[Wien] wrong sign of the off-diagonal magneteoptic permittivity spectra (file case.jointup)

[Jaroslav Hamrle]

Dear collegues,

based on our measurements of MOKE spectra, we think that the 
magnetooptic off-diagonal permittivity in the file case.jointup has 
opposite sign, as compared to the experiment. For example, in the case 
of [001] magnetization, column Re_eps_xy in the file case.jointup has 
opposite sign, as compared to the experimental spectra.


Namely, we made careful sign tests on bcc Fe. Then, according to our 
experiment, Re_eps_xy should be negative for energy about 2 eV, but the 
permittivity calculated by wien2k, Re_eps_xy, has positive sign.

This statement is further supported for example by spectra in article 
Oppeneer et al, PRB45 10924 (1992),
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.45.10924
figure 3b, where after conversion of the off-diagonal conductivity to 
the permitivity (ep=i*sigma/(omega*ep0)) it provides negative real part 
of the off-diagonal permittivity at about 2eV as well.

Furthermore, we have written our own integration over BZ of the 
transition matrix elements, and transition matrix elements (files 
case.symmatup, case.mommat2up) seems to us to be sign-correct.

We think, wrong sign in Re_eps_xy simply appears in conversion from 
conductivity (calculated by Kubo formula,  OPT1.f) to the outgoing 
permittivity.

We think this step appears on lines 965 and 985 of file joint.f, w2k 
version 18.2:

  VV=EPSF*DENSTY(IB,J,icol)/ENG2(j)

where division by the energy makes basically conversion from the 
conductivity to the permittivity.

However, as the conversion itself handles complex numbers:
eps = i/omega * sig

the conversion between real and imaginary parts have opposite signs
eps_Im =  sigma_Re/omega  (this is correct in code)
eps_Re= - sigma_Im/omega (this is the expression for the off-diagonal 
permittivity induced by magnetization, and in this case, we think minus 
sign is missing in the code, namely for Re_eps_xy, Re_eps_xz and 
Re_eps_yz. )

Probably, those arguments will apply also for X-ray off-diagonal spectra 
elements (line 906 in joint.f).


Hoping my comment will be useful to improve w2k code.

With my best regards

Jaroslav Hamrle & Ondrej Stejskal


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Mgr. Jaroslav Hamrle, Ph.D.
Institute of Physics, room F232
Faculty of Mathematics and Physics
Charles University
Ke Karlovu 5
121 16 Prague
Czech Republic

tel: +420-95155 1340
email: hamrle at karlov.mff.cuni.cz
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