2020/8/22

Role of materials in spintronics

Mie University
Computational Materials Design (CMD ) Workshop
Spintronic Design Course

Spintronicdevices

Spin-related properties@Magnetization

Spintronic  Design  Magnetic control II

Magnetic
thin films

Materials Design based on band structures

HDD

Perpendicular MA

MRAM

Magnetic (tunnel)
resistivity
Spin (Hall) current
Spin Seebeck/Peltier
effectKohji Nakamura
Mie University

Spin (orbital) torque

Outline Introduction
 Electronic structures and magnetism in transition-metals
 Electronic structures and magnetism at surfaces/thin films
 Control of magnetism by tuning atomic-layer alignments
 Control of magnetism by external electric field Summary

Artificial
multilayer
thin-films

Magneticfield

Magnetic domain
memoryElectricfield

Spin microwave/mill-meter wave
oscillator

・・・

Heat

Spin diode/transitor

Requiredhigh-performance

Light・・・

Pressure Current
External-field
response

An example of spintronic development

Role of first principles calculations in materials design(2003 FeCoB/MgO-MTJ)

1857
Discovery of
Magnetoresisitivity

1988(1995)

2006

Giant/Tunneling
Magneto-resisitivity•Quantum mechanics !
•No use of empirical parameters !
•High accuracy in computations !

MRAM(4Mb) Products

1A

30

By Magnetic
field

4A

5A

6A

7A

81B

2B

3B

4B

5B

6B

7B

02

sp-electron systems He
451920678910B C N O F Ne

1213d-electron systemsNa Mg

1Key technology

Magnetization
switching

3ALi Be
11

Magnetization
direction

2A

1H

2122232425262728

1415161718

Al Si P S Cl Ar
29303132

33

3435

36

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

2007
In-plane MA

Out-of-plane MA (PMA)2009
Fe/MgOInterfacial PMA•Interpretation of experiments•Understanding•Prediction
with no restriction of materials

3738

3940412010
By current（spin injection）

Strong correlated systems,
Exited states, etc.

43444546

47

48

49

50

51

5253

54

Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
55

56

57

72

73

74

75

76

77

78

79

80

8182

83

84

85

86

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
87

88

89

f-electron systems

Fr Ra Ac
58

Unresolved issues

425960

61

62

63

64

65

66

67

68

6970

71

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
9091

92

9394

95

96

97

98

99100

101102103

Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr

Goal: Prediction of material properties
from the periodic table1

2020/8/22

First principles calculations①Kohn-Sham equationexchange correlation potential
ExcLDA n    n(r ) exLDA n(r )  V (r) V (r) (r)  (r)2effcCoulomb potentiali

 Introductioni i Electronic structures and magnetism in transition-metals

wave function (basis) Electronic structures and magnetism at surfaces/thin films②Total energy
Etotal  Control of magnetism by tuning atomic-layer alignments
Kohn-Sham eigenvalues(band structure, density of states)Nii 1, i  E F

 Control of magnetism by external electric field

 11
VC r n r dr    vexc r    exc r  n (r ) dr    Z VC ,  R  2   2 

 Summarydouble counting term

Eigenvalues and eigenstates of electron orbitals in atoms

Hybridization：bonding and anti-bonding orbitals
Antibonding statea 1
1  2 2b 1
1  2 
2

①Orthogonalization in orbitals

 nlm (r )  Rnl (r )Ylm

 j | i  01s

23s
Li :1s22s

Bonding state

Na :1s22s22p63s

2s

K :1s22s22p63s23p64s
Atomic core

②Spatial spread of wave function
Hybridization in crystals

V2  2 | V | 1spxpz

1

Homo bonds

Polar bonds

Antibonding

Antibonding

2V1

2

2
12V12V2py
Bonding

Bonding22020/8/22

Occupation of electrons

Electrons in crystal
Free-electron-like
 2

 
 V0   
 2
k22



w

0

1
H2+

2

3

H2He2+

stable4

Number ofelectrons

Density ofstates, D()

 2
 
 V (r )  v   v
 2
V (r  R j )  V (r )He2unstable

Bloch function

 v | c  0atomic-like
 2

 
 Vatom (r )  c   c
 2
Magnetism

LDA results vs. experiments
1A

Cohesive energy

Non-spin Polarizeduk (r  R j )  uk (r )Orthogonal   nCohesive energy and spin polarization in transition-metals

 k (r )  eik r uk (r )Question:Why do ferromagnetism
appear only in Fe, Coand Ni?

2A

3A

4A

5A

6A

7A

81B

2B

3B

4B

5B

6B

7B

0

12HHe

34

5111213Na Mg
1920

678910B C N O F NeLi Be

1415161718

Al Si P S Cl Ar
21222324

25

26

27

28

2930

3132

33343536

Bulk modulus Wigner-Seitz radius

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
373839404142434445464748495051

525354Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
5556577273747576777879808182838485

86

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

V. L. Moruzzi, J.F. Janak, A.R. Williams,
Calculated electronic properties ofmetals (Pergamon Press, New York, 1978)

Magnetic order

Transition
Temperature(K)Crystalstructure

Number ofvalenceFe

Ferromagnetic

1043

bcc

8Co

Ferromagnetic

1388

hcp

9Ni

Ferromagnetic

627

fcc

103

2020/8/22Band structures of transition-metals
Nv=6Non-spin polarized

Nv=1055Band structure
D3d(EF)> D4d(EF)> D5d(EF)
Antibonding bonding

W3d
> W4d
> W5d

Density of states (/eV-atom)

V (bcc)
4332A

3A

4A

5A

6A

7A

81B

2B

34B

5B

6B

7B

567891102He
410B C N O F Ne

1213

AFM FMNa Mg
1923B

1HLi Be

20212223242526

27

1415161718

Al Si P S Cl Ar
282930313233343536

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr

2373839404142434445464748495051525354Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
11555657727374757677787980818283848586

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn
0–8–6–4–2

02

Energy (eV)04 –8
5–6–4–2

0

243dSpin polarized

LDA results
Density of states (/eV-atom-spin)

Fermi level

1AFe (bcc)

4EFTi< EFCr< EFNiJ. Kübler, Theory of itinerant electron magnetism (Oxford University Press, Oxford, 2000)

4d4Minority

3

Majority

ID(EF)

Nv=4Magnetism in transition metals

2Stoner criteria
ID(EF)>1

10–8–6

–4–2

0

2

4

J. Kübler, Theory of itinerant electron magnetism (OxfordUniversity Press, Oxford, 2000)

Energy (eV)Band structures and spin polarization in transition metal monolayers
LDA resultsz2
Density of states (/eV-atom)

5

 Introduction
 Electronic structures and magnetism in transition-metals
 Electronic structures and magnetism at surfaces/thin films

 Control of magnetism by external electric field Summary

3xy,yzV bulk

210–4

–3

–2

1234234xyx2-y2

V(001) monolayer
44

Mminority

Majority

322

1

10–4

0553–1

Energy (eV)Spin-polarized
Density of states (/eV-atom-spin) Control of magnetism by tuning atomic-layer alignments

4–3

–2–1

0

1

Energy (eV)

23

40–4

–3

–2–1

0

1

Energy (eV)42020/8/22

Ferromagnetism in transition metal monolayers

Effect of substrates to magnetism in transition metal monolayers

Co4dbandwidthRuRh

Density of states (/eV-atom)

FeMonolayer on Ag(001)

3d5d6EF543210–8–404Energy (eV)P. Ferriani et.al., Phys. Rev. B 72, 024452 (2005)

Substrates

E=EAFM-EFM (mRy)OsIrmonolyaron Ag(001)
S. Blügel, Phys. Rev. Lett. 68, 851(1992)

Ti

VCr Mn Fe Co Ni

Density of states (/eV-atom)

Ag (a=2.89Å)Energy difference between FM and AFM
Free-standing
monolayer

Total energy difference

Fe(001) monolayer (a=2.87Å)Magnetic moments

Pd (a=2.75Å)W (a=2.23Å)

EFEFEF
Energy (eV)Energy (eV)Energy (eV)

Magnetocrystalline anisotropy (MCA)MTJ deviceNon-volatility
Large capacity
Ferromagnetic High-speed[1] Introduction

Insulator

 Electronic structures and magnetism in transition-metals
 Electronic structures and magnetism at surfaces/thin films
Magnetocrystalline anisotropy (MCA)
 Control of magnetism by tuning atomic-layer alignments
 Control of magnetism by external electric fieldFerromagnetic[1] S. Yuasa, et al., Nature Materials 3, 868 (2004).

In-plane MCA

Large advancefor applications

Many Applications• MRAM• Magnetic sensor

Out-of-plane MCA

 SummaryWe, here, design thinfilms with large MCA

5

2020/8/22

Perpendicular MCA of Fe thin film on MgO(001): experiments

First principles calculations of MCA energy
Admixture of spin-up
and down components

Spin-orbit coupling
1 1 dV
H SOC  2  σ   (r )  z
4c r dr    z 

SOC strength, (r)~50 meV for 3d-metals
Magnetocrystalline anisotropy energy

EMCA < 0 : in-plane MCA

EMCA  Etotal    Etotal  ~0.1 meV/atom

EMCA > 0 : Perpendicular MCAForce theorem E  0 , m 0   E  0 , m 0       k ,i      k ,i  k  ioioRule in origin of MCA in Edd

Perturbation method of MCA energy


EMCA ( )  ESOC E( x)  E
 EddSOC( z)EFoudo | L z | u

Spin‐up2 o | L x | uu  ouoEex

E dd  E dd ( x)  E dd ( z )  2 E dd   2 Spin‐down2E ud  E ud ( x)  E ud ( z )2 o | 3L  L | oEex o2z2o | L z | uu2 o | L x | uu  oPositive EMCA

Negative EMCA|<o|Lz|u>|2|<o|Lx|u>|2

energyenergyxy, x2-y2 (m=2)
xz, yz (m=1)

xy, x2-y2 (m=2)
xz, yz (m=1)

EF2z2 (m=0)

EFz2 (m=0)

xz, yz (m=1)

xz, yz (m=1)xy, x2-y2 (m=2)

xy, x2-y2 (m=2)|<xz,yz|Lz|xz,yz>|2|<xz,yz|Lx|z2>|2Perpendicular MCA

In-plane MCA

R. Wu, A.J. Freeman, J. Magn. Magn. Mater. 200, 498(1999)

62020/8/22

Band structure of Fe monolayer

Rule in the origin of MCA
Surface statex2-y2(m=2)

xz,yz(m=1)

xy (m=2)D4hz2-r2 (m=0)

EMCA(k) (eV)

EMCA= 0.19 meV/atom
Discussion from perturbation theory

50energy

2221100

xy, x2-y2 (m=2)
xz, yz (m=1)

without SOCz2

EFxz, yz−1−1−2xy, x2-y2

Majority

dd

xy, x2-y2 (m=2)0|<xz,yz|Lz|xz,yz>|2
Positive EMCA

−2MinorityMX
a=5.45a.u.

−3z2 (m=0)
xz, yz (m=1)−1

Minority-spin−3dd

Energy (eV)Energy (eV)

EF1

EF

energy−5−2−101−22

Minority-spinMX

DOS (states/eV)

MCA energy in 3d transition metal monolayers

> |<xz,yz|L |z >|x22

Negative EMCA

PMA arises from SOC
between m=1 orbitals

Effect of substrates to MCA in transition metal monolayers

Perpendicular MCA

Substrate

Perpendicular MCA(a=aCu)R. Wu, A.J. Freeman, J. Magn. Magn. Mater.
200, 498(1999)
R. Wu, A.J. Freeman, J. Magn.
Magn. Mater. 200, 498(1999)7

2020/8/22

Perpendicular MCA at Fe/MgO(001) interface: Theory

Fe dz2 – O pz hybridization at Fe/MgO interface

EMCA  E SOC    E SOC  

0.19

Fe/MgO

1.28

Au3/Fe3/MgO

0.94

FeOxz, yzxy, x2-y2O pz

OWeekhybridization

O pzLDANakamura et.al., PRB 81, 220409, (2010)energyEFFe

Weekhybridization

Anti-bondingdz22.07 ÅFe dz2

EMCA (meV/a2)
Free-standing
Fe monolayer

energyFe dz2pz
Bonding

Fe/MgO interface structure
Urano and Kanaji, J. Phys. Soc. Jpn. 57, 3403, (1988 )Li and Freeman, Phys. Rev. B 43, 780, (1991)
Meyerheim et.al., Phys. Rev. B 65, 144433, (2002)

Femonolyar

Origin ofinterfacial perpendicular MCA
2Fe dz - O pz hybridization

Oin MgO
Shimabukuro, Physica E , 42, 1014 (2010).
Nakamura et.al., PRB 81, 220409, (2010)

Control of MCA by tuning atomic-layer alignments
Interfaces, superlattices, multilayers
Thin films with large
perpendicular MCA,
consisting of only 3d metals

 Introduction
 Electronic structures and magnetism in transition-metals
 Electronic structures and magnetism at surfaces/thin films
 Control of magnetism by tuning atomic-layer alignments

1A

2A

3A

4A

5A

6A

7A

81B

2B

5B

6B

7B

0234

5Li Be111978910

B C N O F Ne

122061314151617

18

Al Si P S Cl Ar
21222324252627282930313233343536

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr37

 Summary

4BHeNa Mg

 Control of magnetism by external electric field

3B

1H38394041424344454647484950515253

54Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
55

565772737475767778

7980

8182838485

86

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

82020/8/22

MCA of 3d transition metal thin films with seven-atomic-layer

Search for 3d thin films with giant perpendicular MCA
Upper limit for perpendicular MCA in 3d thin films

FeMn, Co, or Ni
FeFe2/Ni/Fe/Ni/Fe/Ni/Fe/Ni/Fe2④Guess

3⑥Guess
Fe2/Ni/Fe/Ni/Fe/Fe/Fe/Ni/Fe/Ni/Fe2

EMCA(k) (meV)2015
1050Assumed

7-layer
Fe film
MnNiCo−50.6bcc-layer stacking

surface Fe layer

Energy (eV)0.3symmetric structure

along z-axis Ni xy

0.0

I1

II2

4IV

V56VI

2(X+M)/2M

Fe/Fe/Ni/Fe/Ni/FeFe film

MgO|Fe/Fe/Ni/Fe/Ni/Fe/Fe|MgO
Tetragonal Fe0.4Co0.6
c/a=1.2~1.2

1

Thermal stability limit KuV/kBT> ~60

Pure Fe thin films

Fe2/Ni/Fe2①Full search

A candidate for perpendicular MCA


Fe2/Ni/Fe/Ni/Fe2

Burkert et.al., PRL93,027203 (2004)

Ni x2-y2−0.6⑤Guess②Full search

Hotta et.al., PRL110, 267206 (2013)

−0.3



3
III

Fe2/Ni/Fe/Ni/Fe/Ni/Fe/Ni/Fe/Ni/Fe2
EMCA (meV/a2)

EMCA (meV/a2)

Fe2/Ni/Fe/Ni/Fe/Ni/Fe2③Guess0Weller et.al., IEEE Trans. Magn. 36, 10 (2000)

57911

Number of layers

13

E-field-control of magnetism
Electrons Introduction

Electric field

Charge Electronic structures and magnetism in transition-metals
 Electronic structures and magnetism at surfaces/thin films
 Control of magnetism by tuning atomic-layer alignments
 Control of magnetism by external electric field Summaryat the nano-scale witha low-energy power
consumption

leading to semiconductor
technology

Magnetic field
Currents

Magnetizationor spins Non-volatileLarge capacity
High-speed
Low power

9

2020/8/22

Control of magnetism of metal thin films by electric field

An example:
Voltage-assist magnetization switching

Magnetocrystalline anisotropy Magnetocrystalline anisotropy (MCA)
Weisheit et.al., Science 315, 349 (2007)
Maruyama et.al., Nature Nanotech. 4, 349 (2009)
Duan et.al., PRL101, 137201 (2008)
Nakamura et.al., PRL102, 187201 (2009); PRB 80, 172402 (2009)
Tsujikawa et.al., PRL102, (2009)….

Voltage-assist

MgO/Fe/Au(001)
Negative
Voltage
Positive
Voltage Curie temperature (TC)

Chiba et.al., Nat. Mater. 10, 853-856 (2011)
Oba et.al., PRL114, 107202 (2015)

Maruyama et.al., Nature Nanotech. 4, 349 (2009) Dzyaloshinskii-Moriya interaction (DMI)

Curie temperatures

Nawaoka et.al., Appl. Phys. Express 8, 063004(2015)
Nakamura et.al., (2015)

MgO/Co/Pt(111)
Positive
Voltage Magnetic moments

Negative
Voltage

Obinata et.al., Sci. Rep. 5, 14303 (2015)

ＥＭＣＡ

 Magneto-optical conductivity

ＥＭＣＡ

Hibino et.al., (2015)
Nakamura et.al., J. Korean Phys. Soc. 63, 612 (2013)

ＥＭＣＡ

Chiba et.al., Nat. Mater. 10, 853-856 (2011)

 Magnetic dumping
Okada et.al., Appl. Phys. Lett. 105, 052415 (2014)

 Magnetic phase-transition (bcc Fe vs fcc Fe)
Gerhard et.al., Nat. Nanotech., 5, 792 (2010)

 etc.

Modification of band structure of Fe monolayer by electric field
2Duan et.al., PRL101, 137201 (2008),
Nakamura et.al., PRL102, 187201 (2009); PRB 80, 172402 (2009),
Tsujikawa et.al., PRL102, (2009).

Eext

Eext

＋―Zero field
1 V/Å
Majority–0.001–40–0.002

VS （V）

–20

n0.5

00.0

–20

–0.5

–40

–1.0

VSS-–30

3

Position along z‐axis (Å)–80–9–6S+C–3036Position along z‐axis (Å)

5*0.6150EF–1

1

0.3
0.0

EF

–0.3
3–0.6

54

3–0.9 Minority-spin

–3–4



–4

–2

024MX



Change in band structure around Fermi level

DOS (states/eV spin)
External E-field
[001]
[100]

–60

–60

n, (10-3/a2)

0.000

n,m (a-2)

m0

Fe surface

0.9

1

1.0

n=n1V/Å-nzero 0.001(a=5.45a.u.)
1: dz2 (m=0) 3: dx2-y2 (m= 2)
4: dxy (m= 2) 5, 5*: dxz,yz (m= 1)

Minority-spin

Minority–2Femonolayer
VS （V）

Energy (eV)Redistribution in charge/spin densities at surfaces/interfaces by E-field.

Energy (eV)Electric-field-induced charges at surfaces

Change of MCA energy

910

2020/8/22

Modification of Curie temperature of Co thin film on Pt

Modification of MCA energy at Fe/MgO

EMCA=E()-E(↑)

Experiments𝑀∝ 10.6

Co

0.5

Pt

0.4

M/Ms

1.2

Theoryexperiments

TC

830

320

TC

20K

10K



0.26

0.18

0.7+

Theory1.4

EMCA （meV/atom）

Co/Pt(111)

𝑇5 V/nm0.30.2𝑇5 V/nm0.1-200V

1.00.0600+200VMgO/Co/Pt(111)

700

800

T (K)

900

Agreed with experiments qualitatively

0.8
MgO
Co 2~3原子層Pt

0.6–1012

External E-field Eext (V/Å)
Nakamura et.al., PRB 81, 220409 (2010)

0.2V/nm
Shito et.al., Appl. Phys.
Express 2, 063001 (2009)

Oba et.al., PRL114, 107202 (2015)

Summary

Spintronic  Design  Magnetic control
Artificial multilayer
thin-films

magnetic properties

Importance ofunderstanding
electronic structures

Perpendicularmagnetization
Tunnel magneto
resistanceSpin current andtorqueetc.

Key ideas for PMCA
•Interface-induced PMCA•

Atomic-layer-alignment-tuned
PMA (artificial multilayers) Crystal structures and atomic arrangements
 The number of valence electrons
 Eigenvalues and eigenstates of s, p, d, f orbitals
 d-d (d-sp) hybridization

11