Constrained magnetic calculations strategy

[sophie_weber]

Dear all,

A student of mine is using constrained magnetic calculations to try to stabilize magnetic configurations (which are collinear, and close to the ground state ironically) of an extremely pesky heterostructure with Cr2O3 and a strong spin-orbit-coupled heavy metal. I know that the common strategy for non collinear constrained calculations in VASP is to start with a small (lambda=1-10) lambda value to avoid instabilities, and then gradually increase lambda starting from a converged WAVECAR until the penalty energy is sufficiently small.

However, my understanding is that this is assuming that with the initial, small lambda value, the magnetic moments converged to the desired directions specified by M_CONSTR, just with a larger penalty energy than is desired. However, the student is getting the opposite issue, where when she sets lambda to 5 or 10, the final penalty energy is tiny (10^-9 eV), BUT the moments are nowhere near the desired magnetic configuration, and instead many are flipped with respect to M_CONSTR. It almost is as if the constrained formalism is just not kicking in.

In this situation, my intuition would be to actually attempt setting lambda to a much larger value; I know that people generally say that Ep is inversely proportional to lambda, but my understanding is that this is only in the limit where the moments are very close to their desired direction (small theta limit). Just looking at the functional from of the penalty energy, I would assume that when the moments are far away from their desired direction, a larger lambda will give a larger penalty energy and thus be more likely to force the moments to do what we want. Is this intuition correct/would you suggest this (I know it might fail due to instability issues or other problems)? Or are there any other strategies to use if the normal constrained magnetic procedure does not result in the moments pointing where you want them?

Thank you in advance!

[andreas.singraber]

Dear Sophie Weber,

I discussed this issue with my colleagues and we agree with your intuition to increase the LAMBDA value as the first thing to try. However, even if this works better there is still a chance that there remain flipped moments with respect to the desired M_CONSTR vectors. This is due to the construction of the penalty term for I_CONSTRAINED_M = 1 which is only sensitive to differences in direction but not in the sign of the desired and actual magnetic moments. Hence, antiparallel vectors result in the same penalty as parallel vectors. Actually, as of version 6.4.0 VASP comes with another I_CONSTRAINED_M mode that is sensitive to direction and sign which you could try as well:

Code: Select all

I_CONSTRAINED_M = 4

implements the penalty term described in this publication: https://journals.aps.org/prb/abstract/1 ... .91.054420. Unfortunately, this feature was previously undocumented, I just added it to our Wiki. I hope this is helpful, if there are further questions please also add the relevant input/output files to your posts. Thank you!

All the best,
Andreas Singraber

[sophie_weber]

Dear Andreas,

Thank you very much for your response! That's quite sad about I_CONSTRAINED_M=1 only constraining absolute direction. I hadn't realised this before but indeed it is clear from the penalty energy form as you say. Unfortunately we don't currently have access to VASP 6.4, but. hopefully will in the future. In the meantime, we will try larger Lambda.

Thank you for your help, I appreciate it.

Best,
Sophie