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

[Peter Blaha]

Hi,
I think everything is ok. It can happen that the resulting magnetic 
moments point into a different direction as the principle axis defined 
for spin-orbit interaction.

The rotij matrices are printed in case.output2up/dn and yes, your "c)" 
makes sense.

PS: You can always break further symmetry (split equivalent atoms and 
label them 1,2,3...) down to P1 and check your results.

Am 07.06.2022 um 16:07 schrieb 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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-- 
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
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