[Wien] Non-collinear magnetism in WIEN2k? Total magnetic moment, spin moment and orbital moment...

[Pablo de la Mora]

When one adds spin-orbit coupling for a magnetic system one has to 
define a magnetization direction in '<case>.inso':
   0.  1.  0.                 direction of magnetization (lattice vectors)

The results of the calculation come out in the <case>.scf file. There 
are three different results, the total magnetic moment, the spin moment 
and the orbital moment:
MAGNETIC MOMENT IN SPHERE   1    =    1.24926
SPIN MOMENT:  -0.03321   1.15380   0.00000 PROJECTION ON M  1.15380
ORBITAL MOMENT:  0.14357 -1.02102  0.00000 PROJECTION ON M -1.02102

There are two kind of questions that I have:
1) Why are these spin and orbital moments given in vector form?
    Does this imply a kind of non-colinear magnetism?
    If this is the case I would presume that it is valid for small 
deviations from the magnetization direction, in this case the deviation 
is of 8 degrees for the orbital moment and 1.5 degrees for the spin 
moment. For these relatively small angles, are these values correct?

2) In the <case>.scf file :MMI001 gives the 'MAGNETIC MOMENT IN SPHERE', 
but with spin-orbit coupling the 'SPIN MOMENT' and the 'ORBITAL MOMENT' 
appear. So what is the total magnetic moment in this case?

Adding spin and orbital gives:
0.11036  0.13278  0.00000 PROJECTION ON M 0.13278

as it can be seen it is much smaller than the MAGNETIC MOMENT IN SPHERE.

I have observed that magnetic moment in sphere and the spin moment are 
quite symmilar but not equal, Do they have, in principle, the same 
meanning? Which is the correct one?

    Yours

                   Pablo de la Mora