凝聚态物理前沿讲座.ppt

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1、10/27/2022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10/27/2022 Contents 1.Quantum simulations based on DFT (1)Simple introduction to first-principles calculations (2)Our method

2、,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 double perovskites 4.

3、Surface of transition-metal oxides10/27/2022Quantum Simulation based on DFTAtoms+electronsElectronsMany-bodyElectronsSingle-particleDensityFunctionalAdiabatic ApproximationHohenberg-KohnKohn-ShamHellmann-FeynmanForce and StressMDSCF10/27/2022Self-consistent Solver for KS problemSCFLDAGGALDA+U10/27/2

4、022LDA+U method10/27/2022Pseudopotential SchemeNormal-conservingPseudopotentialUltra-SoftPseudopotential10/27/2022Virtual Crystal Approxmation(VCA)For virtual atomsSolve Schrodinger equationIonic unscreened potential10/27/2022How to solve the single particle problem Real Space (no FFT)Finite element

5、 Finite difference Multi-grid Adaptive Wavelet Reciprocal Space (with FFT)LACO LMTO FLAPW PAW Plane-wave Greens function Pseudopotential,ASA,10/27/2022Other Problems in Simulations1.Exchange-correlation functional2.Strongly-correlated systems3.Force calculation&Molecular dynamics4.Magnetic,optical&e

6、lectronic properties5.Excited States6.Non-equilibrium&Time-dependent process7.Order(N)method&Large scale8.Catalysis,Chemical reaction,Bio-systems9.10/27/20221.First-principles calculations based on DFT2.Plane-wave basis3.Ultra-soft Pseudo-potential4.LDA,GGA,LDA+U,etc5.Virtual crystal approximation(V

7、CA)6.Real space RMM for larger systems7.Full parallelization by MPI8.SGI,IBM-SP,Alpha,Cray,VPP,PC-ClusterOur Method10/27/2022 STATE Code:(Simulational Tool for Atom Technology)Main Contributors:Z.Fang,Y.Morikawa,T.Ikeda,H.Sawadaand other JRCAT membersFor details:Z.Fang,J.Phys:Cond.Matt.,14,3001(2001

8、).(review article)100,000 lines,Accuracy 1meV/Atom,200 atoms.Widely used in Japan,Taiwan,Korea,Denmark,etc.10/27/2022IBM SP690,64 CPUs,128G,1T-disk10/27/2022Three Characters of Electron Charge Spin Orbitalwell known “hot”topic newExtensively used being used will be usedI,V,Charge currentCharge excit

9、ation spin wave orbitonCharge current spin current movement anisotropy functionality .10/27/2022SpintronicsThe 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 lo

10、wer power consumption for spin-based device.Spin-based electronics also promises a greater integration between the logic and storage devices10/27/2022Problems for Spintronic devices spin injection into semiconductor Ohmic injection from ferromagnet Low efficiency(Difficulty):Ferromagnetic metal:cond

11、uctivity 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 ferromagnet spin transport in semiconductor spin relaxation timeOptical pump and probe10/27/2022Onl

12、y 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 under T.In the QHE,the Hall conductivity is proportional to the magnetic field B,which is odd

13、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.10/27/2022New dissipationless transport in solidsdue to spin-orbital coupling!Anomalous Hall Effect(charge current):1,.,PRL,

14、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 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,.,co

15、nd-mat/040305.5&,cond-mat/0403083.Spin current is even under T10/27/2022BjHFMjAHEConventional HallAnomalous HallEESpinjSHEESpin Hall10/27/2022Merit 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).10/27/2022 Spin-

16、Orbital Coupling Berry Phase Magnetic Monopoles in Momentum SpaceAnomalous Hall current and Spin Hall current (Both are dissipationless)Intrinsic Mechanism10/27/2022Effective Hamiltonian for adiabatic transportEquation of motion(Dirac monopole)Drift velocityTopological termNontrivial spin dynamics c

17、omes from the Dirac monopole at the center of k space,witheg=l:Adiabatic transport=potential V does not cause inter-band transitions only retain the intra-band matrix elements 10/27/2022Full Quantum Calculations Based on Kubo FormularAnomalous Hall conductivitywithSpin Hall conductivityJys10/27/2022

18、Conserved Spin Current(,.,cond-mat/0310005)Conserved spinwhich satisfydefine current i,n,m =band index,=kramers doublets index10/27/2022Z.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10/27/2022Calculated Gauge Flux for kz=0 in SrRuO3bz(kz=0)GMMMMZ.Fang,SCIENCE,302,92(2003)10/27/202

19、2SrRuO310/27/2022SrRuO310/27/2022Calculated Spin Hall Current in GaAs10/27/2022Calculated Spin Current for GaAs and SnTe10/27/2022One Example for Half-MetalMnAs10/27/2022Fully spin polarized anomalous Hall current in MnAsSpin conductivityAHE conductivity10/27/2022Anomalous Nernst EffectBVFMVConventi

20、onalAnomalous10/27/2022Inverse Anomalous Nernst Effect:Cooling and refrigeratorFMHeat current jQExHeat current:Eq.of motion:10/27/2022egt2g3z2-r2x2-y2xyyzzxOrbitronics10/27/2022Orbital Degrees of Freedom(ODF)EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg2-fold(ODF)3-fold“Half-metal”10/27/2022Various Ord

21、eringsFMA-typeC-typeG-typeLatticeSpinChargeOrbitalSC,TMR,CMR,M-I Transition,Anomalous Hall Effect,Magneto-optical,Ferroelectricity,Piezoelectricity,etc 10/27/2022ExperimentalTheoreticalSCIENCE 288,462(2000).J.Phys.Soc.Jap.68,3790(1999).Phase Diagram of Tetragonal La1-xSrxMnO3(Controlling of Orbital

22、and Spin Orderings)Z.Fang&K.Terakura,PRL 84,3169(2000).10/27/2022FMA-AFC-AFG-AFOrbital and Spin OrderingsPhysics:Spin Orbital Lattice Double exchange Super-exchange Compression Less conductivity10/27/2022Electric-Field-induced Orbital SwitchingK.Hatsuda,APL 83,3329(2003).10/27/2022LatticeSpinChargeO

23、rbitalElectronic Structures of Ca2-xSrxRuO4EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg3-fold10/27/2022Ca2-xSrxRuO4:Isovalent substitution Rotation Rotation Rotation +Tilting Tilting +CompressionAF MottInsulatorNearlyFM MetalS.Nakatsuji,et al.,PRLO.Friedt,et al.,PRB10/27/2022Issues:1.(1)How to underst

24、and the complicated 2.phase diagram.3.(2)Whats the rule of orbital.10/27/2022Effects of Structure DistortionsZ.Fang&K.Terakura,PRB64,R20509(2001)Rotationxy orbitalVHSFMTiltingyz,zxnestingAF10/27/2022Occupations and MagnetizationsZ.Fang et al.PRB(2004).10/27/2022Orbital Phase Diagram of Ca2-xSrxRuO4C

25、aSrDoping xEEfxyyz,zxEEfxyyz,zxEEfxyyz,zxxyxy ferro-orbital orderingAF,S=1 from 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).10/27/2022110RuO6 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

26、,Z.Fang,.,SCIENCE 289,746(2000).2.Z.Fang,.,PRB 64,R20509(2001)10/27/2022PDOS of various doping x10/27/2022Exp.XASCalculated XAS90K300K10/27/2022Optical conductivityExperimentsCalculationsJ.H.Jung,Z.Fang,et al.PRL(2003).10/27/2022FeFeMSr2FeMO6(M=Mo,W,Re)8 1.Why Tc is so high for M=Mo,Re?2.Why M=W cas

27、e is AF insulator?10/27/2022EFd statesd statesMajority 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)As10/27/2022Fe(t2g)SpinEF M(t2g)(M=Mo,Re)Fe(t2g)Electron

28、ic Structure of Sr2FeMoO610/27/2022Surface of SrTiO3 with Oxygen Vacancy Important substrate Surface gas sensitivity Ferroelectricity Catalytically active10/27/2022STMSTST.Kubo,.,PRL 86,1801(2001)H.Tanaka,.,Jpn.J.Appl.Phys.32,1405(1993)10/27/202210/27/2022StructureChargeMagnetizationSrOTiO2Sr Ti OLD

29、A+USurface of SrTiO3 with oxygen vacancy (Spin polarized surface)Z.Fang,.,Surf.Sci.Lett.470,L75(2001)10/27/202210/27/2022SrO termination(GGA)TiO2 termination(GGA)262626TiO2 termination(LDA+U)5 x 5 STM of SrTiO3 surface10/27/2022100100001001SurfaceCentral（La,Sr)O terminationMnO2 terminationMnOrbital

30、polarization on the surfaces of La1-xSrxMnO3,.,J.Phys.Soc.Jpn.70,3356(2001).10/27/2022 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