Non-collinear magnetism in WIEN2k

Augmentation (...)ϕ AP W⃗Gσ(⃗k)ϕ LO⃗Gσ α == ∑ σ α ∑(LA ⃗ Gσ αL(A ⃗ Gσσ αu σαlLu σαl+ B ⃗ Gσσ αL+ B ⃗ Gσσ αL˙u σαl+ C ⃗ Gσ αL)˙u σαl Y L χ σ α,)u σα2,l Y L χ σ αA L , B L , C L are calculated from sphere boundary conditions.for APW/LAPW matching is done to ↑ and ↓ plane waves in aglobal spin coordinate frame. Thus A L , B L depend on global σand local σ α spin indexes, and on k-point.LO has to vanish at a sphere boundary. It is a pure spinor in alocal coordinate frame (A L , B L , C L depend only on σ α ).for APW type of basis B = 0 in PW and LO, and additional localorbital “lo” is introduced with C = 0, and B ≠ 0.wien workshop 2003 – p.19/40