2019/8/23

Role of materials in spintronics

Mie University

Spintronic Design Course

Spintronicdevices

Spin-related properties

Computational Materials Design (CMD@) Workshop

Magnetization

Spintronic  Design  Magnetic control II

Magnetic
thin films

HDD

Perpendicular MA

MRAM

Magnetic (tunnel)
resistivity
Spin (Hall) current

Materials Design based on band structures

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

Artificialmultilayer
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

1988(1995)

Discovery of
Magnetoresisitivity

2006

Giant/Tunnling
Magneto-resisitivity

MRAM(4Mb) Products

MRAM(256Mb) Products•Quantum mechanics !
•No use of empirical parameters !
•High accuracy in computations !

1A

2A

3A

4A

5A

6A

7A

81B

2B

11520676B

87B

9010B C N O F Ne

1219Key technology

5B

2413d-electron systems

Na Mg

14B

sp-electron systems He

3Li Be03B

1H

2122232425262728

1415161718

Al Si P S Cl Ar
2930313233343536

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

Magnetization
direction

2007
In-plane MA

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

37

38

3940

4155

56

57

72

7387

88

2010

First principles calculations①Kohn-Sham equation

Coulomb potentiali

Nii 1, i  E F

76

4577

46

78

47

79

48

80

49

81

50

82

51

83

52

84

53

85

54

86

89

f-electron systems
5960

61

62

63

64

65

66

67

68

69

70

71

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu90

Strong correlated systems,
Exited states, etc.

91

92

93

94

95

96

97

98

99

100

101

102

103

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

Goal: Prediction of material properties
from the periodic table

Eigenvalues and eigenstates of electron orbitals in atoms

ExcLDA n    n(r ) exLDA n(r ) ①Orthogonalization in orbitals

4si i

3d

wave function (basis)

 j | i  0

1s

3s②Total energy
Etotal 44

 nlm (r )  Rnl (r )Ylm

2

eff

75

exchange correlation potential V (r) V (r) (r)   (r)c43

Fr Ra Ac

Unresolved issues

By current（spin injection）

By Magneticfield74

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

58

Magnetizationswitching

42Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

2sKohn-Sham eigenvalues(band structure, density of states)

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

double counting term

②Spatial spread of wave function
Hybridization in crystals

Li :1s22s
Na :1s22s22p63s
K :1s22s22p63s23p64sAtomic corespxpzpy

1

2019/8/23

Hybridization：bonding and anti-bonding orbitals
Antibonding stateElectrons in crystal

Free-electron-like11  2 a 2 2  V0    2k22w

0

21
1  2 2b V2  2 | V | 1

1

Homo bonds

Polar bonds

Antibonding

Antibonding

2

2V1

Bloch function

2
1Bonding

2V12V2 2  2  Vatom (r )  c   cBonding

Bulk modulus Wigner-Seitz radiuswnd (10  nd )20Density of states, D()w= 5 eV (3d)6 eV (4d)7 eV (5d)dn( )d

LDA results vs. experiments

Cohesive energy

EFD( )  D( )d  nEF

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

dBand structures of transition-metals
Nv=6Magnetism in transition metals
Non-spin polarized

Nv=1055W3d
Antibonding bonding

> W4d
> W5d

433EFTi< EFCr< EFNi

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

2A

3A

4A

5A

6A

7A

81B

2B

34B

5B

6B

7B

567891102He
42010B C N O F Ne

1213AFM FMNa Mg
1923B

1HLi Be

212223242526271415161718

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
0–8–6–4–20

Energy (eV)Fermi level

1AFe (bcc)

4204 –8
5–6–4–20243dSpin polarized

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

D3d(EF)> D4d(EF)> D5d(EF)Density of states (/eV-atom)

V (bcc)Band structure

4d4

Minority

3

Majority

ID(EF)

Nv=4uk (r  R j )  uk (r )Orthogonal   nNon-spin PolarizedEC    D( )(   0 ) d

 k (r )  eik r uk (r )Cohesive energy and spin polarization in transition-metals

0 v | c  0atomic-liked-band structures and cohesive energy oftransition-metalsw

Density ofstates, D() 2  V (r )  v   v
 2V (r  R j )  V (r )Bonding state2

Stoner criteria
ID(EF)>1

1

0–8–6–4–2

0

Energy (eV)2

4

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

2

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Band structures and spin polarization in transition metal monolayers

Ferromagnetism in transition metal monolayers

LDA results

Magnetic moments

z2Monolayer on Ag(001)

3RhOsIr

4d5d

1

–3

–2–1

0

12

3

4xyx2-y2

Energy (eV)
5V(001) monolayer

Energy difference between FM and AFM

44

Mminority

Majority

33

2

2

1

1

0–4

–3

–2

–1

0

1

Energy (eV)

2

30–4

4

–3

–2

–1

0

12

3

Free-standing
monolayer

E=EAFM-EFM (mRy)

Density of states (/eV-atom-spin)

RuV bulk

2Spin-polarized

4monolyar
on Ag(001)
S. Blügel, Phys. Rev. Lett. 68, 851(1992)

Energy (eV)Ti

Effect of substrates to magnetism in transition metal monolayers

Cr Mn Fe Co Ni

MTJ device

6EF5V

Magnetocrystalline anisotropy (MCA)

Total energy difference

Fe(001) monolayer (a=2.87Å)Density of states (/eV-atom)

Coxy,yz

0–45Fe3d4bandwidth

Density of states (/eV-atom)5

Non-volatility
Large capacity
Ferromagnetic High-speed[1]

43Many Applications

Insulator

2• MRAM• Magnetic sensor

Ferromagnetic10–8–404[1] S. Yuasa, et al., Nature Materials 3, 868 (2004).

Energy (eV)P. Ferriani et.al., Phys. Rev. B 72, 024452 (2005)

Substrates
Density of states (/eV-atom)

Ag (a=2.89Å)Pd (a=2.75Å)W (a=2.23Å)In‐plane MCA

EFLarge advancefor applications

Out‐of‐plane MCA

EFEF
Energy (eV)Energy (eV)We, here, design thinfilms with large MCA

Energy (eV)First principles calculations of MCA energy
Spin-orbit coupling

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

Perturbation method of MCA energy

Admixture of spin-up
and down components

EMCA ( )  E SOC ( x)  E SOC ( z ) E dd  E ud

SOC strength, (r)~50 meV in
3d-metals

E dd  E dd ( x)  E dd ( z )Magnetocrystalline anisotropy energy

EMCA  Etotal   Etotal  

EMCA < 0 : in-plane MCA

 E  0 , m 0   E  0 , m 0       k ,i     k ,i  k  ioioEex  2 oForce theorem



EF

EMCA > 0 : Perpendicular MCASpin‐upo | L z | u2 o | L x | uu  ou

2Spin‐downE ud  E ud ( x)  E ud ( z )2 o | 3L  L | oEex o

2z2



3

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Rule in origin of MCA

Band structure of Fe monolayer

Positive EMCA

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

energyenergyx2-y2(m=2)

221

100xz, 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−1−2−3MCA depends sensitively on orbitals states between EF

Rule in the origin of MCA

dd

xy, x2-y2Majority−2MinorityX
a=5.45a.u.

M−3−2−101

DOS (states/eV)2

MCA energy in 3d transition metal monolayers
Perpendicular MCA

EMCA= 0.19 meV/atom
EMCA(k) (eV)ddEFxz, yz−1In-plane MCAz2EF

Minority-spin

Discussion from perturbation theory

50

energyenergy−52xy, x2-y2 (m=2)
xz, yz (m=1)

without SOC

EFz2 (m=0)
xz, yz (m=1)

1xy, x2-y2 (m=2)0|<xz,yz|Lz|xz,yz>|2−1

Positive EMCA
−2

Minority-spin


MX



> |<xz,yz|L |z >|x2

2

Negative EMCA

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

PMA arises from SOC
between m=1 orbitals

Effect of substrates to MCA in transition metal monolayers

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

EMCA  E SOC    E SOC  Fe dz2

EMCA (meV/a2)

Perpendicular MCA

Substrate

Energy (eV)z2-r2 (m=0)

z2 (m=0)EF

Energy (eV)z2 (m=0)xz,yz(m=1)

xy (m=2)

D4hxy, x2-y2 (m=2)
xz, yz (m=1)

xy, x2-y2 (m=2)
xz, yz (m=1)

EF

Surface state

Free-standing
Fe monolayer

0.19

Fe/MgO

1.28

Au3/Fe3/MgO

0.94

FeO
O pz
Week
hybridization

LDA
Nakamura et.al., PRB 81, 220409, (2010)

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

Origin ofinterfacial perpendicular MCA
Fe dz2 - O pz hybridization

42019/8/23

Fe dz2 – O pz hybridization at Fe/MgO interface
energyFe dz2Anti-bonding

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

energy2.07 Ådz2EFOxz, yz
xy, x2-y2O pz
Weekhybridizationpz
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

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

Control of MCA by tuning atomic-layer alignments

MCA of 3d transition metal thin films with seven-atomic-layer
FeInterfaces, superlattices, multilayers

Mn, Co, or Ni
Fe

EMCA (meV/a2)

Thin films with large
perpendicular MCA,
consisting of only 3d metals
202A

3A

4A

5A

6A

7A

8

1B

2B

3B

4B

5B

6B

7B

5678912HHe

34Li Be
111220

10B C N O F Ne13Na Mg
190EMCA(k) (meV)

1A

1415161718

Al Si P S Cl Ar
2122232425262728293031323334353839404142434445464748495051525357

7273747576

7778

7980818283

84

85

0AssumedMn

0.3symmetric structure

along z-axis Ni xy

86

Energy (eV)

56

5NiCo

surface Fe layer

54

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

107-layerFe film

−50.6bcc-layer stacking

36

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr3715Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn

0.0

I1II2(X+M)/2M

36VI

Fe/Fe/Ni/Fe/Ni/FeFe film

E-field-control of magnetism

Upper limit for perpendicular MCA in 3d thin films
Fe2/Ni/Fe/Ni/Fe/Ni/Fe/Ni/Fe2④GuessV5

A candidate for perpendicular MCA−0.6

Search for 3d thin films with giant perpendicular MCA

4IV

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

−0.3

3III

Ni x2-y2Electrons⑥Guess
Fe2/Ni/Fe/Ni/Fe/Fe/Fe/Ni/Fe/Ni/Fe2

Electric field

Fe2/Ni/Fe/Ni/Fe/Ni/Fe2③GuessChargeEMCA (meV/a2)

Fe2/Ni/Fe/Ni/Fe/Ni/Fe/Ni/Fe/Ni/Fe2

2⑤Guess

Fe2/Ni/Fe/Ni/Fe2

MgO|Fe/Fe/Ni/Fe/Ni/Fe/Fe|MgO②Full search

Tetragonal Fe0.4Co0.6
c/a=1.2~1.2

at the nano-scale witha low-energy power
consumption

leading to semiconductor
technology

Magnetic field
Currents

Magnetizationor spins Non-volatile

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

1

Thermal stability limit KuV/kBT> ~60

Pure Fe thin films

Fe2/Ni/Fe2①Full search0Weller et.al., IEEE Trans. Magn. 36, 10 (2000)

57911

Number of layers

13

Large capacity
High-speed
Low power

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An example:
Voltage-assist magnetization switching

E-field-induced modification of magnetocrystalline anisotropy
Experiment
Pt/Co/Gd1-xOx [8], [9]Au/Fe/MgO [5]Voltage-assist

Giant E-field effects
over 5000 fJ/Vm

Au/FeCo/MgO [6], [7]FePt/Ionic riquid [1]First observation

Demonstration of switching2007 2008 2009 20102014

2012

2016

TheoryＥＭＣＡ

3d transition-metal surfaces[2]ＥＭＣＡ

3d transition-metal monolayers[3]ＥＭＣＡ

Pt/Fe/Pt (001)[4][1] M. Weisheit, et al., Science 315, 349 (2007). [5] T. Maruyama, et al., Nat. Nanotech. 4, 158 (2009).
[2] C.-G. Duan, et al., Phys. Rev. Lett. 101, 137201 (2008). [6] T. Nozaki, et al., Appl. Phys. Lett. 96, 022506 (2010). [9] U. Bauer, et al., Nat. Mater. , 14, 174 (2015).
[3] K. Nakamura, et al., Phys. Rev. Lett. 102, 187201 (2009).[7] Y. Shiota, et al., Nat. mater. 11, 39 (2010). [10] T. Nozaki, et al., Phys. Rev. Appl. 5, 044006 (2016).
[4] M. Tsujikawa, et al., Phys. Rev. Lett. 102, 247203 (2009). [8] Chong Bi, et al., Phys. Rev. Lett. 113, 267202 (2014).

Control of magnetism of metal thin films by electric field

Electric-field-induced charges at surfaces

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)….

Redistribution in charge/spin densities at surfaces/interfaces by E-field.

MgO/Fe/Au(001)
Negative
Voltage
Positive
VoltageDuan et.al., PRL101, 137201 (2008),
Nakamura et.al., PRL102, 187201 (2009); PRB 80, 172402 (2009),
Tsujikawa et.al., PRL102, (2009).

 Curie temperature (TC)

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

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

MgO/Co/Pt(111)
Negative
VoltageFemonolayer

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

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

0.000–20–0.001–40–0.002

Gerhard et.al., Nat. Nanotech., 5, 792 (2010)

–0.5

–40

–1.0

VS

0–80

3–9–6

Minority

0.9
5*

0.6

10.0

EF–0.3
3–0.6

–2

54

3–0.9 Minority-spin–3

MX



–2

02

4

Change in band structure around Fermi level

External E-field
[001]
[100]

9EMCA  E()  E()
0.2

0.02

0.1

0.01

0.0

0.00

–0.1

–0.01

–0.2
0.0

DOS (states/eV spin)

6–0.02
0.2

0.4

0.6

0.8

1.0

1.2

1.4

morbit=m001-m100 (B)

–1

Energy (eV)

EF

10.3

3(a=5.45a.u.)

1: dz2 (m=0) 3: dx2-y2 (m= 2)
4: dxy (m= 2) 5, 5*: dxz,yz (m= 1)500

Modification of MCA energy of Fe monolayer

EMCA （meV/atom）

Majority–3

Position along z‐axis (Å)(a=5.45a.u.)
Minority-spin

S+C

S–3

Modification of band structure of Fe monolayer by electric field–4

0.0–20

Position along z‐axis (Å)

10.5

0–60 etc.

Zero field
1 V/Å

n–60

 Magnetic phase-transition (bcc Fe vs fcc Fe)

Energy (eV)VS （V）

0Hibino et.al., (2015)
Nakamura et.al., J. Korean Phys. Soc. 63, 612 (2013)

Fe surface

n,m (a-2)

 Magneto-optical conductivity

1.0n=n1V/Å-nzero 0.001mn, (10-3/a2)

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

VS （V）

PositiveVoltage

 Magnetic moments–4＋―Curie temperatures

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

2Eext

External E-field (V/Å)

The MCA is modified by an E-field
due to the change in band structures around EF.
Change of MCA energy

Nakamura et.al., PRL102, 187201 (2009)62019/8/23

Modification of MCA energy at MgO/Fe interface

Comparison to experiments

TheoryCo/Pt(111)

MgO/FeB/MgO

𝑀∝ 1

0.6

Co

0.5

Pt

0.4

M/Ms

Experiments

Theoryexperiments

830

320

0.7+

𝑇

5 V/nm

0.3
0.2

𝑇5 V/nm

TC
TC

20K

10K



0.26

0.18

0.1
0.0600

MgO/Co/Pt(111)

700

800

T (K)

900

Agreed with experiments qualitatively

MgO
Co 2~3原子層Pt

0.2V/nm
Nozaki et.al., Appl. Phys. Express 6, 123001 (2013)

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

Shimabukuro, Physica E , 42, 1014 (2010)

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

7