Computational materials design and its application to spintronics
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1 Papan-Germany Joint Workshop 2009 Kyoto, Jan Computational materials design and its application to spintronics H. Akai, M. Ogura, and N.H. Long Department of Physics, Osaka University
2 What is CMD? CMD : computational materials design To create/synthesize materials in computers Based on first principles electronic structure calculation, i.e., quantum simulation Traditional materials design 21st century's alchemist CMD
3 Simulation and design Design: the inverse problem of simulation Quantum Simulation Materials & Structure predict predict Properties & Functionalitie s Quantum Design
4 How to solve the inverse problem? CMD Engine Verify Functionality Predict New Materials Quantum Simulation Find Mechanisms Analyze Physical Mechanism Experimental Verification Integrate Mechanisms
5 Submicron physics Simulation/design of whole submicron structures fm pm nm Most important but difficult scale range submicron μm mm Quantal Yet large scale Real devices
6 An example Transport properties of real device structures Parallel coupling Antiparallel coupling MnPt Ru CoFe Cu CoFe NiFe Ta CoFe 25nm
7 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.
8 1. Halfmetallic AF (compensated ferrimagnets) When two magnetic ions exist One ion more than half d, the other less than half Ferromagnetic coupling V d 3 DOS energy metallic J H E F Co J H d 7 Superexchange works (no degeneracy)
9 Mechanisms In the case of anti-parallel coupling Antiferromagnetic coupling V d 3 half-metallic E F Co d 7 2J H Double exchange works (degeneracy)
10 (ZnCrFe)S (Zn 0.9 Cr 0.05 Fe 0.05 )S AP DOS (states/ry) Antiferro Up spin Down spin total (left) 80 Cr 3d (right) Fe 3d (right) VB half metallic CB P DOS (states/ry) Ferro VB metallic CB D DOS (states/ry) Spin glass Energy relative to Fermi energy (Ry) VB metallic CB
11 Transport properties ferro antiferro Anti-phase domain boundary
12 Transport properties of HM AF DMS? Anti-phase domain boundary
13 (Zn,Cr,Fe)S films Parallel coupling Anti-parallel coupling
14 DC conductivity of (Zn,Cr,Fe)S 1.36x10-3 Ωcm 6.79x10-3 Ωcm Parallel coupling Anti-parallel coupling H. Akai and M.O. J Phys. D 40 (2007) 1238
15 New type of HM AF: (AB)X 2 A 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)Se 2, Structures: NiAs-, Zinc-blende-, chalcopyrite-, wurtzite-, NaCl-type. NiAs-type wurtzite-type ZB-type NaCl-type Chalcopyrite-type
16 NiAs-type (FeCr)Se 2 DOS (states/ry) total Cr d Fe d VB CB AF half metallic total Cr d Fe d DOS (states/ry) 40 0 F metallic total Cr d Fe d DOS (states/ry) metallic SG Energy relative to Fermi energy (Ry)
17 Robust half-metallicity total Cr d Fe d antiferromagnetic disordered state (A 0.5 B 0.5 )X DOS (states/ry) NiAs-type (Fe 0.5 Cr 0.5 )Se Energy relative to Fermi energy (Ry) more than two components (AB 0.5 C 0.5 )X 2 DOS (states/ry) total Cr d Co 0.5 d Mn 0.5 d NiAs-type (CrCo 0.5 Mn 0.5 )Se Energy relative to Fermi energy (Ry)
18 Magnetic moments and total energy Total energy: E AF E LMD = mry E F E LMD = 2.76 mry E ordered E disordered = mry E formation = E CrSe + E FeSe 2E (FeCr)Se2 = 33.5 mry Magnetic moments: Materials Local magnetic moment (μb) Total (μb) (FeCr)Se 2 Cr Fe Se Ordered state Disordered state Stable in antiferromagnetic ordered state
19 Many cases exhibit HM AF Crystal structure NiAs-type structure Zinc-blende structure Wurtzite structure Chalcopyrite structure NaCl-type structure Materials 1E AF - E LMD 2E FR - E LMD (mry) E order - E disorder (mry) Formation E A +E B -2E AB (mry) MF T N (K) (FeCr)Se (VCo)Se (FeCr)Te (VCo)S (FeCr)Se (FeCr)Te (FeCr)Po (FeCr)Te (FeCr)Se (VCo)S non (FeCr)Se non (FeCr)S (VCo)S Transition metal chalcogenides CA
20 (AB)N 2 Crystal structure NiAs-type structure Zinc-blende structure Wurtzite structure Chalcopyrite structure NaCl-type structure Materials 1E AF - E LMD 2E FR - E LMD (mry) E order - E disorder (mry) Formation E A +E B -2E AB (mry) MF T N (K) (MnCo)N (MnCo)N (MnCo)N (MnCo)N non (MnCo)N CA
21 Applications to GMR and TMR devices ال Bit line Bit line Pinned-layer Magnetic free layer Nonmagnetic layer Inner-layer Ru Outer-layer Antiferromagnetic layer Write word line Magnetic free layer Nonmagnetic layer Half-metallic antiferromagnets Write word line Structure using HM AF Currently used structure
22 GMR ratio of GMR/TMR devices currently used structure GMR ratio 19% 1.85Å resistivity µωcm Fe 0.85 Co 0.15 resistivity µωcm 3.70Å Cu 1.85Å 1.85Å 1.85Å Fe 0.85 Co 0.15 Ru Fe 0.85 Co Å Mn
23 Our design of new MRAM cell resistivity µωcm GMR ratio 720% resistivity µωcm 5.77Å Fe 2 Se Å Cu 2 Se Å ZB (FeCr)Se 2
24 Magnetic metallic layers: bcc-cu and bcc-fe GMR ratio 54% resistivity µωcm resistivity µωcm 4.33Å Fe 7.21Å Cu 5.77Å ZB (FeCr)Se 2 Cu Fe Cr
25 Half-metallic diluted antiferromagnetic semiconductors resistivity 2.25 µωcm GMR ratio 264% resistivity 8.18 µωcm 5.67Å GaMnAs 5.67Å GaAlAs 5.67Å ZB Zn(CrFe)Se
26 TMR devices: nonmagnetic spacer resistivity 473 µωcm TMR ratio 3300% resistivity µωcm 5.37Å Cr 2 S Å Ca 2 S Å NiAs (FeCr)S 2
27 2. Spin transport Transport properties and spin dynamics are of vital interest GMR spin injection / accumulation current induced magnetization reversal spin relaxation spin-pumping / battery Spin-Hall effect F/N/F cpp GMR structure F N F
28 What is spin transport? Electric motive force charge/spin current Spin motive force spin/charge current Aims: First principles calculation of DC conductivity Spin conductivity Spin Hall conductivity Inverse spin Hall conductivity Spin injection Spin accumulation
29 Charge and spin currents Current operators J c = e v J s = (h /2)σv Charge current vector Spin current tensor Correlation functions J c J c, J c J s, J s J c, J s J s where O 1 O 2 RR = Tr O 1 G R (E F )O 2 G R (E F ) O 1 O 2 RA = Tr O 1 G R (E F )O 2 G A (E F )
30 Conductivities e.g. σ zz cc = 1 2 R ( j c j c RR z c c RA ) z jz j z cs σ z,zz ( RR c jz j s RA ) zz = 1 2 R j c s z j zz sc σ zz,z = 1 2 R j s zz ( c RR j z s c RA ) jzz j z ss σ zz,zz ( RR s jzz j s RA ) zz = 1 2 R j s s zz j zz
31 Spin-orbit coupling Spin-diagonal components scalar relativistic + l z σ z Spin-off-diagonal components Δt Lσ,L 'σ ' ; r 2 dr R ( Lσ l x σ x + l y σ y )R L 'σ '
32 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
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