[Wien] Magnetooptics: possible bug

[Igor I Mazin]

I have used before the OPTICS code in WIEN2k to calculate magnetooptics, 
i.e., nondiagonal elements of optical conductivity generated in some 
magnetic structures by spin-orbit. Before, I used only orthorhombic 
symmetry or higher, and the results were in perfect agreement with the 
symmetry analysis and with calculations by other codes, such as VASP. My 
latest example was antiferromagnetics FeSb2.

Recently, I needed to do the same for a hexagonal crystal, MnTe (the 
structure follows). The results are patently wrong, at least if the 
quantization axis in .inso is defined in the lattice coordinates, as 
usual. Indeed, it is easy to show that a nondiagonal conductivity is not 
allowed if this axis is 100 (along the Mn-Mn triangle side) or 001, but 
is allowed in the xy channel (100=x) for 210 (perpendicular to the 
bond). Vasp reproduces this behavior exactly.

Wien does give a zero contribution for 001, but strongly nonzero for 
100. To add injustice to injury, the calculated sigma_xy is exactly 30% 
smaller for 010 than for 100, despite them being symmetry equivalent for 
a hexagonal structure.

Calculations for various SOC directions suggest that the calculations 
are correct, but the SOC direction used internally is not the same as 
the one put in in the .inso file.

Besides, it is unclear even how the x,y,z axes are defined in the JOINT 
output for a hexagonal structure, since apparently there is no such 
thing as a global Cartesian system in WIEN.

Here is the structure:

   7.840474  7.840474 12.755651 90.000000 90.000000120.000000
Te   -1: X=0.00000000 Y=0.00000000 Z=0.00000000
Te   -2: X=0.33333334 Y=0.66666666 Z=0.50000000
Mn up  -3: X=0.66666667 Y=0.33333333 Z=0.75000000
Mn dn  -4: X=0.66666667 Y=0.33333333 Z=0.25000000


P.S. I am using WIEN2k_21.1 (Release 14/4/2021)