凝聚態(tài)物理前沿講座方忠QuantumSimulationintheFieldofSpintronicsandOrbitronics市公開課獲獎課件

1、方 忠中國科學院物理研究所，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頁第1頁 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頁第2頁Quantum Simulation based on DFTAtoms+electronsElectronsMany-bodyElectronsSingle-particleDensityFunctionalAdiabatic ApproximationHohenberg-KohnKohn-ShamHellmann-FeynmanForce and StressMDSCF第3頁第3頁Self-consistent Solver for KS problemSCFLDAGGALDA+U第4頁第4頁LDA+U method第5頁第5頁Pseudopot

4、ential SchemeNormal-conservingPseudopotentialUltra-SoftPseudopotential第6頁第6頁Virtual Crystal Approxmation (VCA)For virtual atomsSolve Schrodinger equationIonic unscreened potential第7頁第7頁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頁第8頁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頁第9頁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頁第10頁 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頁第11頁IBM SP690, 64 CPUs, 128G, 1T-disk第12頁第12頁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頁第13頁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頁第14頁Problems 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頁第15頁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頁第16頁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頁第17頁BjHFMjAHEConventional HallAnomalous HallEESpinjSHEESpin Hall第18頁第1

16、8頁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頁第19頁 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頁第20頁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頁第21頁Full Quantum Calculations Based on Kubo FormularAnomalous Hall conductivitywithSpin Hall conductivityJys第22頁第22頁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頁第23頁Z. Fang, et.al., SCIENCE 302, 92 ()反常Hall效應與動量空間中磁單極第24頁第24頁Calculated Gauge Flux for kz=0 in SrRuO3bz(kz=0)GMMMMZ. Fang, et.al, SCIENCE, 302, 92 ()第25頁第25頁SrRuO3第26頁第26頁SrRuO3第27頁第27頁Calculated Spin Hall Current in GaAs第28頁第28頁Calculated Spin Current for GaAs and SnTe第29頁第29頁One Exa

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

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

22、ity, etc 第36頁第36頁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頁第37頁FMA-AFC-AFG-AFOrbital and Spin OrderingsPhysics: Spin Orbital Lattice Double e

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

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

25、509()Rotationxy orbitalVHSFMTiltingyz, zxnestingAF第43頁第43頁Occupations and MagnetizationsZ. Fang et al. PRB ().第44頁第44頁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頁第45頁110RuO6 八面體在表面旋轉Sr2RuO4表面電子結構LEEDSTM1. R. Matzdorf, Z. Fang, et.al., SCIENCE 289,746().2. Z. Fang, et.al., PRB 64, R20509 ()第46頁第46頁PDOS of various doping x第47頁第47頁Exp. XASCa

27、lculated XAS90K300K第48頁第48頁Optical conductivityExperimentsCalculationsJ. H. Jung, Z. Fang, et al. PRL ().第49頁第49頁FeFeMSr2FeMO6 (M=Mo, W, Re)8 Why Tc is so high for M=Mo, Re?Why M=W case is AF insulator?第50頁第50頁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頁第51頁Fe (t2g)SpinEF M (t2g)(M=Mo, Re)Fe (t2g)Electronic Structure of Sr2FeMoO6第52頁第5