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1、9/17/2024方方 忠忠中国科学院物理研究所，理论室中国科学院物理研究所，理论室 Quantum Simulation in the Field ofSpintronics and OrbitronicsAcknowledgement: Y. G. Yao, K. Terakura N. Nagaosa Y. Tokura凝聚态物理前沿讲座凝聚态物理前沿讲座9/17/2024 Contents 1. Quantum simulations based on DFT (1) Simple introduction to first-principles calculations (2) Ou
2、r method, code, and computer facilities 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 dou
3、ble perovskites 4. Surface of transition-metal oxides9/17/2024Quantum Simulation based on DFTAtoms+electronsElectronsMany-bodyElectronsSingle-particleDensityFunctionalAdiabatic ApproximationHohenberg-KohnKohn-ShamHellmann-FeynmanForce and StressMDSCF9/17/2024Self-consistent Solver for KS problemSCFL
4、DAGGALDA+U9/17/2024LDA+U method9/17/2024Pseudopotential SchemeNormal-conservingPseudopotentialUltra-SoftPseudopotential9/17/2024Virtual Crystal Approxmation (VCA)For virtual atomsSolve Schrodinger equationIonic unscreened potential9/17/2024How to solve the single particle problem Real Space (no FFT)
5、 Finite element Finite difference Multi-grid Adaptive Wavelet Reciprocal Space (with FFT) LACO LMTO FLAPW PAW Plane-wave Greens function Pseudopotential, ASA, 9/17/2024Other Problems in Simulations1. Exchange-correlation functional2. Strongly-correlated systems3. Force calculation & Molecular dynami
6、cs4. Magnetic, optical & electronic properties5. Excited States6. Non-equilibrium & Time-dependent process7. Order (N) method & Large scale8. Catalysis, Chemical reaction, Bio-systems9. 9/17/20241.First-principles calculations based on DFT2.Plane-wave basis3.Ultra-soft Pseudo-potential4.LDA, GGA, LD
7、A+U, etc5.Virtual crystal approximation (VCA)6.Real space RMM for larger systems7.Full parallelization by MPI8. SGI, IBM-SP, Alpha, Cray, VPP, PC-ClusterOur Method9/17/2024 STATE Code: (Simulational Tool for Atom Technology)Main Contributors: Z. Fang,Y. Morikawa, T. Ikeda, H. Sawadaand other JRCAT m
8、embersFor details: Z. Fang, , J. Phys: Cond. Matt., 14, 3001 (2001). (review article) 100,000 lines, Accuracy 1meV/Atom, 200 atoms.Widely used in Japan, Taiwan, Korea, Denmark, etc.9/17/2024IBM SP690, 64 CPUs, 128G, 1T-disk9/17/2024Three Characters of Electron Charge Spin Orbitalwell known “hot” top
9、ic newExtensively used being used will be usedI, V, Charge currentCharge excitation spin wave orbitonCharge current spin current movement anisotropy functionality .9/17/2024SpintronicsThe electron has both charge and spin.Mostly only the charge property is used. Energy scale for the charge interacti
10、on is high, 1eV, energy scale for the spin interaction is low, 10-100 meV. Much lower power consumption for spin-based device. Spin-based electronics also promises a greater integration between the logic and storage devices9/17/2024Problems for Spintronic devices spin injection into semiconductor Oh
11、mic injection from ferromagnet Low efficiency(Difficulty): Ferromagnetic metal : conductivity mismatch 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 ferromag
12、net spin transport in semiconductor spin relaxation timeOptical pump and probe9/17/2024Only two known 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
13、under T. In the QHE, the Hall conductivity is proportional to the magnetic field B, which is odd under 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. 9/17/2024New dissipation
14、less transport in solidsdue to spin-orbital coupling! Anomalous Hall Effect (charge current): 1 , ., PRL, 88, 207208(2002); 2 , , SCIENCE, 302, 92 (2003) 3 , , PRL, 92, 37204 (2004); 4 , , SCIENCE, 303, 1647 (2003) Conventional: xy = R0H + 4RSM Intrinsic Mechanism:xyxy(M) Thus Jx=xyEy is T invariant
15、 J is odd, E is even, M is odd Dissipationless spin Hall current:1 , , SCIENCE, 301, 1348 (2003); 2 , ., PRL, 83, 1834 (1999)3 , , PRL, 92, 126603 (2004) 4 , ., cond-mat/040305.5 & , cond-mat/0403083. Spin current is even under T9/17/2024BjHFMjAHEConventional HallAnomalous HallEESpinjSHEESpin Hall9/
16、17/2024Merit 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).9/17/2024 Spin-Orbital Coupling Berry Phase Magnetic Monopoles in Momentum SpaceAnomalous Hall current and Spin Hall current (Both are dissipation
17、less)Intrinsic Mechanism9/17/2024Effective 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 transiti
18、ons only retain the intra-band matrix elements 9/17/2024Full Quantum Calculations Based on Kubo FormularAnomalous Hall conductivitywithSpin Hall conductivityJys9/17/2024Conserved Spin Current(, ., cond-mat/0310005)Conserved spinwhich satisfydefine current i, n, m = band index, = kramers doublets ind
19、ex9/17/2024Z. Fang, ., SCIENCE 302, 92 (2003)反常反常HallHall效应与动量空间中的磁单极效应与动量空间中的磁单极9/17/2024Calculated Gauge Flux for kz=0 in SrRuO3bz(kz=0)GMMMMZ. Fang, , SCIENCE, 302, 92 (2003)9/17/2024SrRuO39/17/2024SrRuO39/17/2024Calculated Spin Hall Current in GaAs9/17/2024Calculated Spin Current for GaAs and Sn
20、Te9/17/2024One Example for Half-MetalMnAs9/17/2024Fully spin polarized anomalous Hall current in MnAsSpin conductivityAHE conductivity9/17/2024Anomalous Nernst EffectBVFMVConventionalAnomalous9/17/2024Inverse Anomalous Nernst Effect:Cooling and refrigeratorFMHeat current jQExHeat current:Eq. of moti
21、on:9/17/2024egt2g3z2-r2x2-y2xyyzzxOrbitronics9/17/2024Orbital Degrees of Freedom (ODF)EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg2-fold (ODF)3-fold“Half-metal”9/17/2024Various OrderingsFMA-typeC-typeG-typeLatticeSpinChargeOrbitalSC, TMR, CMR,M-I Transition,Anomalous Hall Effect,Magneto-optical,Ferroe
22、lectricity,Piezoelectricity, etc 9/17/2024ExperimentalTheoreticalSCIENCE 288, 462(2000).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(2000).9/17/2024FMA-AFC-AFG-AFOrbital and Spin OrderingsPhys
23、ics: Spin Orbital Lattice Double exchange Super-exchange Compression Less conductivity9/17/2024Electric-Field-induced Orbital SwitchingK. Hatsuda, APL 83, 3329 (2003).9/17/2024LatticeSpinChargeOrbitalElectronic Structures of Ca2-xSrxRuO4EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg3-fold9/17/2024Ca2-xS
24、rxRuO4 : Isovalent substitution Rotation Rotation Rotation + + Tilting Tilting + CompressionAF MottInsulatorNearlyFM MetalS. Nakatsuji, et al., PRLO. Friedt, et al., PRB9/17/2024Issues:1. (1) How to understand the complicated 2. phase diagram.3. (2) Whats the rule of orbital.9/17/2024Effects of Stru
25、cture DistortionsZ. Fang & K. Terakura, PRB64, R20509(2001)Rotationxy orbitalVHSFMTiltingyz, zxnestingAF9/17/2024Occupations and MagnetizationsZ. Fang et al. PRB (2004).9/17/2024Orbital Phase Diagram of Ca2-xSrxRuO4CaSrDoping xEEfxyyz, zxEEfxyyz, zxEEfxyyz, zxxyxy ferro-orbital orderingAF, S=1 from
26、yz, zxFM, S=1/2 from xyItinerant yz, zx with small SNM stateWith VHS from xy1. J. H. Jung, Z. Fang, ., PRL 91, 056403(2003).2. Z. Fang, ., PRB 69, 045116 (2004).9/17/2024110RuO6 八面体在表面的旋转八面体在表面的旋转Sr2RuO4的表面电子结构的表面电子结构LEEDSTM1. R. Matzdorf, Z. Fang, ., SCIENCE 289,746(2000).2. Z. Fang, ., PRB 64, R20
27、509 (2001)9/17/2024PDOS of various doping x9/17/2024Exp. XASCalculated XAS90K300K9/17/2024Optical conductivityExperimentsCalculationsJ. H. Jung, Z. Fang, et al. PRL (2003).9/17/2024FeFeMSr2FeMO6 (M=Mo, W, Re)8 1.Why Tc is so high for M=Mo, Re?2.Why M=W case is AF insulator?9/17/2024EFd statesd state
28、sMajority spinMinority spinMo d stateor other p statesFMZ. Fang, ., PRB 63, R180407 (2001) EFd statesd statesMajority spinMinority spinMo d statesor other p statesAFNew Mechanism for Sr2FeMO6 and (Ga1-xMnx)As9/17/2024Fe (t2g)SpinEF M (t2g)(M=Mo, Re)Fe (t2g)Electronic Structure of Sr2FeMoO69/17/2024S
29、urface of SrTiO3 with Oxygen Vacancy Important substrate Surface gas sensitivity Ferroelectricity Catalytically active9/17/2024STMSTST. Kubo, ., PRL 86, 1801 (2001)H. Tanaka, .,Jpn. J. Appl. Phys. 32, 1405 (1993)9/17/20249/17/2024StructureChargeMagnetizationSrOTiO2Sr Ti OLDA+USurface of SrTiO3 with
30、oxygen vacancy (Spin polarized surface)Z. Fang, ., Surf. Sci. Lett. 470, L75 (2001)9/17/20249/17/2024SrO termination (GGA)TiO2 termination (GGA)262626TiO2 termination (LDA+U) 5 x 5 STM of SrTiO3 surface9/17/2024100100001001SurfaceCentral（ （La, Sr)O terminationMnO2 terminationMnOrbital polarization o
31、n the surfaces of La1-xSrxMnO3, ., J. Phys. Soc. Jpn. 70, 3356(2001).9/17/2024 SummaryQuantum Simulation Charge Spin Orbital(Electronics) (Spintronics) (Orbitronics)Problems: 1. Efficient method for cross-correlated systems 2. Towards large scale (surface & interface) 3. Accurate method for many-body systems
