Papan-Germany Joint Workshop 2009 Kyoto, 21-23 Jan. 2009 Computational materials design and its application to spintronics H. Akai, M. Ogura, and N.H. Long Department of Physics, Osaka University
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
Simulation and design Design: the inverse problem of simulation Quantum Simulation Materials & Structure predict predict Properties & Functionalitie s Quantum Design
How to solve the inverse problem? CMD Engine Verify Functionality Predict New Materials Quantum Simulation Find Mechanisms Analyze Physical Mechanism Experimental Verification Integrate Mechanisms
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
An example Transport properties of real device structures Parallel coupling Antiparallel coupling MnPt Ru CoFe Cu CoFe NiFe Ta CoFe 25nm
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 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)
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)
(ZnCrFe)S (Zn 0.9 Cr 0.05 Fe 0.05 )S AP DOS (states/ry) 30 20 10 0 10 20 Antiferro Up spin Down spin total (left) 80 Cr 3d (right) Fe 3d (right) 40 0 40 VB half metallic CB 30 80 P DOS (states/ry) 30 20 10 0 10 20 Ferro 80 40 0 40 VB metallic CB 30 80 D DOS (states/ry) 30 20 10 0 Spin glass -0.4-0.2 0 0.2 Energy relative to Fermi energy (Ry) 80 40 0 VB metallic CB
Transport properties ferro antiferro Anti-phase domain boundary
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 Parallel coupling Anti-parallel coupling H. Akai and M.O. J Phys. D 40 (2007) 1238
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
NiAs-type (FeCr)Se 2 DOS (states/ry) 80 40 0 total Cr d Fe d VB CB AF -40-80 half metallic -0.4-0.2 0.0 0.2 80 total Cr d Fe d DOS (states/ry) 40 0 F -40-80 metallic -0.4-0.2 0.0 0.2 60 total Cr d Fe d DOS (states/ry) 40 20 metallic SG 0-0.4-0.2 0.0 0.2 Energy relative to Fermi energy (Ry)
Robust half-metallicity 60 40 total Cr d Fe d antiferromagnetic disordered state (A 0.5 B 0.5 )X DOS (states/ry) 20 0-20 -40-60 NiAs-type (Fe 0.5 Cr 0.5 )Se -0.4-0.2 0.0 0.2 Energy relative to Fermi energy (Ry) more than two components (AB 0.5 C 0.5 )X 2 DOS (states/ry) 80 40 0 total Cr d Co 0.5 d Mn 0.5 d -40-80 NiAs-type (CrCo 0.5 Mn 0.5 )Se 2-0.4-0.2 0.0 0.2 Energy relative to Fermi energy (Ry)
Magnetic moments and total energy Total energy: E AF E LMD = -17.83 mry E F E LMD = 2.76 mry E ordered E disordered = -19.1 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 3.2353-3.1364-0.1754 0.0009 Disordered state 3.2996-3.1815-0.1871 0.0014 Stable in antiferromagnetic ordered state
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 2-17.83 2.76-19.10 33.50 1094 873 (VCo)Se 2-7.83 7.69-37.58 67.90 565 426 (FeCr)Te 2-12.74 1.47-8.26 4.89 612 521 (VCo)S 2-22.14 3.44-93.70 212.86 1101 1048 (FeCr)Se 2-20.96 14.50-10.90 33.48 1038 817 (FeCr)Te 2-15.53 9.85-9.20 15.60 807 647 (FeCr)Po 2-12.59 6.87-14.81 15.02 794 630 (FeCr)Te 2-10.16 6.98-2.18 6.35 588 498 (FeCr)Se 2-12.50 10.18-0.90 13.61 728 535 (VCo)S 2-24.13 4.15 non 200.5 1159 1025 (FeCr)Se 2-22.65 15.98 non 27.24 1235 1097 (FeCr)S 2-7.00-4.66-1.39 4.96 420 306 (VCo)S 2-1.15 6.39-29.80 68.09 94 67 Transition metal chalcogenides CA
(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 2-31.85-8.28-8.03 23.42 347 327 (MnCo)N 2-29.34 9.71-10.97 14.89 519 420 (MnCo)N 2-24.15 3.51-2.42 14.50 295 268 (MnCo)N 2-29.61 9.17 non 15.11 530 445 (MnCo)N 2-26.46-1.14-6.87 15.79 196 143 CA
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
GMR ratio of GMR/TMR devices currently used structure GMR ratio 19% 1.85Å resistivity 78.60 µωcm Fe 0.85 Co 0.15 resistivity 63.33 µωcm 3.70Å Cu 1.85Å 1.85Å 1.85Å Fe 0.85 Co 0.15 Ru Fe 0.85 Co 0.15 3.70Å Mn
Our design of new MRAM cell resistivity 65.58 µωcm GMR ratio 720% resistivity 536.78 µωcm 5.77Å Fe 2 Se 2 5.77Å Cu 2 Se 2 5.77Å ZB (FeCr)Se 2
Magnetic metallic layers: bcc-cu and bcc-fe GMR ratio 54% resistivity 61.89 µωcm resistivity 95.05 µωcm 4.33Å Fe 7.21Å Cu 5.77Å ZB (FeCr)Se 2 Cu Fe Cr
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
TMR devices: nonmagnetic spacer resistivity 473 µωcm TMR ratio 3300% resistivity 16103 µωcm 5.37Å Cr 2 S 2 5.37Å Ca 2 S 2 5.37Å NiAs (FeCr)S 2
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
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
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 )
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
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 '
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