[Wien] Non-collinear magnetic moments from LAPWDM in (collinear) Wien2k

[Jindrich Kolorenc]

Dear Wien2k users and developers,

I would be grateful for your opinion about a somewhat peculiar behavior
I am getting.

I calculate the electronic structure of the beta phase of uranium
hydride (UH3). It has a cubic primitive cell with 8 formula units in
it. There are two nonequivalent U positions, one with multiplicity 2
(site 2a, higher symmetry, Th), the other with multiplicity 6 (site
6c, lower symmetry, D2d), struct file is attached. I run a
spin-polarized calculation (PBE) with spin-orbit coupling and direction
of magnetization 111 (struct file with the lowered symmetry is also
attached). Then I calculate the orbital (and spin) moments using LAPWDM
(the resulting case.scfdmup is attached).

For the uranium site with multiplicity 2 I get moments along 111 as
expected but for the lower-symmetry site the direction deviates from
111 for the orbital as well as spin moment. In particular, for the f
shell I get

  mS =  ( 1.21, 1.16, 1.16 ) = (mx,my,mz),
  mL = -( 1.42, 1.18, 1.18 ).

Now to my questions:

a) Is this a valid result or is such non-collinearity a sign of
something being broken?

b) In particular, is this (local) moment deviating from 111 compatible
with the assumption of SYMMETSO (magnetization along 111)?

c) If the result is valid, would I get the moments at the individual 6c
sites by applying the rotation matrices ROTIJ to the moments returned
by LAPWDM?

c') Side question: Are these ROTIJ matrices printed out somewhere? I
get them by uncommenting a few lines in SRC_lapw1/atpar.F.

An analogous behavior was recently reported in 

  https://doi.org/10.1016/j.jnucmat.2022.153817

using PBE+U in VASP. When I do the rotations suggested in c) above, I
reconstruct the pattern shown in Table 3 of the linked reference. When
the moments of all the equivalent 6c sites are added together, the
resulting moment points along 111 so that the total magnetization has
the direction as assumed at the beginning. That may mean that c) makes
sense but I am not sure.

Best regards
Jindrich Kolorenc
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