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1、,方 忠中国科学院物理研究所，理论室,Quantum Simulation in the Field ofSpintronics and Orbitronics,Acknowledgement:Y.G.Yao,K.Terakura N.Nagaosa Y.Tokura,凝聚态物理前沿讲座,Contents 1.Quantum simulations based on DFT(1)Simple introduction to first-principles calculations(2)Our method,code,and computer facilities 2.Dissipationl
2、ess 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 transition-metal oxides,Quantum Simulat
3、ion based on DFT,Atoms+electrons,ElectronsMany-body,ElectronsSingle-particle,DensityFunctional,Adiabatic Approximation,Hohenberg-Kohn,Kohn-Sham,Hellmann-Feynman,Force and Stress,MD,SCF,Self-consistent Solver for KS problem,SCF,LDAGGALDA+U,LDA+U method,Pseudopotential Scheme,Normal-conservingPseudopo
4、tential,Ultra-SoftPseudopotential,Virtual Crystal Approxmation(VCA),For virtual atoms,Solve Schrodinger equation,Ionic unscreened potential,How to solve the single particle problem,Real Space(no FFT)Finite element Finite difference Multi-grid Adaptive Wavelet,Reciprocal Space(with FFT)LACO LMTO FLAP
5、W PAW Plane-wave Greens function,Pseudopotential,ASA,Other Problems in Simulations,Exchange-correlation functional Strongly-correlated systems Force calculation&Molecular dynamics Magnetic,optical&electronic properties Excited States Non-equilibrium&Time-dependent process Order(N)method&Large scale
6、Catalysis,Chemical reaction,Bio-systems,First-principles calculations based on DFTPlane-wave basisUltra-soft Pseudo-potentialLDA,GGA,LDA+U,etcVirtual crystal approximation(VCA)Real space RMM for larger systemsFull parallelization by MPI SGI,IBM-SP,Alpha,Cray,VPP,PC-Cluster,Our Method,STATE Code:(Sim
7、ulational 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(2001).(review article),100,000 lines,Accuracy 1meV/Atom,200 atoms.Widely used in Japan,Taiwan,Korea,Denmark,etc.,IBM SP690,64 CPUs,128G,1T-
8、disk,Three Characters of Electron,Charge Spin Orbitalwell known“hot”topic newExtensively used being used will be usedI,V,Charge currentCharge excitation spin wave orbitonCharge current spin current movement anisotropy functionality.,Spintronics,The electron has both charge and spin.Mostly only the c
9、harge 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 consumption for spin-based device.Spin-based electronics also promises a greater integration between the logic and storage devices,Problems for Spintron
10、ic devices,spin injection into semiconductor Ohmic 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 tunne
11、l junction.spin detection by ferromagnet spin transport in semiconductor spin relaxation timeOptical pump and probe,Only 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 u
12、nder T,charge current=odd 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.,Ne
13、w dissipationless transport in solidsdue to spin-orbital coupling!,Anomalous Hall Effect(charge current):1 T.Jungwirth,et.al.,PRL,88,207208(2002);2 Z.Fang,et.al,SCIENCE,302,92(2003)3,et.al,PRL,92,37204(2004);4,et.al,SCIENCE,303,1647(2003)Conventional:xy=R0H+4RSM Intrinsic Mechanism:xyxy(M)Thus Jx=xy
14、Ey is T invariant J is odd,E is even,M is odd,Dissipationless spin Hall current:1 S.Murakami,et.al,SCIENCE,301,1348(2003);2,et.al.,PRL,83,1834(1999)3 J.Sinova,et.al,PRL,92,126603(2004)4,et.al.,cond-mat/040305.5 Y.Xiong&,cond-mat/0403083.Spin current is even under T,B,jH,FM,jAHE,Conventional Hall,Ano
15、malous Hall,E,E,Spin,jSHE,E,Spin Hall,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).,Spin-Orbital Coupling Berry Phase Magnetic Monopoles in Momentum SpaceAnomalous Hall current and Spin Hall current(Both
16、 are dissipationless),Intrinsic Mechanism,Effective Hamiltonian for adiabatic transport,Equation of motion,(Dirac monopole),Drift velocity,Topological term,Nontrivial spin dynamics comes from the Dirac monopole at the center of k space,witheg=l:,Adiabatic transport=potential V does not cause inter-b
17、and transitions only retain the intra-band matrix elements,Full Quantum Calculations Based on Kubo Formular,Anomalous Hall conductivitywith,Spin Hall conductivity,Jys,Conserved Spin Current(S.Murakami,et.al.,cond-mat/0310005),Conserved spinwhich satisfydefine current,i,n,m=band index,=kramers double
18、ts index,Z.Fang,et.al.,SCIENCE 302,92(2003),反常Hall效应与动量空间中的磁单极,Calculated Gauge Flux for kz=0 in SrRuO3,bz(kz=0),G,M,M,M,M,Z.Fang,et.al,SCIENCE,302,92(2003),SrRuO3,SrRuO3,Calculated Spin Hall Current in GaAs,Calculated Spin Current for GaAs and SnTe,One Example for Half-Metal,MnAs,Fully spin polariz
19、ed anomalous Hall current in MnAs,Spin conductivity,AHE conductivity,Anomalous Nernst Effect,B,V,FM,V,Conventional,Anomalous,Inverse Anomalous Nernst Effect:Cooling and refrigerator,FM,Heat current jQ,Ex,Heat current:Eq.of motion:,eg,t2g,3z2-r2,x2-y2,xy,yz,zx,Orbitronics,Orbital Degrees of Freedom(O
20、DF),Energy,Down spin,Up spin,EF,O-2p,O-2p,t2g,t2g,eg,eg,2-fold(ODF),3-fold,“Half-metal”,Lattice,Spin,Charge,Orbital,SC,TMR,CMR,M-I Transition,Anomalous Hall Effect,Magneto-optical,Ferroelectricity,Piezoelectricity,etc,Experimental,Theoretical,SCIENCE 288,462(2000).J.Phys.Soc.Jap.68,3790(1999).,Phase
21、 Diagram of Tetragonal La1-xSrxMnO3(Controlling of Orbital and Spin Orderings),Z.Fang&K.Terakura,PRL 84,3169(2000).,FM,A-AF,C-AF,G-AF,Orbital and Spin Orderings,Physics:Spin Orbital Lattice Double exchange Super-exchange Compression Less conductivity,Electric-Field-induced Orbital Switching,K.Hatsud
22、a,APL 83,3329(2003).,Lattice,Spin,Charge,Orbital,Electronic Structures of Ca2-xSrxRuO4,Energy,Down spin,Up spin,EF,O-2p,O-2p,t2g,t2g,eg,eg,3-fold,Ca2-xSrxRuO4:Isovalent substitution,Rotation Rotation Rotation+Tilting Tilting+Compression,AF MottInsulator,NearlyFM Metal,S.Nakatsuji,et al.,PRLO.Friedt,
23、et al.,PRB,Issues:(1)How to understand the complicated phase diagram.(2)Whats the rule of orbital.,Effects of Structure Distortions,Z.Fang&K.Terakura,PRB64,R20509(2001),Rotation,xy orbital,VHS,FM,Tilting,yz,zx,nesting,AF,Occupations and Magnetizations,Z.Fang et al.PRB(2004).,Orbital Phase Diagram of
24、 Ca2-xSrxRuO4,Ca,Sr,Doping x,0.0 0.2 0.5 2.0,E,Ef,xyyz,zx,E,Ef,xyyz,zx,E,Ef,xyyz,zx,xy,xy ferro-orbital orderingAF,S=1 from yz,zx,FM,S=1/2 from xyItinerant yz,zx with small S,NM stateWith VHS from xy,1.J.H.Jung,Z.Fang,et.al.,PRL 91,056403(2003).2.Z.Fang,et.al.,PRB 69,045116(2004).,RuO6 八面体在表面的旋转,Sr2
25、RuO4的表面电子结构,LEED,STM,1.R.Matzdorf,Z.Fang,et.al.,SCIENCE 289,746(2000).2.Z.Fang,et.al.,PRB 64,R20509(2001),PDOS of various doping x,Exp.XAS,Calculated XAS,90K,300K,Optical conductivity,Experiments,Calculations,J.H.Jung,Z.Fang,et al.PRL(2003).,Fe,Fe,M,Sr2FeMO6(M=Mo,W,Re),8,Why Tc is so high for M=Mo,R
26、e?Why M=W case is AF insulator?,EF,d states,d states,Majority spin,Minority spin,Mo d stateor other p states,FM,Z.Fang,et.al.,PRB 63,R180407(2001),EF,d states,d states,Majority spin,Minority spin,Mo d statesor other p states,AF,New Mechanism for Sr2FeMO6 and(Ga1-xMnx)As,Fe(t2g),Spin,EF,M(t2g)(M=Mo,R
27、e),Fe(t2g),Electronic Structure of Sr2FeMoO6,Surface of SrTiO3 with Oxygen Vacancy,Important substrate Surface gas sensitivity Ferroelectricity Catalytically active,STM,STS,T.Kubo,et.al.,PRL 86,1801(2001),H.Tanaka,et.al.,Jpn.J.Appl.Phys.32,1405(1993),Structure,Charge,Magnetization,SrO,TiO2,Sr Ti O,L
28、DA+U,Surface of SrTiO3 with oxygen vacancy(Spin polarized surface),Z.Fang,et.al.,Surf.Sci.Lett.470,L75(2001),SrO termination(GGA),TiO2 termination(GGA),26,26,26,TiO2 termination(LDA+U),5 x 5 STM of SrTiO3 surface,100,100,001,001,Surface,Central,（La,Sr)O termination,MnO2 termination,Mn,Orbital polari
29、zation on the surfaces of La1-xSrxMnO3,Z.Fang,et.al.,J.Phys.Soc.Jpn.70,3356(2001).,Summary,Quantum 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,
