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

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20 th WIEN2k WorkshopPennStateUniversity – 2013Talk constructed using the following documents:Slides of:Robert Laskowski, Stefaan Cottenier, Peter Blaha and Georg MadsenNotes of:- Pavel Novak (Calculation of spin-orbit coupling)http://www.wien2k.at/reg_user/textbooks/- Robert Laskowski (Non-collinear magnetic version of WIEN2k package)Books:- WIEN2k userguide, ISBN 3-9501031-1-2- Electronic Structure: Basic Theory and Practical Methods, Richard M. MartinISBN 0 521 78285 6- Relativistic Electronic Structure Theory. Part 1. Fundamentals, PeterSchewerdtfeger, ISBN 0 444 51249 7web:- http://www2.slac.stanford.edu/vvc/theory/relativity.html- wienlist digest - http://www.wien2k.at/reg_user/index.html- wikipedia …
Few words about Special Theory of RelativityLightComposed of photons (no mass)Speed of light = constantAtomic units:ħ = m e = e = 1c 137 au
Page 1: 20 th WIEN2k WorkshopPennStateUnive
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 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
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WienNCM: Spin spiralsTransverse spi
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Relativistic effects, spin-orbit coupling and non-collinear ... - WIEN 2k

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