 (2013).

0.022μB
2.774μB
2.461μB
2.541μBx  y ,  Lz xy , 222LDOS of Fe d states at Ag/Fe(001) interfaces is very similar to LDOS of Fe(001) surface
around Fermi level because of the absence of Ag d states around the Fermi level.

Pd/Fe(001) interfaces (EMCA=－0.616[mJ/m2])
Interfacial Pd atom mainly
contribute to the in-plane MCA
Relatively large induced spin
moment of interfacial Pd

yz ,  Lz z , 
2Second-order contribution to MCA energy

0.309μB
2.915μB
2.537μB
2.513μB

2

Y. Miura, et al., JAP 113, 233908 (2013).

Pd d orbital strongly hybridize with the Fe d orbital at the Pd/Fe(001) interface,leading to the significant change of the LDOS of Fe d orbital around EF.

Hf/Fe(001) interfaces (EMCA=+1.49[mJ/m2])
Second-order contribution to MCA energy

Spin down-up term of interfacial
Hf shown by yellow bar has large
positive contribution to MCA-0.186μB
2.484μB
2.450μB
2.476μBz ,  L x yz , 
2

Y. Miura, et al., JAP 113, 233908 (2013).

2

Hf is transition metal elementwith less than half d orbital, andit has large unoccupied d states.

The unoccupied states significantly contribute to the perpendicular MCA thorough thesecond perturbation from occupied spin-down states to unoccupied spin-up states.

Experiments

MCA of nonmagnetic
at Fe(001):
periodic t
Summary metalsof the fourth
topic
2

3
4
5
6

3

4

Li

Be

11

12

Na

Mg

19

X
(perpendicularmagnetization)X(in-plane
magnetization)

5

6

7

8

9

10

B

C

N

O

F

Ne

13

14

15

16

17

18

d s d s d s d s d s d s d s d s d s d s

1 2

2 2

3 2

5 1

5 2

6 2

7 2

8 2

10 1

10 2

Al

Si

P

S

Cl

Ar

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

K

Ca

Sc

Ti

V

Cr

Mn

Fe

Co

Ni

Cu

Zn

Ga

Ge

As

Se

Br

Kr

37

38

39

40

41

42

43

44

45

46

47

48

49

50

51

52

53

54

Rb

Sr

Y

Zr

Nb

Mo

Tc

Ru

Rh

Pd

Ag

Cd

In

Sn

Sb

Te

I

Xe

55

56

71

72

73

74

75

76

77

78

79

80

81

82

83

84

85

86

Cs

Ba

Lu

Hf

Ta

W

Re

Os

Ir

Pt

Au

Hg

Tl

Pb

Bi

Po

At

Rn

*

DOS

Nonmagnetic metal (fcc)dεEnergy

dγ
EF

s
EF

dε=dxy, dyz,dzx
dγ=dx2-y2, d3z2-r2

EF

1. Fe(001) interfaces with noble metals (Cu,Ag,Au) or typical metal elements(Zn,Cd,Mg) without d orbital around EF tends to show perpendicular MCA.
2. Fe(001) interfaces with elements having partially filled d orbitals (Pd, Pt, Rh, Ir,
Os, Cr, Nb, Ta, V, W, Ti) tends to show in-plane MCA except for Hf.
3. Hf/Fe(001) show the strong perpendicular MCA corresponding to Fe/MgO(001).

Summary of this talk
MRAM

Magnetic censer

HDD read-out-head

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

Corresponding to SQUID

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

Required properties for
spintronic materials

The fourth topics

The first andsecond topics

High spinpolarization
with low
resistance

Strongperpendicul
ar magnetic
anisotropy

Small magnetic damping
and small saturation
magnetization
The third topics