2017/9/4

Role of materials in spintronics

Mie University

Spintronicdevices

Spin-related properties

Computational Materials Design (CMD@) Workshop

Spintronic Design Course

Magnetization

Magnetic
thin films

Spintronic  Design  Magnetic control II

HDD

Perpendicular MA

MRAM

Magnetic (tunnel)
resistivity
Spin (Hall) current

Materials Design based on band structures

Spin Seebeck effectKohji Nakamura
Mie University

Spin (orbital) torque

Magnetic
field

Magnetic domain
memoryElectricfield

Spin microwave/
mill-meter wave
oscillator・・・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 SummaryRequiredhigh-performance

Artificial
multilayer
thin-films

Heat

Spin diode/transitor

Light・・・

Pressure Current
External field
response

Role of first principles calculations in materials design•Quantum mechanics !
•No use of empirical parameters !
•High accuracy in computations !

1A

2A

3A

4A

5A

6A

7A

8

1B

2B

3B

4B

5B

First principles calculations

6B

7B

0

1

3

4

5

Li Be
1120678910exchange correlation potential
ExcLDA n    n(r ) exLDA n(r )  V (r) V (r) (r)   (r)2effcii i

B C N O F Ne

1213d-electron systems

Na Mg
19①Kohn-Sham equation

2sp-electron systems He

H

2122

23

2425

26

2728

1415161718

Al Si P S Cl Ar
2930

3132

33

34

35

Coulomb potential

wave function (basis)

36

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr•Interpretation of experiments•Understanding•Prediction
with no restriction of materials

373839404155

5657

7273

Strong correlated systems,
Exited states, etc.

74

4375

4476

457746784779488049815082518352845385

54

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

42

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

59

60

61

62

63

64

65

66

67

68

69

70

②Total energy
Etotal 91929394

95

96

9798

99

100

101102ii 1, i  E F

Kohn-Sham eigenvalues(band structure, density of states)71

Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu90N





103

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

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

double counting term

Goal: Prediction of material properties
from the periodic table

Eigenvalues and eigenstates of electron orbitals in atoms

 nlm (r )  Rnl (r )Ylm
4s

 Introduction

3d Electronic structures and magnetism in transition-metals①Orthogonalization in orbitals

 j | i  01s3s

 Electronic structures and magnetism at surfaces/thin films
 Control of magnetism by tuning atomic-layer alignments2s Control of magnetism by external electric field Summary

Li :1s22s
Na :1s22s22p63s②Spatial spread of wave function
Hybridization in crystals

K :1s22s22p63s23p64s
Atomic core1

2017/9/4

Valence electrons and electron configurations

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

3u
1g1
1  2 2b 
Bonding stateV2  2 | V | 1Polar bonds

Antibonding

Antibonding

2V111ubonding

1u3g2g223g2u

Homo bonds

1antibonding

2V1

Number ofelectrons

2V224

10

1214

16

H2He2

N2O2

F2Ne2

Valence top (Fermi level) is determined by the number of electrons
Bonding

Bonding

Cohesive energy and spin polarization in transition-metals
LDA results vs. experiments

Band structures of transition-metals
Nv=4

Nv=6

Nv=10Cohesive energy

Non-spin PolarizedBand structure

Bulk modulus Wigner-Seitz radius

D3d(EF)> D4d(EF)> D5d(EF)
Antibonding bonding

W3d
> W4d
> W5d

Fermi levelEFTi< EFCr< EFNiV. L. Moruzzi, J.F. Janak, A.R. Williams,
Calculated electronic properties ofmetals (Pergamon Press, New York, 1978)
J. Kübler, Theory of itinerant electron magnetism (Oxford University Press, Oxford, 2000)

Magnetism in transition metals

Stability of magnetic structures

Non-spin polarized
551AFe (bcc)
43

32A

3A

4A

5A

6A

7A

81B

2B

32114B

5B

6B

7B

567891102He42010B C N O F Ne

1213AFM FMNa Mg
1923B

1HLi Be

212223242526271415161718Al Si P S Cl Ar
282930313233343536

K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
373839404142434445464748495051525354Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe
555657727374757677787980818283848586

Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn–6–4–20

Energy (eV)

204 –8
5–6–4–20243dSpin polarized

LDA results

4d4Minority

3Majority

ID(EF)

0–8

Density of states (/eV-atom-spin)

Density of states (/eV-atom)

V (bcc)42

Stoner criteria
ID(EF)>1

1

J. Kübler, Theory of itinerant electron magnetism (Oxford University Press, Oxford, 2000)
0–8–6–4–20

Energy (eV)24

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

22017/9/4

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

32

10–4

Density of states (/eV-atom-spin) Control of magnetism by tuning atomic-layer alignments SummaryFerromagnetism in transition metal monolayers

4dbandwidthRuRh

Density of states (/eV-atom)

Co

3d123

42

3

4xyx2-y2

V(001) monolayer
44

Mminority

Majority

3221

10–4–3–2–10

1

Energy (eV)

230–4

4–3–2–10

1

Energy (eV)Total energy difference

6EF543210–8–4

04

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

Substrates

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

Density of states (/eV-atom)

Energy difference between FM and AFM
E=EAFM-EFM (mRy)0553–1

Energy (eV)

Ag (a=2.89Å)

V–2Fe(001) monolayer (a=2.87Å)FeMonolayer on Ag(001)Ti–3

Effect of substrates to magnetism in transition metal monolayers

Magnetic moments

Free-standingmonolayerxy,yz
V bulkSpin-polarized Control of magnetism by external electric field

5d4

Pd (a=2.75Å)W (a=2.23Å)EFEF
EF
Energy (eV)Cr Mn Fe Co Ni

Energy (eV)Energy (eV)First principles calculations of MCA energy
Spin-orbit couplingH Introduction
 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 field SummarySOC
1 1 dV 2  σ   (r )  z
4c r dr    z Admixture of spin-up
and down components

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

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

Very sensitive toband structures !!

32017/9/4

Perturbation method of MCA energy

Band structure of Fe monolayer
Surface state

EMCA ( )  E SOC ( x)  E SOC ( z )x2-y2(m=2)

 E dd  E ud
E dd  E dd ( x)  E dd ( z )Eex

Spin‐upo | L z | u  2 o2 o | L x | uu  ou

2Energy (eV)EF

Spin‐down

22

1

100

2−1−2 o | 3L2z  L2 | o

EMCA(k) (eV)dddd

−2−3

Rule in the origin of MCA

MinorityMX
a=5.45a.u.

−3−2−101DOS (states/eV)

2MCA energy in 3d transition metal monolayers

Simple picture from perturbation theory

5|<o|Lz|u>|2|<o|Lx|u>|20

Positive EMCA

Negative EMCA

−5energy

energy2EFxy, x2-y2

Majority

Minority-spin

Eex o

EMCA= 0.19 meV/atomz2

EFz2-r2 (m=0)

xz, yz−1

E ud  E ud ( x)  E ud ( z )xz,yz(m=1)

xy (m=2)

D4hPerpendicular MCA

xy, x2-y2 (m=2)
xz, yz (m=1)

without SOC

z2 (m=0)EF

1xy, x2-y2 (m=2)0

PerpendicularMCA−1|<xz,yz|Lz|xz,yz>|2−2

Minority-spinMX

PMA arises from SOC
between m=1 orbitals

(a=aCu)In-planeMCA>|<xz,yz|Lx|z2>|2

MCA energy of 3d, 4d, and 5d transition metal monolayers

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

Effect of substrates to MCA in transition metal monolayers

GGA results

60

Ru

CoRh

NiPdOs30

Perpendicular MCAFeRu

0NiCoRh
Pd−30
OsIr

Pt

Pt

Ir−600Substrate

Fe

EMCA (mJ/m2)

Energy (eV)xz, yz (m=1)

100

200

300

400

SOC strength (meV)
1 meV/unit-area = 1.8 mJ/m2

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

42017/9/4

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

Fe dz2 – O pz hybridization at Fe/MgO interface

EMCA  E SOC    E SOC  

0.19

Fe/MgO

1.28

2.07 Ådz2OFexz, yz
xy, x2-y2O pz
Weekhybridization

O pz0.94Weekhybridization

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

Au3/Fe3/MgO

Anti-bonding

FeFe dz2

EMCA (meV/a2)
Free-standing
Fe monolayer

energyFe dz2pzBonding

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

1A

2A

3A

4A

5A

6A

7A

81B

2B

3B

4B

5B

6B

7B

5678

91He

3

 Control of magnetism by tuning atomic-layer alignments

4Li Be1119

1220

MTJ Junction

10B C N O F Ne
13Na Mg

 Control of magnetism by external electric field02H1415161718212223242526272829303132333435++Al Si P S Cl Ar
36K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr
373839404142434445464748495051525354Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe

 Summary

55

5657

72

737475

76

7778

7980

8182

83

8485

MgO86Cs Ba La Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn--MCA of 3d transition metal thin films with seven-atomic-layer

Nonvolatile
High capacity
High speed

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)

20
15
10
50Assumed7-layer
Fe film
MnNiCoEnergy (eV)−50.6bcc-layer stacking

surface Fe layer
0.3symmetric structure
along z-axis Ni xy0.0I1II24IVV56VI2MFe/Fe/Ni/Fe/Ni/FeFe film

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(X+M)/2

MgO|Fe/Fe/Ni/Fe/Ni/Fe/Fe|MgO

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

Ni x2-y2−0.6⑤Guess

Fe2/Ni/Fe/Ni/Fe2②Full 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/Fe2③Guess

0Weller et.al., IEEE Trans. Magn. 36, 10 (2000)

57911

Number of layers

1352017/9/4

Control of magnetism of metal thin films by electric field
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)….

 Introduction

MgO/Fe/Au(001)
Negative
Voltage
PositiveVoltage

 Curie temperature (TC)

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

 Electronic structures and magnetism in transition-metals

Maruyama et.al., Nature Nanotech. 4, 349 (2009) Dzyaloshinskii-Moriya interaction (DMI) Electronic structures and magnetism at surfaces/thin films

Curie temperatures

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

MgO/Co/Pt(111)
PositiveVoltage

 Control of magnetism by tuning atomic-layer alignments

 Magnetic moments

 Control of magnetism by external electric field Magneto-optical conductivityNegative
Voltage

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

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

 Summary

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
2

Duan 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/ÅMajority(a=5.45a.u.)
0.9

1–0.001–40–0.002

VS （V）–20

n, (10-3/a2)

0.000

n,m (a-2)

m0

Fe surface

n

0.5

0

0.0

–20

–0.5

–40

–1.0

VS50EF

–1

–3

03

–9–6

Position along z‐axis (Å)

S+

C

S–80

–3

03

6

Position along z‐axis (Å)

1

0.3
0.0

EF

–0.3
3

–0.6

54

3

–0.9 Minority-spin

–3–4

–4

–2

02MX

Change in band structure around Fermi level

4DOS (states/eV spin)
External E-field
[001]
[100]

–60

–60

15*

0.6

1.0

n=n1V/Å-nzero 0.001

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

Minority-spin

Minority–2

Femonolayer

Change of MCA energy

9Modification of MCA energy of Fe monolayer(a=5.45a.u.)

Modification of MCA energy at MgO/Fe interface
Theory

EMCA  E()  E()
0.2

0.02

0.1

0.01

0.00.00

–0.1

–0.01

–0.2
0.0

–0.02
0.2

0.40.60.8

1.0

1.2

1.4

Experiments
MgO/FeB/MgO

morbit=m001-m100 (B)

EMCA （meV/atom）

VS （V）

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

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

External E-field (V/Å)

The MCA is modified by an E-field
due to the change in band structures around EF.
Nozaki et.al., Appl. Phys. Express 6, 123001 (2013)

Nakamura et.al., PRL102, 187201 (2009)
Shimabukuro, Physica E , 42, 1014 (2010)

62017/9/4

Control of Cure temperature by electric fieldPt(111)/Co/MgO

Modification of frozen magnon (spin-spiral structure) dispersion

Pt(111)/Co/Ionic liquid film

electrodePt(111)

Tc=300 K
Tc ~ 100 K
Tc ~ 10 K

Pt(111)/Fe/Ionic liquid film

TC (+V) > TC (V)
D. Chiba et al., Nat. Mater., 10, 853-856 (2011).
K. Shimamura et al., Applied Physics Letters 100, 122402 (2012).
M. Kawaguchi at.al. Appl. Phys. Express 5, 063007 (2012).

Modification of exchange interaction by electric field60

J0j (meV)55

J03

J0 j 1
 exp iq  r0j E q N q5 V/nm

34

∝ 1

0.6

Co

0.5Pt

0.4

5 V/nm

0.30.2

J03experiments5 V/nm

TC

830

320

TC

20K

10K



0.26

0.18

0.1

MgO/Co/Pt(111)

J02

J05



K

0.7+i j

5 V/nmJ04

M



TheoryCo/Pt(111)H    J ijei  e j

J02

−5M
Γ

−250

0.0600K−200

Heisenberg model

J01

50−150Comparison to experiments

M/Ms

J0j (0.5V/Å)-J0j (0.5V/Å)(meV)

65+5 V/nm

−100

−300

1.2
0.8
0.4
0.0−0.4

5 V/nm−50

TC in positive E-field is higher thanthat in negative E-fieldCo/Pt(111)40−4−8−120electrodeE(q) (meV/Co-atom)

Tc=326 K+5 V/nm
and-5 V/nm

E(q,0.5V/Å) - E(q,0.5V/Å)(meV/Co-atom)

Co

700

800

T (K)

900

Agreed with experiments qualitatively

MgO

J01

Co 2~3原子層
Pt−10−1515V/nm

2Distance (a)55V/nm10.3 meV6

0.2V/nm
Oba et.al., PRL114, 107202 (2015)

Summary

Spintronic  Design  Magnetic control
Artificial multilayer
thin-films

magnetic properties

Importance ofunderstandingelectronic structures

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

 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