[Wien] spin and orbital moments

[Kateryna Foyevtsova]

Dear Wien2k developers,

I use wien2k version 11.1 to run spin-polarized GGA+U calculations with
SO coupling for a molibdenum oxide.
The symmetry of the system is the following

blebleble                                s-o calc. M||  1.00  1.00 -1.00
P                           15 2 P-
             RELA
 13.669712 13.669712 13.669712 60.000000 60.000000 60.000000

As you see, I set magnetization axis to 1 1 -1, which should be in terms
of (non-orthogonal) lattice vectors.
With the help of xcrysden and case.outsymso, I can deduce that this
direction corresponds to the 0.577350, 0.816497, 0 direction in terms of
the cartesian global coordinate system.

When I converge the electron density with (without using any previously
converged non-relativistic calculation)

runsp_lapw -p -orb -so -dm

I get the following data for the first and the last iteration on one of
the Mo atoms:

1. iteration:
:SPI005:  SPIN MOMENT:   0.46560   0.80642  -0.53749 PROJECTION ON M
1.07518
:ORB005:  ORBITAL MOMENT: -0.08361 -0.01872  0.02851 PROJECTION ON M
-0.06454
:MMI005: MAGNETIC MOMENT IN SPHERE   5    =    1.86180

last iteration (converged solution):
:SPI005:  SPIN MOMENT:   0.61653   1.06239  -0.70860 PROJECTION ON M
1.41804
:ORB005:  ORBITAL MOMENT: -0.08361 -0.01872  0.02851 PROJECTION ON M
-0.06454
:MMI005: MAGNETIC MOMENT IN SPHERE   5    =    1.43149

Now, I am struggling to understand two things:
1) In which coordinate system are SPI005 and ORB005 given?
If they were given in the global cartesian coordinate system, they would
be parallel to 0.577350, 0.816497, 0, but they are not.

2) Why for the first iteration MMI005 is not even roughly equal to
SPI005 + ORB005?

Thank you very much!
Kateryna Foyevtsova

P.S. When I perform relativistic calculations starting with a
preconverged electron density of the non-relativistic solution I get the
same final result.