Relativistic effects, spin-orbit coupling and non-collinear ... - WIEN 2k

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Dirac equation in a spherical potentialFor a spherical potential V(r):The resulting equations for the radial functions (g n and f n ) are simplifiedif we define:2 ' V ' m ecrEnergy:Radially varying mass: Mer me22cThen the coupled equations can be written in the form of the radial eq.:1ddrdgl22l1 dV dg dV 122 2 nnr Vg2 2 n2 22 22Mer dr 2Mer 4Mdr drec4Mecdrrgn ' gnMass-velocity effectDarwintermSpin-orbitcoupling22me12rddrr2dRdrn,l V22mel l 12rRn,l Rn,lOne electron radialSchrödinger equation in aspherical potentialNote that:1ll1
Dirac equation in a spherical potentialFor a spherical potential V(r):The resulting equations for the radial functions (g n and f n ) are simplifiedif we define:2 ' V ' m ecrEnergy:Radially varying mass: Mer me22cThen the coupled equations can be written in the form of the radial eq.:1ddrdgl22l1 dV dg dV 122 2 nnr Vg2 2 n2 22 22Mer dr 2Mer 4Mdr drec4Mecdrrgn ' gnanddfnk 1 1 V' gndr crNote that:fn1ll1DarwintermDue to spin-orbit coupling, is not an eigenfunctionof spin (s) and angular orbital moment (l).Instead the good quantum numbers are j and Spin-orbitcouplingNo approximationhave been madeso far
Page 1 and 2: 20 th WIEN2k WorkshopPennStateUnive
Page 3 and 4: Few words about Special Theory of R
Page 5 and 6: Few words about Special Theory of R
Page 7 and 8: Relativistic effects+Ze1) The mass-
Page 9 and 10: Relativistic effects+Ze1) The mass-
Page 11 and 12: One electron radial Schrödinger eq
Page 13 and 14: One electron radial Schrödinger eq
Page 15 and 16: Dirac Hamiltonian: a brief descript
Page 17 and 18: Dirac equation: H D and are 4-dime
Page 19: Dirac equation in a spherical poten
Page 23 and 24: Dirac equation in a spherical poten
Page 25 and 26: Implementation in WIEN2kAtomic sphe
Page 27 and 28: Implementation in WIEN2k: core elec
Page 29 and 30: Implementation in WIEN2k: valence e
Page 31 and 32: Implementation in WIEN2k: valence e
Page 33 and 34: Controlling spin-orbit coupling in
Page 35 and 36: Relativistic effects in the solid:
Page 37 and 38: Relativistic effects in the solid:
Page 39 and 40: (1) Relativistic orbital contractio
Page 41 and 42: (1) Orbital Contraction: Effect on
Page 43 and 44: (2) Spin-Orbit splitting of p state
Page 45 and 46: (2) Spin-Orbit splitting of p state
Page 47 and 48: (3) Orbital expansion: Au(d) states
Page 53 and 54: Atomic spectra of goldSO splittingS
Page 55 and 56: Relativistic semicore states: p 1/2
Page 57 and 58: Relativity in WIEN2k: SummaryWIEN2k
Page 59 and 60: CuO interludeATOMIC STRUCTURE OF Cu
Page 61 and 62: CuO interludeATOMIC STRUCTURE OF Cu
Page 63 and 64: CuO interludeMAGNETIC STRUCTURE OF
Page 65 and 66: CuO interludeEstimation of the Magn
Page 67 and 68: Pauli Hamiltonian for magnetic syst
Page 69 and 70: Pauli Hamiltonian for magnetic syst
Page 71 and 72:
Exchange and correlationFrom DFT ex
Page 73 and 74:
Collinear magnetismMagnetization in
Page 75 and 76:
Magnetism and WIEN2kWien2k can only
Page 77 and 78:
Non-collinear magnetismIn case of n
Page 79 and 80:
WienNCM: Spin spiralsTransverse spi
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Relativistic effects, spin-orbit coupling and non-collinear ... - WIEN 2k

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