Can only get one of two energetically equivalent magnetic domains to converge in a slab

[sophie_weber]

Hello,

I am performing collinear, spin-polarized (no spin-orbit coupling) calculations on a vacuum-terminated slab of a metallic, antiferromagnetic compound (RuO2). I am try to examine the magnetic moment magnitudes as function of Hubbard U value (this compound undergoes a metal-insulator transition between U=2 and 4 eV for Ru d states), but in doing so I realised a disturbing phenomenon; I seem to be able to only successfully converge one magnetic domain for the slab (this is not an issue for the bulk). If I try to initialise the opposite domain, the moments either go all over the place, or even if it does converge to the opposite domain, the magnitudes of the moments printed in the OUTCAR are not equivalent for the two domains, as they should be by symmetry.

Interestingly, this occurs across U values, so it is not just a case of the system being metallic (it occurs for U=4, when RuO2 is an insulator). For the insulating case at least, I can converge both domains if I start relaxing with opposite domains and then read in the CHGCAR for the self-consistent run, but it fails to converge to the proper domain specified in MAGMOM if I start with a relaxed structure and no CHGCAR (see input files). for the metallic case, where I attach U=1.2 eV as an example, the convergence to the desired domain fails even at the slab relaxation stage (see attached input files.

If anyone has an idea what I may be doing wrong I'd greatly appreciate it. I realize this is complicated problem and I may not have explained it adequately, so please let me know if more files or explanations are needed.

Thank you in variance.

[jonathan_lahnsteiner2]

Dear sophie_weber,

I am not sure if I properly understand your question. I am not sure what you mean by magnetic domains.

So you are saying that you have the same slab structure and start with different initial magnetizations to converge to
either one or the other magnetic structure. In the bulk, you can compute both of the magnetic structures.
But as soon as you are trying to do this for the slab structure only one stable magnetic structure forms.
Does this maybe mean, that slab structure breaks some symmetry and only one stable magnetic structure
exists?

All the best Jonathan

[sophie_weber]

Dear Jonathan

Thank you for the reply. Yes, I think you understand quite well, despite my poor explanation. When I say opposite magnetic domains, I just refer to flipping the sign (again, these are without spin-orbit coupling so there is no direction) of magnetization, i.e. "up down up down" becomes "down up down up" in the opposite domain.

And precisely, the issue is that with the slab structure, I am not able to reliably converge both domains; even when, by luck, I have managed to get two converged calculations with opposite domains, the magnitudes of the moments, and the total energies, are not equivalent. It's a very good suggestion that the slab breaks the symmetry correspondance, but I'm quite sure that the opposite magnetic domains should be equivalent by symmetry in this slab structure. I am familiar with a compound, FeF2, which is isostructural to RuO2 (except it is a large-gap insulator). If I perform an analogous calculation for the same (110) oriented slab of FeF2, where I relax the internal positions and then do two self-consistent, spin-polarized calculations with the two opposite domains, the calculations converge easily such that the magnitudes of all Fe moments are exactly the same, except with the opposite signs, and the energies are the same within the resolution of my calculation (see attached input and output files). Also, if you check the OUTCARs the two domains have identical symmetry as recognized by VASP. And this is the same symmetry of the (110) slab for RuO2 (see attached files for a calculation with a relaxed slab where domain converged properly and forces on the structure were very small).
However, if you now try to repeat this calculation for RuO2 with all the values in MAGMOM multiplied by minus one, in my experience, the moments will either flip with respect to initialisation, or the domain will converge by not by symmetrically equivalent in terms of moment magnitudes and energy to the attached RuO2 calculation. I noticed interestingly, that in some cases, the forces in these calculations which converged "by luck" were quite large, even though the structure had been relaxed to <0.01 eV/angstrom per atom and the forces for the domain which reliable converges are, as expected, tiny.

All this to say, it seems like it is not a symmetry issue, and is really just something with RuO2 properties being somehow more finicky than FeF2 (the magnetization is itinerant experimentally, so perhaps this is related), and the calculations keep getting stuck in metastable configurations.

If you have any insights or hints I'd greatly appreciate it. Let me know if I can provide more information.

[jonathan_lahnsteiner2]

Dear sophie_weber,

In the case of your FeF2 calculations, the two magnetic domains have the same energy. As input
the same POSCAR is used. So this result is expected.

In the case of RuO2 the used POSCARs differ for the calculations of the two different magnetic domains.
So I was wondering should the POSCARs in the case of the RuO2 calculation not also be completely the same.
Or is there a reason why they are different. Because for differing POSCAR files I would
not expect to get symmetrically equivalent magnetic domains with the same energies.

All the best Jonathan

[sophie_weber]

Dear Jonathan,

This is true, sorry, the two initial sets I gave you for RuO2 were perhaps bad examples. The structures differ very slightly because I was trying at one point to re-relax in case this was the issue.

But the point was primarily that it is not even possible to reliably converge both domains (the additional concern that in the very lucky cases I manage, the moments and energies are not equivalent even for identical POSCARs, is only relevant if the first concern is overcome). I attach as an example two calculations with an identical relaxed POSCAR for RuO2. For the first domain, this is a self-consistent calculation initialised from the relaxed WAVECAR/CHGCAR, and you can see from the OUTCAR that it converged to the magnetic order I specified in MAGMOM. However, for the second domain ("domain2_failed"), note that in the MAGMOM I now initialised the opposite domain, but it just flips and converged back to the other domain. This is not the same behavior as in FeF2, and since, as you can see for FeF2, the domains should be symmetrically equivalent, the behavior is unexpected.

If you have any insight into input parameters or particular features of the compound that may be leading to convergence issues it would really help me.

Thank you for your patience,
Sophie

[jonathan_lahnsteiner2]

Dear Sophie Weber,

How did you initialize the second simulation? Did you start both simulations from the same WAVECAR file?
If not could you please try to start both simulations from the same WAVECAR file.

Best Jonathan

[sophie_weber]

Hi Jonathan,

The second one I did not initialise from a WAVECAR (since I have no WAVECAR corresponding to the magnetic ground state that I want). I tried just now your suggestion to initialise it using the same WAVECAR as for domain1, and is certainly converges faster, but again, to domain1, not the opposite domain which I specified in MAGMOM (I think this makes sense, as the WAVECAR corresponds to wave functions with have converged to domain1, so if I understand correctly, the MAGMOM is just ignored in this case and the initialisation starts out in the converged domain 1 state.

Best
Sophie

[sophie_weber]

Dear Jonathan,

I just wanted to update you that I was able to finally get the two domains to reliably converge by setting ALGO=All, and crucially TIME=0.05 in my INCAR. This was based on a suggestion I found in the VASP wiki for LDA+U calculation convergence in general.

If you have some understanding of why this might have helped so I can understand it more rigorously, I'd appreciate it!

Thank you for your help and suggestions,
Sophie

[jonathan_lahnsteiner2]

Dear Sophie,

When doing electronic minimization with included magnetism the choice of the algorithm can
determine what minimum you find in your calculation. There is no guarantee that an algorithm will
find the global minimum when dealing with magnetism during electronic minimization. There is always the possibility
that the calculation gets stuck in a local minimum or as in your case that only one of the global minima can be reached.
So it is always a good idea to compare several algorithms and check which one predicts the lowest energy for your system.
From my own experience, the conjugate gradient algorithm is usually the most robust choice for finding the global minimum during
minimization. With ALGO=ALL you already select the conjugate gradient algorithm.


I hope this helps to clarify your problem.

All the best Jonathan

[sophie_weber]

Hi Jonathan,

Thank you for the reply, I appreciate it!

Best
Sophie