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

More documents

Recommendations

Info

Dirac equation: H D and are 4-dimensional is a four-component single-particle wave function that describes spin-1/2particles.spin upspin downH D1 1 2 2 33 4 4 In case of electrons:Largecomponents ()Smallcomponents () factor 1/(m e c 2 ) and are time-independent two-component spinors describing the spatialand spin-1/2 degrees of freedomLeads to a set of coupled equations for and :cc 2 p V m c 2 p V m c ee
Dirac equation: H D and are 4-dimensionalFor a free particle (i.e. V = 0):Solution in the slowparticle limit (p=0)Non-relativistic limitdecouples 1 from 2and 3 from 42 mec 0ˆ pzpˆ ipˆzc m e2 0 , 0 0 ypˆ0 m czpˆ2 ipˆParticles: up & downze 0 2 m ec , 0 0 y pˆz pˆ ˆzip2 mec0c m ey2pˆ 0 0 , 0 xpˆ ipˆ0z m ce2y1234 0 2 0m ec , 0 0Antiparticles: up & down
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: Dirac Hamiltonian: a brief descript
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
Page 79 and 80:
WienNCM: Spin spiralsTransverse spi
show all

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

Create successful ePaper yourself

Delete template?

Save as template?