Non-collinear magnetism in WIEN2k

¡¢ £Collinear caseH P = − 22m ∇2 + V eff + µ B ⃗σ · ⃗B eff + ζ ·(⃗σ · ⃗l)+ . . .If we ignore only spin-orbit term, and allow magnetisation to point in onedirection (z), resulting Hamiltonian will be diagonal in spin-space.− 22m ∇2 + V eff + µ B ⃗σ · ⃗B z 00 − 22m ∇2 + V eff − µ B ⃗σ · ⃗B zϕ = εϕϕ ↑ =⎛⎝ ψ ↑0⎞⎠ , ϕ ↓ =⎛⎝ 0 ψ ↓⎞⎠solutions are pure spinorswith non-degenerateenergiesε ↑ ≠ ε ↓collinear magnetismwien workshop 2003 – p.12/40