[Wien] Orientation of Atomic Spin Moments

[Robert Laskowski]

> > 1) you calculate only S_z.
>
> I just look at my last email, and it seems I didn't make myself clear
> whether I am interested in the atomic spin of one magnetic atom or the
> total spin from 2 such atoms. Here I clarify it: it's for one magnetic
> atom.
> When I run a regular spin-polarized calculation for a single magnetic
> atom in the same environment (the magnetic atoms are on a surface, so
> I can always leave only one), is the S_z from such calculation the
> maximum S_z, which is the atomic spin S_a? If not, can I perform
> several spin-orbit calculations with different magnetization
> directions, find the S_z from the easy-axis case, and use it as S_a?

S_z is a z projection of total spin moment, in collinear calculations only 
this quantity is accessible. The direction of z matters only when SOC is 
present, otherwise spins of your system can be freely rotated. When SOC is 
present  you can chose the spin coordinate frame in inso file. But notice 
that for collinear calculations always other components of the spin
(S_x and S_y) are assumed to be zero. In some cases (depends on the symmetry)
SOC produces non-zero off-diagonal density matric, which leads to non zero
 S_x or S_y, but collinear code does not calculate them. 

> directions, find the S_z from the easy-axis case, and use it as S_a?

it is in principle true

>
> > 2) run ferromagnetic and antiferromagnetic calculations, and get J from
> >    difference of total energies.
>
> Does a regular spin-polarized calculation refer to the ferromagnetic case?
> Is the energy difference related to J as 2JS^2 (FM: JS^2; AFM: -JS^2)?

J couples at least two spins, there is no coupling to the lattice. Chose any 
orientation of the spin frame. Setup your initial moments 
(inst) as ferromagnetic,  do scf. Setup them as antiferromagnetic, do scf.
Resulting moments should be similar, otherwise  Heisenberg model does 
not apply. And for example, in the scalar product ignore S_x, S_y, 
J=(E_f-E_af)/(S_z1f*S_z2f+S_z1af*S_z2af). At leas you have J for high q.
To have it for low q, you can not escape from noncolinear code.

 regards

   Robert