凝聚態(tài)物理前沿講座方忠QuantumSimulationintheFieldofSpintronicsandOrbitronics市公開(kāi)課獲獎(jiǎng)?wù)n件

1、方 忠中國(guó)科學(xué)院物理研究所，理論室 Quantum Simulation in the Field ofSpintronics and OrbitronicsAcknowledgement: Y. G. Yao, K. Terakura N. Nagaosa Y. Tokura凝聚態(tài)物理前沿講座第1頁(yè)第1頁(yè) Contents 1. Quantum simulations based on DFT (1) Simple introduction to first-principles calculations (2) Our method, code, and computer faciliti

2、es 2. Dissipationless quantum current for spintronics (1) Anomalous Hall Effect (2) Spin Hall Current (3) Anomalous Nernst Effect 3. Orbiton and Orbitronics (1) Phase diagram of La1-xSrxMnO3 (2) Orbital-dependent phase control in Ca2-xSrxRuO4 (3) Magnetism in double perovskites 4. Surface of transit

3、ion-metal oxides第2頁(yè)第2頁(yè)Quantum Simulation based on DFTAtoms+electronsElectronsMany-bodyElectronsSingle-particleDensityFunctionalAdiabatic ApproximationHohenberg-KohnKohn-ShamHellmann-FeynmanForce and StressMDSCF第3頁(yè)第3頁(yè)Self-consistent Solver for KS problemSCFLDAGGALDA+U第4頁(yè)第4頁(yè)LDA+U method第5頁(yè)第5頁(yè)P(yáng)seudopot

4、ential SchemeNormal-conservingPseudopotentialUltra-SoftPseudopotential第6頁(yè)第6頁(yè)Virtual Crystal Approxmation (VCA)For virtual atomsSolve Schrodinger equationIonic unscreened potential第7頁(yè)第7頁(yè)How to solve the single particle problem Real Space (no FFT) Finite element Finite difference Multi-grid Adaptive W

5、avelet Reciprocal Space (with FFT) LACO LMTO FLAPW PAW Plane-wave Greens function Pseudopotential, ASA, 第8頁(yè)第8頁(yè)Other Problems in Simulations Exchange-correlation functional Strongly-correlated systems Force calculation & Molecular dynamics Magnetic, optical & electronic properties Excited States Non-

6、equilibrium & Time-dependent process Order (N) method & Large scale Catalysis, Chemical reaction, Bio-systems 第9頁(yè)第9頁(yè)First-principles calculations based on DFTPlane-wave basisUltra-soft Pseudo-potentialLDA, GGA, LDA+U, etcVirtual crystal approximation (VCA)Real space RMM for larger systemsFull parall

7、elization by MPI SGI, IBM-SP, Alpha, Cray, VPP, PC-ClusterOur Method第10頁(yè)第10頁(yè) STATE Code: (Simulational Tool for Atom Technology)Main Contributors: Z. Fang,Y. Morikawa, T. Ikeda, H. Sawadaand other JRCAT membersFor details: Z. Fang, et.al, J. Phys: Cond. Matt., 14, 3001 (). (review article) 100,000 l

8、ines, Accuracy 1meV/Atom, 200 atoms.Widely used in Japan, Taiwan, Korea, Denmark, etc.第11頁(yè)第11頁(yè)IBM SP690, 64 CPUs, 128G, 1T-disk第12頁(yè)第12頁(yè)Three Characters of Electron Charge Spin Orbitalwell known “hot” topic newExtensively used being used will be usedI, V, Charge currentCharge excitation spin wave orb

9、itonCharge current spin current movement anisotropy functionality .第13頁(yè)第13頁(yè)SpintronicsThe electron has both charge and spin.Mostly only the charge property is used. Energy scale for the charge interaction is high, 1eV, energy scale for the spin interaction is low, 10-100 meV. Much lower power consum

10、ption for spin-based device. Spin-based electronics also promises a greater integration between the logic and storage devices第14頁(yè)第14頁(yè)P(yáng)roblems for Spintronic devices spin injection into semiconductor Ohmic injection from ferromagnet Low efficiency(Difficulty): Ferromagnetic metal : conductivity misma

11、tch spin polarization is almost lost at interface. Ferromagnetic semiconductor (e.g. Ga1-xMnxAs) : Curie temperature much lower than room temp. Ferromagnetic tunnel junction. spin detection by ferromagnet spin transport in semiconductor spin relaxation timeOptical pump and probe第15頁(yè)第15頁(yè)Only two know

12、n examples of dissipationless transport in solids! Supercurrent in a superconductor is dissipationless, since London equation related J to A, not to E!Vector potential=odd under T, charge current=odd under T. In the QHE, the Hall conductivity is proportional to the magnetic field B, which is odd und

13、er T.Laughlin argument: all states below the fermi energy contribute to the Hall conductance.Streda formula, TKNN formula relates the Hall conductance to the 1st Chern number. 第16頁(yè)第16頁(yè)New dissipationless transport in solidsdue to spin-orbital coupling! Anomalous Hall Effect (charge current): 1 T.Jun

14、gwirth, et.al., PRL, 88, 207208(); 2 Z.Fang, et.al, SCIENCE, 302, 92 () 3 Y.G.Yao, et.al, PRL, 92, 37204 (); 4 W.L.Lee, et.al, SCIENCE, 303, 1647 () Conventional: xy = R0H + 4RSM Intrinsic Mechanism:xyxy(M) Thus Jx=xyEy is T invariant J is odd, E is even, M is odd Dissipationless spin Hall current:1

15、 S.Murakami, et.al, SCIENCE, 301, 1348 (); 2 J.E.Hirsch, et.al., PRL, 83, 1834 (1999)3 J.Sinova, et.al, PRL, 92, 126603 () 4 S.Q.Shen, et.al., cond-mat/040305.5 Y.Xiong & X.C.Xie, cond-mat/0403083. Spin current is even under T第17頁(yè)第17頁(yè)BjHFMjAHEConventional HallAnomalous HallEESpinjSHEESpin Hall第18頁(yè)第1

16、8頁(yè)Merit of AHE and SHE 1. It works because of spin-orbital coupling, which is active even at room T. 2. It is entirely topological (dissipationless).第19頁(yè)第19頁(yè) Spin-Orbital Coupling Berry Phase Magnetic Monopoles in Momentum SpaceAnomalous Hall current and Spin Hall current (Both are dissipationless)I

17、ntrinsic Mechanism第20頁(yè)第20頁(yè)Effective Hamiltonian for adiabatic transportEquation of motion(Dirac monopole)Drift velocityTopological termNontrivial spin dynamics comes from the Dirac monopole at the center of k space, witheg=l:Adiabatic transport = potential V does not cause inter-band transitions onl

18、y retain the intra-band matrix elements 第21頁(yè)第21頁(yè)Full Quantum Calculations Based on Kubo FormularAnomalous Hall conductivitywithSpin Hall conductivityJys第22頁(yè)第22頁(yè)Conserved Spin Current(S.Murakami, et.al., cond-mat/0310005)Conserved spinwhich satisfydefine current i, n, m = band index, = kramers double

19、ts index第23頁(yè)第23頁(yè)Z. Fang, et.al., SCIENCE 302, 92 ()反常Hall效應(yīng)與動(dòng)量空間中磁單極第24頁(yè)第24頁(yè)Calculated Gauge Flux for kz=0 in SrRuO3bz(kz=0)GMMMMZ. Fang, et.al, SCIENCE, 302, 92 ()第25頁(yè)第25頁(yè)SrRuO3第26頁(yè)第26頁(yè)SrRuO3第27頁(yè)第27頁(yè)Calculated Spin Hall Current in GaAs第28頁(yè)第28頁(yè)Calculated Spin Current for GaAs and SnTe第29頁(yè)第29頁(yè)One Exa

20、mple for Half-MetalMnAs第30頁(yè)第30頁(yè)Fully spin polarized anomalous Hall current in MnAsSpin conductivityAHE conductivity第31頁(yè)第31頁(yè)Anomalous Nernst EffectBVFMVConventionalAnomalous第32頁(yè)第32頁(yè)Inverse Anomalous Nernst Effect:Cooling and refrigeratorFMHeat current jQExHeat current:Eq. of motion:第33頁(yè)第33頁(yè)egt2g3z2-r

21、2x2-y2xyyzzxOrbitronics第34頁(yè)第34頁(yè)Orbital Degrees of Freedom (ODF)EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg2-fold (ODF)3-fold“Half-metal”第35頁(yè)第35頁(yè)Various OrderingsFMA-typeC-typeG-typeLatticeSpinChargeOrbitalSC, TMR, CMR,M-I Transition,Anomalous Hall Effect,Magneto-optical,Ferroelectricity,Piezoelectric

22、ity, etc 第36頁(yè)第36頁(yè)ExperimentalTheoreticalSCIENCE 288, 462().J. Phys. Soc. Jap. 68, 3790(1999).Phase Diagram of Tetragonal La1-xSrxMnO3(Controlling of Orbital and Spin Orderings)Z. Fang & K. Terakura, PRL 84, 3169().第37頁(yè)第37頁(yè)FMA-AFC-AFG-AFOrbital and Spin OrderingsPhysics: Spin Orbital Lattice Double e

23、xchange Super-exchange Compression Less conductivity第38頁(yè)第38頁(yè)Electric-Field-induced Orbital SwitchingK. Hatsuda, APL 83, 3329 ().第39頁(yè)第39頁(yè)LatticeSpinChargeOrbitalElectronic Structures of Ca2-xSrxRuO4EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg3-fold第40頁(yè)第40頁(yè)Ca2-xSrxRuO4 : Isovalent substitution Rotation

24、Rotation Rotation + + Tilting Tilting + CompressionAF MottInsulatorNearlyFM MetalS. Nakatsuji, et al., PRLO. Friedt, et al., PRB第41頁(yè)第41頁(yè)Issues: (1) How to understand the complicated phase diagram. (2) Whats the rule of orbital.第42頁(yè)第42頁(yè)Effects of Structure DistortionsZ. Fang & K. Terakura, PRB64, R20

25、509()Rotationxy orbitalVHSFMTiltingyz, zxnestingAF第43頁(yè)第43頁(yè)Occupations and MagnetizationsZ. Fang et al. PRB ().第44頁(yè)第44頁(yè)Orbital Phase Diagram of Ca2-xSrxRuO4CaSrDoping x0.0 0.2 0.5 2.0EEfxyyz, zxEEfxyyz, zxEEfxyyz, zxxyxy ferro-orbital orderingAF, S=1 from yz, zxFM, S=1/2 from xyItinerant yz, zx with

26、small SNM stateWith VHS from xy1. J. H. Jung, Z. Fang, et.al., PRL 91, 056403().2. Z. Fang, et.al., PRB 69, 045116 ().第45頁(yè)第45頁(yè)110RuO6 八面體在表面旋轉(zhuǎn)Sr2RuO4表面電子結(jié)構(gòu)LEEDSTM1. R. Matzdorf, Z. Fang, et.al., SCIENCE 289,746().2. Z. Fang, et.al., PRB 64, R20509 ()第46頁(yè)第46頁(yè)P(yáng)DOS of various doping x第47頁(yè)第47頁(yè)Exp. XASCa

27、lculated XAS90K300K第48頁(yè)第48頁(yè)Optical conductivityExperimentsCalculationsJ. H. Jung, Z. Fang, et al. PRL ().第49頁(yè)第49頁(yè)FeFeMSr2FeMO6 (M=Mo, W, Re)8 Why Tc is so high for M=Mo, Re?Why M=W case is AF insulator?第50頁(yè)第50頁(yè)EFd statesd statesMajority spinMinority spinMo d stateor other p statesFMZ. Fang, et.al., PRB 63, R180407 () EFd statesd statesMajority spinMinority spinMo d statesor other p statesAFNew Mechanism for Sr2FeMO6 and (Ga1-xMnx)As第51頁(yè)第51頁(yè)Fe (t2g)SpinEF M (t2g)(M=Mo, Re)Fe (t2g)Electronic Structure of Sr2FeMoO6第52頁(yè)第5