Issue with calculating magneto-optical effects

[zeleznyj]

I'm trying to use QATK to calculate the magneto-optical Kerr effect (MOKE). I tried the ferromagnetic bcc Fe as a test case. MOKE is obtained from the off-diagonal components of the optical conductivity. These vanish in the bcc lattice in the absence of magnetism and spin-orbit coupling, but they should be present in the ferromagnetic case with spin-orbit coupling. However, in QATK, when calculating the optical conductivity using the OpticalSpectrum function, the off-diagonal components are zero (The susceptibility is of the order of 1e-16). I'm unsure if I'm doing something wrong or if this is an issue with QATK. I can get offdiagonal components if I strain the lattice so that the symmetry is broken. These are, however, non-magnetic contributions that I'm not interested in, but it shows that QATK can also evaluate the off-diagonal components. I have tried both the MomentumOperator and VelocityOperator, and I'm getting the same result. I also tried turning off the symmetries in the k-mesh, both for the LCAO calculation and the Optical spectrum using:

Code

symmetries = [([[1,0,0],[0,1,0],[0,0,1]],[0,0,0])]

and this didn't help either. Attached is an example of a script I'm using for the calculation.

[Anders Blom]

The way QuantumATK evaluates the optical spectrum is from the Kubo-Green formula which doesn't really apply to metals unless you also include intraband contributions, which makes the calculation a bit more elaborate. See https://docs.quantumatk.com/manual/Types/OpticalSpectrum/OpticalSpectrum.html#NL.Analysis.OpticalSpectrum.OpticalSpectrum.opticalIntrabandParameters.

This is also mentioned in e.g. https://www.sciencedirect.com/science/article/abs/pii/S0304885304017925 which perhaps provides a better test example than bcc Iron. I cannot say how important it is to perform such calculations with an all-electron method as used in that paper, or if the pseudopotential approach is enough, but you will find out, hopefully!

[zeleznyj]

Thank you for the answer. I understand that the intraband contributions may be important in metals, but nevertheless, the MOKE should also be present even in the interband contributions. See, for example, this calculation of bcc Fe: https://www.sciencedirect.com/science/article/pii/S0304885398005356, which does not include intraband contribution.

My calculations with QATK reproduce quite well the sigma_xx, but the sigma_xy is zero.

So this means that either I'm doing something wrong or there's an issue with QATK, because the sigma_xy should not be zero if spin-orbit coupling is included and the system is ferromagnetic. I'm really not an expert with QATK so it is definitely possible that I'm doing something wrong, but it is quite a straightforward calculation, and I've done a lot of testing, so I'm not sure what I could do wrong. So, to me, this seems more like an issue with QATK.

I don't think the problem relates specifically to Fe. I first noticed the issue with a different system and only used Fe for testing.

[Anders Blom]

One thing I already noted in your script before is that you only include 10 bands above the Fermi level. This default is unfortunately way too low for almost all cases, and esp. here it seems the relevant contributions may be from bands as high as 10-30 eV above the Fermi level.

[zeleznyj]

I have tried increasing the number of the bands to 100 and this doesn't change the result.