[Wien] irrep has a problem with SO of ferromagnetic materials: X not equal for all elements in the class

[Fecher, Gerhard]

Dear all,
irrep cannot find the irrep of a state in a ferromagnet  with SO but produces  (here for fcc Ni): 

bnd ndg  eigval     E         2C4          C2         2C2`        2C2"          I        2IC4         IC2        2IC2`       2IC2"  
  1  1 -4.267251 1.00+0.00i  0.71-0.71i  STOP: X=( 0.70711 0.70711) Xold=( 0.70711-0.70711)
           6           7     2C4  
 X not equal for all elements in the class 

This appears also for various other states, as well as various other ferromagnetic materials
here the quantisation axis of Ni was the standard 0 0 1, but it appears also for other directions (indeed for fcc Ni one would use 1 1 1, as this is the easy direction)

There was an old question about that in the Forum some years ago
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2013-May/018981.html
but that concerned a nonmagnetic system Bi2Te3

I did after scf with so converged (no lo's):
create a k-list with the Gamma point only (1 kpoint no shift of k-mesh with kgen -so)
lapw1 up
lapw1 dn
lapwso
irrep -so -up


I am wondering whether the point group used by irrep is correct (compared to the references it claims to use)

On page 104, table 88 in Koster  et al [7] one finds that the point group is C4h when applying H(z) to Oh,
however, irrep finds D4h.
further in Table 41   on page  50 in Koster  et al [7] one finds again that the point group is C4h when applying H(z) to D4h.

It seems that irrep and/or symmetso just ignore the spin reversal (time reversal) operator ' and uses P4/mmm instead of P4/mm'm'
that means some of the mirror operations are only allowed in combination with the spin reversal operator
(thus one should have 4/m instead of 4/mmm  or say better D4h  has mirror operations that change forbiddenly the spin, these are clearly absent in C4h)

For example, in D4h, the representation G6+ contains both |1/2,+1/2> and |1/2,-1/2>
however in a ferromagnetic system I would expect a splitting of the s states into up and down, that is
Gamma 5+  |1/2,+1/2>
Gamma 6+  |1/2,-1/2>
as it appears in C4h.

Worthwhile to note that  the 1 1 1 direction has similar problems (D3d (-3m) instead of C3i (-3m')  where Gamma 4+ of D3d is spin degenerate but split into Gamma 4+ and Gamma 5+ in C3i (sometimes called S6) )
just the message is different, as expected:
  1  1 -4.303243 1.00+0.00i  0.25+0.65i  STOP: X=( 0.24562-0.64686) Xold=( 0.24562 0.64686)
           2           3     2C3  
 X not equal for all elements in the class 


It would be nice if someone has a solution for those problems.

Thanks and Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden