凝聚态物理前沿讲座_方忠_Quantum Simulation in the F.ppt

1、,方 忠 中国科学院物理研究所，理论室,Quantum Simulation in the Field of Spintronics 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 facilitie

2、s 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 transiti

3、on-metal oxides,Quantum Simulation based on DFT,Atoms+electrons,Electrons Many-body,Electrons Single-particle,Density Functional,Adiabatic Approximation,Hohenberg-Kohn,Kohn-Sham,Hellmann-Feynman,Force and Stress,MD,SCF,Self-consistent Solver for KS problem,SCF,LDA GGA LDA+U,LDA+U method,Pseudopotent

4、ial Scheme,Normal-conserving Pseudopotential,Ultra-Soft Pseudopotential,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

5、 ,Reciprocal Space (with FFT) LACO LMTO FLAPW PAW Plane-wave Greens function ,Pseudopotential, ASA, ,Other Problems in Simulations,Exchange-correlation functional Strongly-correlated systems Force calculation 2 Z.Fang, et.al, SCIENCE, 302, 92 (2003) 3 Y.G.Yao, et.al, PRL, 92, 37204 (2004); 4 W.L.Lee

6、, et.al, 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 S.Murakami, et.al, SCIENCE, 301, 1348 (2003); 2 J.E.Hirsch, et.al., PRL, 83, 1834 (1999) 3 J.Sinova, et.al, PRL

7、, 92, 126603 (2004) 4 S.Q.Shen, et.al., cond-mat/040305. 5 Y.Xiong & X.C.Xie, cond-mat/0403083. Spin current is even under T,B,jH,FM,jAHE,Conventional Hall,Anomalous 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. I

8、t is entirely topological (dissipationless).,Spin-Orbital Coupling Berry Phase Magnetic Monopoles in Momentum Space Anomalous Hall current and Spin Hall current (Both are dissipationless),Intrinsic Mechanism,Effective Hamiltonian for adiabatic transport,Equation of motion,(Dirac monopole),Drift velo

9、city,Topological term,Nontrivial spin dynamics comes from the Dirac monopole at the center of k space, with eg=l:,Adiabatic transport = potential V does not cause inter-band transitions only retain the intra-band matrix elements,Full Quantum Calculations Based on Kubo Formular,Anomalous Hall conduct

10、ivity with,Spin Hall conductivity,Jys,Conserved Spin Current (S.Murakami, et.al., cond-mat/0310005),Conserved spin which satisfy define current,i, n, m = band index , = kramers doublets 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)

11、,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 polarized anomalous Hall current in MnAs,Spin conductivity,AHE conductivity,Anomalous Nernst Effect,B,V,FM,V,Conv

12、entional,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 (ODF),Energy,Down spin,Up spin,EF,O-2p,O-2p,t2g,t2g,eg,eg,2-fold (ODF),3-fold,“Half-metal”,Lattice,Spin,

13、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 Diagram of Tetragonal La1-xSrxMnO3 (Controlling of Orbital and Spin Orderings),Z. Fa

14、ng & 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. Hatsuda, APL 83, 3329 (2003).,Lattice,Spin,Charge,Orbital,Electronic Structures of

15、 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 Mott Insulator,Nearly FM Metal,S. Nakatsuji, et al., PRL O. Friedt, et al., PRB,Issues: (1) How to understand the complicated

16、 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 Ca2-xSrxRuO4,Ca,Sr,Doping x,0.0 0.2 0.5 2

17、.0,E,Ef,xy yz, zx,E,Ef,xy yz, zx,E,Ef,xy yz, zx,xy,xy ferro-orbital ordering AF, S=1 from yz, zx,FM, S=1/2 from xy Itinerant yz, zx with small S,NM state With 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,Sr2RuO4的表面电子结构,LE

18、ED,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

19、 for M=Mo, Re? Why M=W case is AF insulator?,EF,d states,d states,Majority spin,Minority spin,Mo d state or other p states,FM,Z. Fang, et.al., PRB 63, R180407 (2001),EF,d states,d states,Majority spin,Minority spin,Mo d states or other p states,AF,New Mechanism for Sr2FeMO6 and (Ga1-xMnx)As,Fe (t2g)

20、,Spin,EF,M (t2g) (M=Mo, Re),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,Ma