1、2021/12/14方方 忠忠中國科學院物理研討所，中國科學院物理研討所，實際室實際室 Quantum Simulation in the Field ofSpintronics and OrbitronicsAcknowledgement: Y. G. Yao, K. Terakura N. Nagaosa Y. Tokura2021/12/14 Contents 1. Quantum simulations based on DFT (1) Simple introduction to first-principles calculations (2) Our method, code,

2、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

3、4. Surface of transition-metal oxides2021/12/14Quantum Simulation based on DFTNeNeHHHH jijiiiiirrrV|121)(2)(| |) ()(21)()(rEdrdrrrrrrTrEXC)()()(2rErrViiiKSAtoms+electronsElectronsMany-bodyElectronsSingle-particleDensityFunctionalAdiabatic ApproximationHohenberg-KohnKohn-ShamHellmann-FeynmanForce and

4、 StressMDSCF2021/12/14Self-consistent Solver for KS problem)()()(212rrrViiieff)(| |) ()(21)()()()(rEdrdrrrrrdrrrvrTrEXCext)()(| |) ()()(rrEdrrrrrvrVxcexteffoccuiir2|)(SCFLDAGGALDA+U2021/12/14LDA+U methodikikikULDAH,mIikikmImIeffmILDAULDAfnnUHH,*)21(,)(21,mImImImIeffmILDAIdcmIULDAmIULDAnnnUENEnEEnEmm

5、IInN,2021/12/14Pseudopotential Scheme)()()(212rrrViiioccuiPSir2|)()()()(212rrrVPSiiPSiPS)()()(212rSrrVPSiiPSiPSNormal-conservingPseudopotentialUltra-SoftPseudopotentialmnIiImIniImnoccuiPSirQr,2)(|)(mnIImInnmqS,12021/12/14Virtual Crystal Approxmation (VCA)()()1 ()(,rxVrVxrVPSbionPSaionPSxionPSxVFor v

6、irtual atomsSolve Schrodinger equationIonic unscreened potential2021/12/14How to solve the single particle problem Real Space (no FFT) Finite element Finite difference Multi-grid Adaptive Wavelet Reciprocal Space (with FFT) LACO LMTO FLAPW PAW Plane-wave Greens function Pseudopotential, ASA, 2021/12

7、/14Other 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 Catalysis, Chemical rea

8、ction, Bio-systems 2021/12/14First-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-ClusterOur Method2021/12/14 100,000

9、lines, Accuracy 1meV/Atom, 200 atoms.Widely used in Japan, Taiwan, Korea, Denmark, etc.2021/12/14IBM SP690, 64 CPUs, 128G, 1T-disk2021/12/14Three Characters of Electron Charge Spin Orbitalwell known “hot topic newExtensively used being used will be usedI, V, Charge currentCharge excitation spin wave

10、 orbitonCharge current spin current movement anisotropy functionality .2021/12/14Spintronics The 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 powe

11、r consumption for spin-based device. Spin-based electronics also promises a greater integration between the logic and storage devices2021/12/14Problems for Spintronic devices spin injection into semiconductor Ohmic injection from ferromagnet Low efficiency (Difficulty): Ferromagnetic metal : conduct

12、ivity 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 time Optical pump and probe2021/12/1

13、4Only 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, w

14、hich 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. tAcEAJjjjSj1,BEJHH,2021/12/14New dissipationless transport in solidsdue to spin-orbital coupling! Anomalous

15、 Hall Effect (charge current): 1 T.Jungwirth, et.al., PRL, 88, 207208(2019); 2 Z.Fang, et.al, SCIENCE, 302, 92 (2019) 3 Y.G.Yao, et.al, PRL, 92, 37204 (2019); 4 W.L.Lee, et.al, SCIENCE, 303, 1647 (2019) Conventional: xy = R0H + 4RSM Intrinsic Mechanism:xyxy(M) Thus Jx=xyEy is T invariant J is odd, E

16、 is even, M is odd Dissipationless spin Hall current:1 S.Murakami, et.al, SCIENCE, 301, 1348 (2019); 2 J.E.Hirsch, et.al., PRL, 83, 1834 (2019)3 J.Sinova, et.al, PRL, 92, 126603 (2019) 4 S.Q.Shen, et.al., cond-mat/040305.5 Y.Xiong & X.C.Xie, cond-mat/0403083. Spin current is even under Tkijkspin

17、ijEJ2021/12/14BjHFMjAHEConventional HallAnomalous HallEESpinjSHEESpin Hall2021/12/14Merit 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).2021/12/14 Spin-Orbital Coupling Berry Phase Magnetic Monopoles in Mo

18、mentum SpaceAnomalous Hall current and Spin Hall current (Both are dissipationless)knknikAkn)(Intrinsic MechanismznknkAkb)()(3|)(b2021/12/14)(22effxVmkH)(kAkiDxiiiiEffective Hamiltonian for adiabatic transportkjijkiiiikEkmkxEk3,ijjiijjijiiFxxikxkk, 0,Equation of motion3kkFkijkij(Dirac monopole)ikEDr

19、ift velocityTopological termijjFeENontrivial 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 only retain the intra-band matrix elements 2021/12/14Full Quantum Calculations Based on Kubo Formularnmm

20、nyxxyknnxykkJJknJkmkmJknkfi2,)()()()(knznknkAkfe,2)()(knknikAkn)(Anomalous Hall conductivitywithSpin Hall conductivitynmmnyxxyknnxykkJJknJkmkmJknkfi2,)()()()(Jys2021/12/14Conserved Spin Current(S.Murakami, et.al., cond-mat/0310005)zcysyzcizzcSjrSrddtdiiSiiS,210)(, , ,Conserved spinwhich satisfydefin

21、e current mSmmnmSnzyzcy, i, n, m = band index, = kramers doublets index2021/12/14Z. Fang, et.al., SCIENCE 302, 92 (2019)反常反常HallHall效應與動量空間中的磁單極效應與動量空間中的磁單極2021/12/14Calculated Gauge Flux for kz=0 in SrRuO3bz(kz=0)GMMMMZ. Fang, et.al, SCIENCE, 302, 92 (2019)2021/12/14SrRuO32021/12/14SrRuO32021/12/14

22、Calculated Spin Hall Current in GaAs2021/12/14Calculated Spin Current for GaAs and SnTe2021/12/14One Example for Half-MetalMnAs2021/12/14Fully spin polarized anomalous Hall current in MnAsSpin conductivityAHE conductivity2021/12/14Anomalous Nernst EffectTBVTFMVConventionalAnomalous2021/12/14Inverse

23、Anomalous Nernst Effect:Cooling and refrigeratorFMHeat current jQExkkzkQxykkkQfkbEekkkrrj)()()(;)(Heat current:Eq. of motion:2021/12/14egt2g3z2-r2x2-y2xyyzzxOrbitronics2021/12/14Orbital Degrees of Freedom (ODF)EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg2-fold (ODF)3-fold“Half-metal2021/12/14FMA-typeC

24、-typeG-typeLatticeSpinChargeOrbitalSC, TMR, CMR,M-I Transition,Anomalous Hall Effect,Magneto-optical,Ferroelectricity,Piezoelectricity, etc 2021/12/14ExperimentalTheoreticalSCIENCE 288, 462(2000).J. Phys. Soc. Jap. 68, 3790(2019).Phase Diagram of Tetragonal La1-xSrxMnO3(Controlling of Orbital and Sp

25、in Orderings)Z. Fang & K. Terakura, PRL 84, 3169(2000).2021/12/14FMA-AFC-AFG-AFOrbital and Spin OrderingsPhysics: Spin Orbital Lattice Double exchange Super-exchange Compression Less conductivity2021/12/14Electric-Field-induced Orbital SwitchingK. Hatsuda, APL 83, 3329 (2019).2021/12/14LatticeSp

26、inChargeOrbitalElectronic Structures of Ca2-xSrxRuO4EnergyDown spinUp spinEFO-2pO-2pt2gt2gegeg3-fold2021/12/14Ca2-xSrxRuO4 : Isovalent substitution Rotation Rotation Rotation + + Tilting Tilting + CompressionAF MottInsulatorNearlyFM MetalS. Nakatsuji, et al., PRLO. Friedt, et al., PRB2021/12/14Issue

27、s: (1) How to understand the complicated phase diagram. (2) Whats the rule of orbital.2021/12/14Effects of Structure DistortionsZ. Fang & K. Terakura, PRB64, R20509(2019)Rotationxy orbitalVHSFMTiltingyz, zxnestingAF2021/12/14Occupations and MagnetizationsZ. Fang et al. PRB (2019).2021/12/14Orbit

28、al 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 small SNM stateWith VHS from xy1. J. H. Jung, Z. Fang, et.al., PRL 91, 056403(2019).2. Z. Fang, et.al., PRB 69, 045116 (201

29、9).2021/12/14110RuO6 八面體在外表的旋八面體在外表的旋轉轉Sr2RuO4的外表電子構造的外表電子構造LEEDSTM1. R. Matzdorf, Z. Fang, et.al., SCIENCE 289,746(2000).2. Z. Fang, et.al., PRB 64, R20509 (2019)2021/12/14PDOS of various doping x2021/12/14Exp. XASCalculated XAS90K300K2021/12/14Optical conductivityExperimentsCalculationsJ. H. Jung,

30、 Z. Fang, et al. PRL (2019).2021/12/14FeFeMSr2FeMO6 (M=Mo, W, Re)8 Why Tc is so high for M=Mo, Re?Why M=W case is AF insulator?2021/12/14EFd statesd statesMajority spinMinority spinMo d stateor other p statesFMZ. Fang, et.al., PRB 63, R180407 (2019) EFd statesd statesMajority spinMinority spinMo d statesor other p statesAFNew Mechanism for Sr2FeMO6 and (Ga1-xMnx)As2021/12/14Fe (t2g)SpinEF M (