The Munich SPRKKR-program package A spin polarised relativistic Korringa-Kohn-Rostoker code for calculating solid state properties

Transcription

1 The Munich SPRKKR-program package A spin polarised relativistic Korringa-Kohn-Rostoker code for calculating solid state properties Ján Minár H. Ebert, M. Battocletti, D. Benea, S. Bornemann, J. Braun, S. Chadov, M. Deng, H. Freyer, T. Huhne, M. Kardinal, D. Kodderitzsch, M. Kosuth, S. Lowitzer, S. Mankovskyy, M. Offenberger, A. Perlov, V. Popescu, Ch. Zecha and many others Ludwig-Maximilians-Universität München, Germany Funding

2 Outline Introduction Green's functions Scattering theory Angular momentum representation Calculating the scattering path operator The impurity problem Substitutationally disordered alloys Flow diagrams of SPR-KKR package Summary 2

3 More information on KKR 3

4 Standard band structure approach I 4

5 Standard band structure approach II 5

6 Band structure methods 6

7 Original KKR method 7

8 KKR secular equation 8

9 Green's functions 9

10 Spectral representation of Green's function 10

11 Densities and expectation values 11

12 Analyticity of Green's functions 12

13 Path integrals in complex energy plane 13

14 Energy paths 14

15 Energy paths Alway take care of semi-core states! SPR-KKR uses automatic search for semi-core states Parameter for number of valence electrons: NVAL 15

16 Dyson Equation 16

17 Example: Dyson equation applied to 0D systems 17

18 Benefits of Green's function based methods 18

19 Early applications of scattering theory 19

20 Principle of scattering theory 20

21 Sometimes solving a problem. 21

22 Calculation of the Green's function 22

23 Calculation of the Green's function: KKR 23

24 Single site scattering problem 24

25 Angular momentum expansion of 25

26 Angular momentum expansion of NLMAX=l_max+1: is in KKR convergence criteria Often helps to use Lloyd formula: LLOYD option (for insulators and semiconductors) 26

27 Expression for the single site t-matrix 27

28 Phase shift and single site t-matrix 28

29 Single site problem in SPR-KKR Default in SPR-KKR: The Dirac Equation within SDFT ASA Full-potential ASA: keep the volume of the unit cell constant assume a spherical symmetric potential within sphere FP: Space filling Wigne-Seitz cell Total energies tested and compared with LAPW NEW: FP implementation in fully relativistic mode (Left + Right hand side solution to Dirac eq. Not all applications are implemented in FP mode yet 29

30 Single site problem in SPR-KKR Default in SPR-KKR: The Dirac Equation within SDFT LSDA, GGA Rotational invariant LSDA+U Fully self consitent (charge + self energy) LSDA+DMFT Breit interaction SOC manipulations Fully relativistic mode (4-component formalism) Scalar relativistic Non-relativistic Spin spiral calculations 30

31 Implementation of LSDA+DMFT using KKR Spin dependent self energy of Ni for d-states Real part 19/06/2013 Imaginary part APCOM13, Jan Minar Bloch spectral function

32 Implementation of LSDA+DMFT using KKR Fully self-consistent (charge + ΣD M F T) Fully relativistic (Dirac eq.) J. Minar, et al, PRB 72, (2005), JPCM Topical review 23, (2011) Applications see e.g.: PRL 95, (2005), 97, (2006), PRL 103, (2009), 19/06/2013 ΣD M F T solver: SPTF (I. Di Marco el al.) and TMA (Chadov et al.) Effects of ΣD M F T on wave functions Disordered alloys: CPA+DMFT and 2D semi-infinite surfaces Spectroscopies + DMFT: ARPES, XAS, XMCD,MOKE APCOM13, Jan Minar

33 Multiple scattering 33

34 Scattering part operator 34

35 Electronic Green's function 35

36 Solving the multiple scattering problem: Real space 36

37 Solving the multiple scattering problem: Real space 37

38 Brillouin zone integration ^ 38

39 Brillouin zone integration ^ Special points method: e.g. Use of symmetry Input Number of k-points: NKTAB gives density of k-points For actual calculations look into output file: mesh parameters 39

40 Tight binding or screened KKR method R. Zeller et al. 40

41 Surface calculations: Slab geometry 41

42 Surface calculations: semi infinite 2D systems R I L 42

43 Comparison between slab and semi-infinite systems Problems: For 2D systems take care of slow convergence (use smaller SCFMIX and MIXRHO O. Sipr et al. PRB 82, (2010) 43

44 Clusters on Surfaces example Shell resolved magneto-crystalline anisotropy S. Ouazi et al., Nat. Comm. 3, 1313 (2012) Embedding in 3D-bulk very well tested and works in ASA and FP Embedding on 2D-surface: in ASA OK but in FP still to be tested 44

45 Substitional disordered alloys In the code In the code 45

46 Coherent potential approximation (CPA) 46

47 DOS and spectral functions for disordered systems A. Gray, J. Minar et al., Nat. Mat. 11, 957 (2012) 47

48 Flow diagram of SPR-KKR package 48

49 Flow diagram of calculations xband create input and starting potential First SCF calculation or embscf (0D system) kkrscf Alloys Surfaces sys-file create input Applications converged potential or embgen (0D system) kkrgen kkrspec kkrchi Clusters 49

50 Self consistent calculations kkrscf System Arbitrary ordered / disordered 3D, 2D systems 2D surfaces in TB mode Semi infinite Slab geometry Embedded clusters in 3D and 2D systems Calculation Mode Spin polarized Scalar relativistic and fully relativistic Non-collinear Spin configurations Spin-Spirals SOC manipulations ASA and Full-potential LDA, GGA, LDA+U, LDA+DMFT (within collaboration) Full-potential LDA+U total energy of NiO LDA EXP D. Ködderitzsch et al., in preparation 50

51 Ground state and electronic properties kkrgen Ground state properties Electronic properties Spin- and orbital moments Density of states Magnetic form factor Dispersion relation Hyperfine fields Exchange coupling parameters (anisotropic) Bloch spectral functions Fermi surface of Ba(Fe0.9Co0.1 )2As2 G. Derondeau et al., in preparation J. Honolka et al., J. Minar et al,, PRL 102, (2009) 51

52 Spectroscopy kkrgen kkrspec X-Ray absorption + XMCD Angle resolved PES within one-step model X-ray magnetooptics Angle integrated PES Magnetic compton scattering SP-LEED All calculations for: Positron annihilation AES and APS CL-PES Arbitrary photon energy (UV, soft Xray, hard X-ray) CPA implementation within one-step model Combination with KKR+DMFT HAXPES of W(110) at 6 kev A. Gray et al., J. Minar et al,, Nature Materials, 10, 759 (2011) Topological surface states M. Scholz et al., J. Minar et al,, PRL 110, (2013) 52

53 Linear response kkrchi Spin and orbital magnetic susceptibility Gilbert damping parameters of alloys Conductivity: Longitudinal charge transport of alloys Field induced XMCD Knight-shift Anomalous Hall effect of Ni Exp. M E D. Ködderitzsch et al., New J. Phys. 15, (2013) 53

54 Summary 54

55 More information on KKR 55

56 Standard band structure approach III 56

57 Lippman Schwinger equation 57

58 Substitutional impurities 58

59 Rh impurity in Au Calculations: set concentration of impurity set to zero Or perform real space calculations: embedding (relaxation of electronic structure around impurity) 59

60 Single site density of states 60

61 Standard scattering experiment 61