Non-collinear magnetism in WIEN2k

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Exchange potential and fieldIn DFT V xc and ⃗ B xc are defined by:V xc = ∂E xc (n, ⃗m)∂nIn local density approximation (LDA):, ⃗ Bxc = ∂E xc (n, ⃗m)∂ ⃗mE xc (n, ⃗m) = nɛ xc (n, m) dr 3what results in:V xc = ɛ xc (n, m) + n ∂ɛ xc (n, m)∂n, ⃗ Bxc = n ∂ɛ xc(n,m)∂mˆmexchange field is parallel to local magnetisationdensity vectorwien workshop 2003 – p.10/40
¡¢ £Non-collinear caseH P = − 22m ∇2 + V eff + µ B ⃗σ · ⃗B eff + ζ ·(⃗σ · ⃗l)+ . . .If we take everything, and also allow magnetisation to vary its directionfrom point to point, we will end up with 2x2 Hamiltonian:− 22m ∇2 + V eff + µ B ⃗σ · ⃗B z + . . . µ B (B x − iB y ) + . . .µ B (B x + iB y ) + . . . − 22m ∇2 + V eff − µ B ⃗σ · ⃗B z + . . .ϕ = εϕwien workshop 2003 – p.11/40
Page 2 and 3: wien workshop 2003 - p.2/40
Page 4 and 5: Outlinetheoretical introduction;wie
Page 6 and 7: Outlinetheoretical introduction;try
Page 8 and 9: Outlinetheoretical introduction;try
Page 11 and 12: ¡¢ £¡¡¢ £¢ £Dirac Hamilton
Page 13 and 14: Dirac HamiltonianH D = c⃗α ·
Page 15 and 16: Dirac equationH D = c⃗α · ⃗p
Page 17 and 18: Dirac equationH D = c⃗α · ⃗p
Page 19 and 20: Pauli HamiltonianH P = − 22m ∇2
Page 25: Exchange potential and fieldIn DFT
Page 30: ¡¢ £Collinear caseH P = − 22m
Page 33 and 34: ConsequencesImplementation of non-c
Page 35 and 36: ConsequencesImplementation of non-c
Page 37 and 38: Implementations of NCM in LAPWψ
Page 39 and 40: Implementations of NCM in LAPWPh. K
Page 41 and 42: Spin coordinate setsα 1α2⎛⎞
Page 43 and 44: Basis functionsspheres - combinatio
Page 45 and 46: Augmentation (...)ϕ AP W⃗Gσ(⃗
Page 47 and 48: Augmentation (...)ϕ AP W⃗Gσ(⃗
Page 49 and 50: Hamiltonian (...)In the interstitia
Page 51 and 52: Hamiltonian - spheres (...)inside s
Page 53 and 54: ¡¢ £Hamiltonian - spheres (...)S
Page 55 and 56: ¡¡¡¢ £¢ £¢ £Hamiltonian -
Page 57 and 58: Allocation of the Hamiltonian and o
Page 59 and 60: Allocation of the Hamiltonian and o
Page 61 and 62: Spin-spiralsspin-spiral is defined
Page 63 and 64: Spin-spiralspure translations are o
Page 65 and 66: Spin-spiralspure translations are o
Page 67 and 68: Spin-spiralsWave function of a spir
Page 69 and 70: Intra-atomic NCM, bcc U(c) plane x
Page 71 and 72: γ Fe, spin spiralAMAFULLSpin densi
Page 73 and 74: Magnetic structure of Mn 3 Snfmwien
Page 75 and 76: Magnetic structure of Mn 3 Snfm afm
Page 77 and 78:
Magnetic structure of Mn 3 Snfm afm
Page 79 and 80:
Magnetic structure of Mn 3 Snso fm
Page 81 and 82:
NCM input filecase.inncm:FULL0 0 06
Page 83 and 84:
How to run it?initialisation - look
Page 85 and 86:
¢£¢¢££¡¡Appendix - augmenta
Page 87 and 88:
¦¡¡¦¢ £Appendix - density mat
Page 89:
¡¢ £¡¢ £Appendix - potential
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Non-collinear magnetism in WIEN2k

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