CMD37
2020/9/1

Lecture 7 (15:00-16:30)

Functional Oxide Spintronics andthe material design
ISIR, Osaka University Teruo Kanki
E-mail: kanki@sanken.osaka-u.ac.jp)

Ceramics

2

Jewelry (Spinel, Garnet)

3

Functional Oxides

4

Transition Metal Oxides

Ferro dielectrics

Transition
Metal Ion

Piezoelectrics

High temperature
superconductors
Conductors

Anti-/Ferro magnetics
Colossal MR

Magnetic head Magnetic recorder
MemoryJosephson junction(DRAM, FRAM、RRAM)
Memory (MRAM) electrode SQUID

Oxide Ion

Piezoelectric devices

Bolometer

Information processing and data storage
materials related with our daily life5Face-centered cubic => Closed pack structure

1st layer

2nd layer

3rd layer

Center face
1/2×6 parts

Corner
1/8×8 parts
6Perovskite structure:ABO3 e.g. SrTiO3Interspace of close packed oxide ions：Octahedral interspace
O2-=1.40 Å ,Sr2+=1.44 Å (12 coordination),0.414r Ti4+=0.42 Å (6 coordination)

7

Orbital bonding
Bonding and Antibonding states
Covalent bonding H

H2

Valence and Conduction bandAH
ψ2Energy

ψ2 =χA -χBA-B
ψ2Ion bonding
ψ2 =a2χA –b2χBψ1 =a1χA +b1χBψ1

ψ1 =χA +χBB

ψ1

Electron density

Heteronuclear diatomic moleculeψ2（Covalent or Ionic characters）↓
Different orbital levelAntibondingψ1HH(a)BondingA

B

Electronegativity
Ionization potential(b)Electron distributions and energies of molecular orbitals in (a) H2 and a heteronuclear molecule AB
8

From orbital to band formation

Orbital energies of (a) atom, (b) small molecule, (c) large molecule, (d) solid, and(e) density of states corresponding to (d)

9

TiO

10

Existence of electrons・Orbital shapezz－p orbitals
x－y＋＋

yyx

xpz
zzzz

－ ＋＋ －－＋＋－＋－ －＋＋－＋z
y－pypx＋ －d orbitals － ＋x
dxy＋

yx

xdyz

Perovskite structure
Oxygen atom

yx

xdzx

y

dx2-y2

Ligand field splitting eg(Crystal field splitting)t2g
3d transition metalyd3z2-r2

x2-y2,3z2-r2
xy,yz,zx11

3d2 3d3 3d5 3d5 3d6 3d7 3d8 3d10 3d10
4s2 4s2 4s1 4s2 4s2 4s2 4s2 4s1 4s2

12

Crystal field splitting of perovskite structure
Octahedral ligands

L LL
LMTransition
metal ion

LOxygen ion

Leg(z2, x2-y2)t2g(yz, xz, xy)

Energy gap

La3+Mn3+O313

Required interaction for material design
Superexchange interaction

Double exchange interaction

LaMnO3(La,Sr)MnO3

Carrierdoping
キャリアドーピング

t2g t2g
H  t Mn Mn cos( )  K HundSMn - J t2g  SMn
SMn
2LMnO

14

Kanamori-Goodenough rules
60 years ago
Kanamori former
president of Osaka Univ.

CrO
Cr-O-Fe-O-CrOCr15

Superexchange interaction

Superexchange interaction→Indirect interaction between two magnetic atoms
through non-magnetic atom

16

Superexchange interaction
Considering an excited state in the case ofelectron transfer from 2p orbital to 3d orbital（transfer integral)t pd    d * V pd p dr■bonding rule

(3d6-2p6-3d6)

Considering a direct exchange interaction (Jpd)
between 2p spin and 3d spin17Superexchange interaction
Sign of Jpd Ferromagnetic Jpd>0、Antiferromagnetic Jpd<0・・・ Orthogonal character of Jpd

Fe2+ O2- Fe2+3d6

2p63d6Jpd<0x2-y2,3z2-r2xy,yz,zx
Orthogonal character table in case that FeO is an antiferromagnetic materiald orbital function locates the origin ands and p orbitals arrenge Orthogonal coordinates of X,Y and Z axies
18Superexchange interactionEx.） Mn4+ -Mn4+ : Antiferromagnetic

Mn4+ O2- Mn4+

3d3

2p6

3d3

Jpd>0x2-y2,3z2-r2
xy,yz,zx
19

Double exchange interaction
Superexchange interaction

Double exchange interaction

LaMnO3(La,Sr)MnO3

Carrier
doping
キャリアドーピング

t2g t2g
H  t Mn Mn cos( )  K HundSMn - J t2g  SMnSMn
2LMnO

20

Magnetism modulation due to change of electron transfer integral

4.0

10.0 [10-2-2 ]

3.0

8.0

2.0

6.0

1.0

4.0

[10 ]

H=500[Oe]
0.0
0

100

200

Resistivity [cm]

Magnetization [B]t2g t2g
H  t Mn Mn cos( )  K HundSMn - J t2g  SMn
SMn
2LMnO

300

Temperature [K]21

Colossal magneto resistance (CMR)
eg
t2g

eg
t2g

(b) La1-xSrxMnO3(T≪Tc )(c) La1-xSrxMnO3(T≧Tc)

H(d) La1-xSrxMnO3(T≧Tc)
H＝0Temperature dependence of resistivity with a variety of magnetic fields in
La1-xSrxMnO3 crystal（negative CMR）.
Tc indicates the Curie temperature at H=0 T.
22

Main parameters of transfer integral changes
zHarrison’s equation

Vpd =<d|H|p> ~ d –7/2

d:結合距離d:the distance between orbitals
xyϕ: the bond angle
角度が曲がった場合
E3 z 2  r 2 ,3 z 2  r 2









3 22 22 222 2
 2 1 2 n  l  m  V dd  3n l  m V dd  l  m V dd
24 cos23

Main parameters of transfer integral changes
Tensile strain

Vpd ~ d–7/2

Compressive strain
Band width W＝2zVz：Coordination number24

Material design for oxide spintronics
Hundcoupling
フント結合

KHund
Exchangeintegral
交換積分

JTransfer integral
電子移動積分t t
Magnetic
磁性層
1 layer 1

J1

Hund coupling(σ)
伝導電子()Localized(S)spin (s)
局在スピン

JInterface

Magnetic
磁性層2 layer 2Ion
イオン

J2
Ion イオン結合距離
bonding distance
integrald electronenergy Coulomb
d電子エネルギー
Coulomb積分項

Hundcoupling
Hund結合項

Exchange integral
交換積分項

1H electron   Ed   U  K Hund Si   J ij Si S j
2ii, j  E p   t  A dQd
電子移動積分項
Transferintegrali25

Material design for oxide spintronics(1) Introduce strain effecthv, H, ENobel
physicalproperties(2)Introduce magnetic interaction
between different layers(3) Integrate different functional
materials

26

Control of crystal field splitting due to strain effectOctahedral coordination

In-plane tensile strain

L LLLM

LLLL
LM

LLLz2eg(z2, x2-y2)t2g(yz, xz, xy)

Energy gap(x2-y2)(yz, xz)(xy)

27

Room Temperature

3.02.0(La0.8Ba0.2)MnO3

B

Magnetization [μB /unit cell]

Design of room temperature CMR materials

1.0Bulk

MR ratio (%) at 0.8 T

0.050 220240260650Å

1000Å

2803001000Å

SrTiO3 substrate

Tensile strain(0.3% )

320650Å

40400Å

3020Bulk
歪みLBMO薄膜
1300Å
3900Å

100220240260280300Temperature [K]320Phys. Rev. B 64, 224418(2001)

28

Strain effect vs TC in LBMO films

Tensile strain

Compressive strain
Tensile strain

Compressivestrain

Increase in TC

decrease in TC

Phys. Rev. B 64, 184404(2001)
29

Stability of double exchange magnetism
Stability of magnetism induced by double exchange interaction  zxtij  zxb cos(ij / 2)Dex

Z: the coordination number of nearest
neighbor atoms ；Z=6
tij： the transfer energy

C. Zener: Phys. Rev. 82 (1951) 403
P. W. Anderson and H. Hasegawa: Phys. Rev. 100 (1955) 675
P. G. de Gennes:Phys. Rev. 118 (1960) 141

θij: the spin angle between Mni and Mnj

Main parameters indicating the stability of double exchange magnetism
x: the number of carriers per a Mn sitebσ: Spin-independent components（dependence of orbital overlap and bond angle of Mn-O-Mn）

30

Carrier density and Hall mobility

2Hall mobility (cm /V s)

10.0

7.0

Normalized values-3

Carrier density (cm )[10 20]

6.0
5.0
4.0

4.0

1050

729 nm198 nm
84 nm
24 nm
17 nm

40
30
20
1050

100
150
200
Temperature (K)

250

10 K

6.0

2.0

3.0

008.0

Hall mobility

Reference point

Carrier density
50 100Thickness (nm)500

Carrier density：Constant the number of carrier x: constant Not generating cataion deficiency

Hall mobility：Increase Increase in transfer integral
 change in orbital overlap state
due to lattice strain effectPhys. Rev. B 71, 012403(2005)31

Stability of transfer integral due to lattice strain effect
LBMO (103)

STO (103)

Lattice constant (Å)

Out-of-plane

d =17 nm

3.91

In-plane

STO(100) lattice constant

3.90
3.89
3.88

In-plane

3.87
10Out-of-plane
50 100Thickness (nm)Calculation of stability in double exchange interaction
every thickness♦ stability of double exchange interaction

Out-of-plane- exD  zxtij  xb  b
x: the number of carriers per a Mn site

500In-plane

Z: the coordination number of nearest
neighbor atoms ；Z=6bσ: Spin-independent components（dependence of orbital overlap and bond angle of Mn-O-Mn）

32

Contribution elements of stability indouble exchange interaction
1. In-plane and Out-of-plane orbital overlap
 determination from lattice constants obtained by experiments-7/2
matrix element between p and d orbitals: Vpd=dMn-O

Mn-O-Mn bond angle: 180°

2. Redistribution of eg electrons due to lattice strain effect  calculation by the DV-Xα method

Tensile strain
d3z2-r2
dx2-y2
3. Anisotropy of d orbital

d3z2-r2O 2p

    

d3z2-r2eg

dx2-y2：stabilizationt2g

Transferstrengthγ

γ’x2  y2
3z 2  r 2

dx2-y2Out-of-plane

In-planex2  y2

3z 2  r 2x2  y2

3z 2  r 2000
1

3/4
√3/4

√3/4
1/4

Phys. Rev. B 64, 224418(2001)
33

Contribution elements of stability indouble exchange interaction
Stability of averaged double exchange interaction
7 exD   (nx 2  y 2 , n3 z 2 r 2 ,  ( i ) ( j ), din7 , dout)Transfer strength from O2p orbital to Mn3d orbital   

i , j Transfer strength from Mn3d orbital to O2p orbital  n3z2-ｒ2

    
nx2-y2In-plane: 4 directions
Out-of-plane : 2 directions

din：the in-plane Mn-O length
dout：the out-of-plane Mn-O length derived by XRD measurement
nx2-y2 ： the ration of occupied electrons in dx2-y2 orbital
n3Z2-r2 ： the ration of occupied electrons in d3z2-r2 orbitalcalculation by the DV-Xα method using experimental
lattice constants

7 exD  (3  3 )nx 2  y 2  (1  3 )n3 z 2  r 2 d in7  2n3 z 2  r 2 d out

34

Stability of double exchange magnetism
1.008

ex

1.006

Stabilization of double exchangeinteraction with decreasing film
thickness

1.004
1.002
1.000
1050 100Thickness (nm)

500 1000

What is main factors of TC increase in strained （La,Ba)MnO3 thin filmseg♦ redistribution effect by eg electrons due
to anisotropy d orbital.
♦ Orbital overlap of in-plane andout-of-planeOut-of-plane
35

Function of interface(1) Introduce strain effecthv, H, E

Nobelphysicalproperties(2)Introduce magnetic interaction
between different layers(3) Integrate different functional
materials

36

Control of interface magnetic interaction
Conductive electron

Localized spin

Hund couplingt2g t2g
H  t Mn Mn cos( )  K HundS Mn - J t2g  S Mn
S Mn
2LMnOt2g
 J Fe  Mn SMn
SFe   J Fe  Fe SFe SFeLFeO
Antiferromagnet LaFeO3

Interface magnetic
interaction

Combined with two materials

Ferromagnet (La,Sr)MnO3
37

Spin frustration superlattice38

High sensitive response by magnetic field
Spin frustration superlattice

JAFJF

Ji

Spin frustration(spin fluctuation)

Monte-Carlo simulation

Ferromagnetic metal(La,Sr)MnO3
Antiferromagnet
LaMO3

M=Cr, Fe, Co,Ni

39

Theoretical prediction：New ferromagnet

60 years ago
Kanamori former
president of Osaka Univ.

CrO
Cr-O-Fe-O-CrO
Cr40

NaCl structure
ClNa

Cl layer

Na layer41

Lattice-direction control superlattice

1st layer

Cl layer

2nd layer

Na layer
3rd layer42

Lattice-direction control superlattice

(111)

(110)
(100)

J. Appl. Phys. 89, 2847(2001)
43

Lattice-direction control superlattice

10.0

M(emu/g)

8.0
6.0
4.0
2.0
0.0
100

Science 280, 5366(1998)

150

200

250

300

350

400

T(K)
44

Integration of different functional materials(1) Introduce strain effecthv, H, E

Nobelphysicalproperties(2)Introduce magnetic interaction
between different layers(3) Integrate different functionalmaterials

45

Ferromagnet/Ferroelectric material combination

Diluted magnetic semiconductor-- (In,Mn)As
Field effect transistor

Nature 408, 944(2000)
46

Ferromagnet/Ferroelectric material combination

Vgate= -15V

2.7

空乏

2.6

Carrier

2.5

蓄積

2.4
2.3

MCD /10-6 deg.

ChannelResistance /105

8.0
2.8

4.0
Vgate= +15V

0.0

Field effect control ofFerromagnet: (La Ba )MnO
ferromagnetism at room
temperature-505Gate Bias (V)Source

1-xx

3-4.0

Drain-8.0-400

Gate

Ferroelectric: Pb(Ti,Zr)O3100

6.050

Electric field0TC /K

Ferroelectirc
Polarization /C/cm25-10nm

Spin
T=296.K-200
0200
Magnetic field/Oe

TC=282K+TC(x=0.15)

3.0

TC=242K+TC-50-100

400(x=0.10)-10-505

Bias (V)100204060

Ferroelectric Polarization /C/cm247

Ferromagnet/Ferroelectric material combination

Conductive electron

Localized spin

Hund couplingt2g t2g
H  t Mn Mn cos( )  K HundS Mn - J t2g  S Mn
S Mn
2LMnO

×N (The number of carriers)
Electric field48

Photonic/Ferroelectric/magnetic material combinationPhoton→Electric dipole → Carrier spinhv
Organic
photoconductive
material
Cu-Pc
Ferroelectric

Decrease resistance（by photon）
Dielectric polarization（electric dipole）

Pb(Zr,Ti)O3

Field effect（Carrier / Spin）(La,Ba)MnO3 Channel

2040

S

PZT(003)

PZT(002)S

Pt(111)Pb(Zr,Ti)O3
Gate

CuPc(200)
PZT(001)

CuPc

Log (Intensity) [a.u]Ferromagnetic(La,Ba)MnO360S

2 /deg49

Summary: Oxide spintronics(1) Introduce strain effect--------

Room temperature CMR(2)Introduce magnetic interaction --- Magnetic superlattice
between different layers
Design of magnetic susceptability(3) Integrate different functional
materials------

Ferromagnetism+ Ferroelectric50