Computational materials design and its application to spintronics
H. Akai, M. Ogura, and N.H. LongDepartment of Physics, Osaka University
Papan-Germany Joint Workshop 2009Kyoto, 21-23 Jan. 2009
What is CMD®?
CMD®: computational materials designTo create/synthesize materials in computersBased on first principles electronic structure calculation, i.e., quantum simulation
CMD®Traditional materials design
21st century's alchemist
Simulation and design
Design: the inverse problem of simulation
Materials&
Structure
Properties&
Functionalities
Quantum Simulation
Quantum Design
predict
predict
QuantumSimulation
Find Mechanisms
Predict New
Materials
Verify Functionality
Integrate Mechanisms
Analyze Physical
Mechanism ExperimentalVerification
CMD®
Engine
How to solve the inverse problem?
QuantalYet large scaleReal devices
Submicron physics
μmnm
pm
fm
mm
submicron
Most important but difficult scale range
Simulation/design of whole submicron structures
Transport propertiesof real device structures
Parallel coupling Antiparallel couplingMnPt
CoFe
Ru
CoFe
Cu
CoFeNiFe
Ta
25nm
An example
Our approach
First-principles LDA calculation of transport properties of metals, semiconductors, alloys, layered systems and hetero structures.
KKR Green’s function method combined with Kubo-Greenwood formula and CPA.
1. Halfmetallic AF(compensated ferrimagnets)
When two magnetic ions existOne ion more than half d, the other less than half
metallic
Ferromagnetic coupling
VEF
Co
DOS
energy
d3
d7
Superexchange works (no degeneracy)
JH
JH
EF
V
Co
Antiferromagnetic coupling
Mechanisms
In the case of anti-parallel coupling
d3
d7
Double exchange works (degeneracy)
half-metallic
2JH
(ZnCrFe)S
Energy relative to Fermi energy (Ry)
0
10
20
30
0
40
80total (left)Cr 3d (right)Fe 3d (right)
Up spin
Down spin
DOS
(sta
tes/
Ry)
Antiferro
10
20
30
40
80
0
10
20
30
0
40
80Ferro
DOS
(sta
tes/
Ry)
10
20
30
40
80
-0.4 -0.2 0 0.20
10
20
30
0
40
80
DOS
(sta
tes/
Ry)
Spin glass
half metallic
VB CB
metallic
VB CB
metallicVB CB
AP
P
D
(Zn0.9Cr0.05Fe0.05)S
Transport properties
Anti-phase domain boundary
ferro
antiferro
Transport properties of HM AF DMS?
Anti-phase domain boundary
(Zn,Cr,Fe)S films
Parallel coupling Anti-parallel coupling
DC conductivity of (Zn,Cr,Fe)S
1.36x10-3 Ωcm 6.79x10-3 Ωcm
H. Akai and M.O. J Phys. D 40 (2007) 1238
Parallel coupling Anti-parallel coupling
New type of HM AF: (AB)X2A and B are transition metals, X is chalcogens or pnictogens,Choose A and B such that total valence d electrons number is 10: one
being less than half-filled, another being more than half-filled: ex. (FeCr)Se2,Structures: NiAs-, Zinc-blende-, chalcopyrite-, wurtzite-, NaCl-type.
ZB-type
NiAs-type wurtzite-type
NaCl-type
Chalcopyrite-type
NiAs-type (FeCr)Se2
-0.4 -0.2 0.0 0.2
-80
-40
0
40
80
DO
S (s
tate
s/R
y)
total Cr d Fe d
-0 .4 -0.2 0.0 0.20
2 0
4 0
6 0
DO
S (s
tate
s/Ry)
E n e rg y r ela tiv e to Fe rm i e ne rg y (R y )
tota l C r d F e d
-0.4 -0.2 0.0 0.2
-80
-40
0
40
80
DO
S (s
tate
s/Ry)
total Cr d Fe d
AF
half metallic
VB CB
SG
F
metallic
metallic
antiferromagnetic disordered state (A0.5B0.5)X
-0.4 -0.2 0.0 0.2
-60
-40
-20
0
20
40
60
NiAs-type (Fe0.5Cr0.5)Se
DO
S (s
tate
s/Ry)
Energy relative to Fermi energy (Ry)
total Cr d Fe d
more than two components (AB0.5C0.5)X2
-0.4 -0.2 0.0 0.2
-80
-40
0
40
80
NiAs-type (CrCo0.5Mn0.5)Se2
DO
S (s
tate
s/Ry)
Energy relative to Fermi energy (Ry)
total Cr d Co
0.5 d
Mn0.5
d
Robust half-metallicity
Magnetic moments and total energy
Magnetic moments:
Materials (FeCr)Se2
Local magnetic moment (μB) Total (μB)
Cr Fe SeOrdered state 3.2353 -3.1364 -0.1754 0.0009
Disordered state 3.2996 -3.1815 -0.1871 0.0014
Total energy:EAF – ELMD = -17.83 mRyEF –ELMD = 2.76 mRyEordered – Edisordered = -19.1 mRyEformation = ECrSe + EFeSe – 2E(FeCr)Se2 = 33.5 mRy
Stable in antiferromagnetic ordered state
Crystal structure
Materials ①EAF - ELMD②EFR - ELMD
(mRy)
Eorder -Edisorder(mRy)
Formation EA+EB-2EAB
(mRy)
TN (K)
MF CA
NiAs-type structure
(FeCr)Se2 -17.83 2.76 -19.10 33.50 1094 873(VCo)Se2 -7.83 7.69 -37.58 67.90 565 426(FeCr)Te2 -12.74 1.47 -8.26 4.89 612 521
Zinc-blende structure
(VCo)S2 -22.14 3.44 -93.70 212.86 1101 1048(FeCr)Se2 -20.96 14.50 -10.90 33.48 1038 817(FeCr)Te2 -15.53 9.85 -9.20 15.60 807 647(FeCr)Po2 -12.59 6.87 -14.81 15.02 794 630
Wurtzite structure
(FeCr)Te2 -10.16 6.98 -2.18 6.35 588 498(FeCr)Se2 -12.50 10.18 -0.90 13.61 728 535
Chalcopyrite structure
(VCo)S2 -24.13 4.15 non 200.5 1159 1025(FeCr)Se2 -22.65 15.98 non 27.24 1235 1097
NaCl-type structure
(FeCr)S2 -7.00 -4.66 -1.39 4.96 420 306(VCo)S2 -1.15 6.39 -29.80 68.09 94 67
Transition metal chalcogenides
Many cases exhibit HM AF
Crystal structure
Materials ①EAF - ELMD②EFR - ELMD
(mRy)
Eorder -Edisorder(mRy)
FormationEA+EB-2EAB
(mRy)
TN(K)MF CA
NiAs-type structure
(MnCo)N2 -31.85 -8.28 -8.03 23.42 347 327
Zinc-blende structure
(MnCo)N2 -29.34 9.71 -10.97 14.89 519 420
Wurtzite structure
(MnCo)N2 -24.15 3.51 -2.42 14.50 295 268
Chalcopyrite structure
(MnCo)N2 -29.61 9.17 non 15.11 530 445
NaCl-type structure
(MnCo)N2 -26.46 -1.14 -6.87 15.79 196 143
(AB)N2
Applications to GMR and TMR devicesال
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Magnetic free layerNonmagnetic layer
Half-metallic antiferromagnets
Structure using HM AF
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Magnetic free layerNonmagnetic layerInner-layer
Outer-layer
Antiferromagnetic layer
Pinned-layer
Currently used structure
Ru
GMR ratio of GMR/TMR devices
1.85Å
3.70Å
3.70Å
1.85Å
1.85Å
1.85Å
Fe0.85Co0.15
Cu
Fe0.85Co0.15
Ru
Fe0.85Co0.15
Mn
GMR ratio 19%resistivity
63.33 µΩcmresistivity
78.60 µΩcm
currently used structure
Our design of new MRAM cell
5.77Å
5.77Å
5.77Å
Fe2Se2
Cu2Se2
ZB‐(FeCr)Se2
GMR ratio 720%resistivity
65.58 µΩcmresistivity
536.78 µΩcm
Magnetic metallic layers: bcc-Cu and bcc-Fe
4.33Å
5.77Å
7.21Å
Fe
Cu
ZB‐(FeCr)Se2
GMR ratio 54%resistivity
61.89 µΩcmresistivity
95.05 µΩcm
Fe
Cr
Cu
Half-metallic diluted antiferromagnetic semiconductors
5.67Å
5.67Å
5.67Å
GaMnAs
GaAlAs
ZB‐Zn(CrFe)Se
GMR ratio 264%resistivity
2.25 µΩcmresistivity
8.18 µΩcm
TMR devices: nonmagnetic spacer
5.37Å
5.37Å
5.37Å
Cr2S2
Ca2S2
NiAs‐(FeCr)S2
TMR ratio 3300%resistivity 473 µΩcm
resistivity 16103 µΩcm
2. Spin transport
Transport properties and spin dynamics are of vital interestGMRspin injection / accumulationcurrent induced magnetization reversalspin relaxationspin-pumping / batterySpin-Hall effect
F/N/F cpp GMR structure
F N F
What is spin transport?
Electric motive force → charge/spin currentSpin motive force → spin/charge current
Aims: First principles calculation ofDC conductivitySpin conductivitySpin Hall conductivityInverse spin Hall conductivitySpin injectionSpin accumulation
Charge and spin currents
J c = − e v
Js = (h / 2)σv
Charge current vector
Spin current tensor
Current operators
Correlation functions
J c J c , J cJs , JsJ c , JsJs
O1O2RR
= Tr O1GR (EF )O2G
R (EF )
O1O2RA
= Tr O1GR (EF )O2G
A (EF )
where
Conductivities
σ zzcc =
12ℜ jz
c jzc RR
− jzc jz
c RA( )σ z,zz
cs =12ℜ jz
c jzzs RR
− jzc jzz
s RA( )σ zz,z
sc =12ℜ jzz
s jzc RR
− jzzs jz
c RA( )σ zz,zz
ss =12ℜ jzz
s jzzs RR
− jzzs jzz
s RA( )
e.g.
Spin-orbit coupling
Spin-diagonal componentsscalar relativistic + lzσ z
Spin-off-diagonal components
ΔtLσ ,L 'σ ' ; r2∫ dr RLσ lxσ x + lyσ y( )RL 'σ '
Summary
First-principles calculation of charge and spin transport properties
Half-metallic AF and new type of GMR
Spin conductivity of alloy systems
Co/CoCu/Cu hetero structure
Quantitative discussion of spin injection/accumulation and relaxation
