[Wien] What's the meaning of "up" and "down" in a band structure including spin-orbit interaction?

Peter Blaha pblaha at theochem.tuwien.ac.at
Fri Dec 30 09:52:42 CET 2011

>      I have two question about spin-orbit calculation.
>      As far as I know, the spin-up and spin-down states will coupling together, and the direction of spin angular moment can rotate in the three dimension space, if
> spin-orbit coupling is included in the DFT Hamiltonian. In a usual pseudopotential code, non-collinear spin is necessary to do a spin-orbit interaction. My question is:
> 1. It looks like wien2k does not need non-collinear spin to do a spin-orbit coupling calculation. Why?

In regular WIEN2k calculations with SO we "fix" the direction of the magnetization and
specify it as input in case.inso. Thus we force a collinear state and you may even calculate
the energies for different magnetization directions.

> 2. What's the meaning of spin-up and spin-down in a band structure including spin-orbit interaction?

Of course, SO couples spin-up and dn in a single state. But still you can project out the
spin-up and dn parts of each of these states (eigenvalues). Thus the bandstructure is
"identical", but a "fat-band" plot could still show you for which eigenvalue spin-up or dn
dominates (and the same is true for the DOS).
Peter Blaha
Inst. Materials Chemistry, TU Vienna
Getreidemarkt 9, A-1060 Vienna, Austria
Tel: +43-1-5880115671
Fax: +43-1-5880115698
email: pblaha at theochem.tuwien.ac.at

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