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

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Implementation in WIEN2k: valence electronsSOC is added in a second variation (lapwso):- First diagonalization (lapw1):- Second diagonalization (lapwso):H 1 111H 1 H SO The second equation is expanded in the basis offirst eigenvectors ( 1 )Ni j ji ij 1 ij 1HSO 1 11sum include both up/down spin states N is much smaller than the basis size in lapw1Atomic sphere (RMT) RegionValenceelectronsScalar relativistic(no SOC)Possibility to add SOC(2 nd variational)
Implementation in WIEN2k: valence electronsSOC is added in a second variation (lapwso):- First diagonalization (lapw1):- Second diagonalization (lapwso):H 1 111H 1 H SO The second equation is expanded in the basis offirst eigenvectors ( 1 )Ni j ji ij 1 ij 1HSO 1 11sum include both up/down spin states N is much smaller than the basis size in lapw1Atomic sphere (RMT) RegionValenceelectronsScalar relativistic(no SOC)Possibility to add SOC(2 nd variational) SOC is active only inside atomic spheres, only spherical potential (V MT ) is taken intoaccount, in the polarized case spin up and down parts are averaged. Eigenstates are not pure spin states, SOC mixes up and down spin states Off-diagonal term of the spin-density matrix is ignored. It means that in each SCF cyclethe magnetization is projected on the chosen direction (from case.inso)V MT : Muffin-tin potential (spherically symmetric)
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 and 20: 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: 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

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

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