[Wien] Orientation of Atomic Spin Moments

[Robert Laskowski]

> In a collinear non-SOC calculation, if the atomic spin can be freely
> rotated, shouldn't the S_z change? 

Without SOC nothing couples real space degrees of freedom to the spin 
coordinates and whole spin space can be freely rotated relative to 
lattice (whole space means all atoms and interstitial). This means
that energy is independent on the direction of magnetisation. 
In a colinear case (colinear magnetisation density, all vectors point in one 
direstion) Z axis of the spin frame is chosen parallel to the magnetisation, 
and the density matrix is diagonal in spin space. If the density matrix is 
diagonal, then the potential is diagonal and the Hamiltonian is diagonal.
Diagonalisation is done separately for (up,up) and (down, down) parts.
So this means that there is no sense of talking about direction of the 
magnetisation in a non-SOC case. 

> Or is the z-axis always rotated 
> with the spin? 

yes, it is.

> How is the spin z-axis related to the global and local 
> coordinates that are defined in Wien2k (in case.struct)? 

in non-SOC case, it is arbitrary. in SOC case the direction of magnetisation 
is defined in insoc file, in a frame used to define unitcell.

> I may be 
> asking very basic questions. It would be nice that you can give some
> references that discuss these basics in detail.

K\"ublers book ``Theory of Intenerant Electron Magnetism''.
Sandrackii, Advances in Physics 47, 91 (1998)

>
> Thanks,
> Chiung-Yuan
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