Effect of BEXT (doesn't seem to do anything)?

[sophie_weber1]

Hello,

Sorry to ask another question when I have another still pending. I would like to calculate different contributions to the magnetoelectric response, including the "clamped ion" contribution which comes from the motion of electrons in response to an applied magnetic field (or electric field), when the ions are frozen. The most common way to do this is by computing the change in electric polarization, via for example a Berry phase method, due to different values of applied magnetic field (see for example https://journals.aps.org/prl/abstract/1 ... 106.107202)

I noticed that it seems like it is now possible to apply an external magnetic field in VASP via BEXT https://vasp.at/wiki/BEXT (for reference I'm using VASP 6.5.1). However, I wanted to clarify how this tag works. If it indeed acts as magnetic field (i.e. the electronic minimization in a self-consistent calculation uses an energy function which includes a zeeman term), then for a material with a ground-state antiferromagnetic order I would expect that applying BEXT of a sufficiently large value (i.e. above the saturation field) should lead to a ferromagnetic configuration. But when I apply up to a 20 tesla (corresponding to 0.0023 eV using the VASP unit) field to antiferromagnetic Cr2O3, which is about 3 times the saturation field, the compound stays in its antiferromagnetic configuration (and the energy is identical regardless of the value of BEXT; though this is not surprising since the AFM state is unaffected). So I am confused at what BEXT is actually doing.

Can you clarify if my understanding is correct (basically if the field as implemented in VASP is analogous to the self-consistent implementation, eqs. 1-2 in the PRL I linked), and if so, why the spin reorientation might not be occuring?

Thank you in advance!

[andreas.singraber]

Hello!

Unfortunately I am not familiar with the method you are describing... however, I will forward your message to our experts. In the meantime, could you please provide us with a minimal working example (with all relevant input and output files, according to the forum posting guidelines). Thank you!!

All the best,
Andreas Singraber

[sophie_weber1]

Hello,

That's fine, thank you very much! I look forward to the response.

Attached are the input and output files for three calculations; in one the magnetic moments are oriented antiferromagnetically (as is the ground state of this compound) But as you can see from the OUTCAR the magnetization doesn't seem to respond to the field (also the energy doesn't change for different values of field, but this is not surpising).

There are also two cases where the moment are aligned ferromagnetically; in this case the energy does change for zero versus nonzero field values. So the BEXT is clearly doing something, but it is confusing that it doesn't seem to affect AFM ordering.

Best
Sophie

[sophie_weber1]

Hello,

I just wanted to check if there is any followup on this?

Thank you!

[sophie_weber1]

Hello,

Could you please let me know if there has been any progress on this, or if there is some other resource I could look into. This has been holding me up for awhile in something.

Thank you!

[andreas.singraber]

Hello!

First, let me apologize for the long delay.. I am very sorry that it took so long for me to reply, this is certainly not the reaction time we seek to achieve in this forum.

As I mentioned, I am not an expert on this topic. Nevertheless, I tried to reproduce your results and familiarize to some extent with the given problem. Indeed, I was also not able to see the ferromagnetic configuration appearing, even with very large values of BEXT. However, upon some literature research I do not think that this is actually expected to happen here. You mentioned roughly 6-7T for the saturation field (Bsat) for Cr2O3 but actually this does not seem to be the field required for transitioning towards the ferromagnetic configuration. Instead, 6-7T is the magnetic field where the spin-flop transition occurs (Bsf), see for example this paper:

H. Wiegelmann , A. G. M. Jansen , P. Wyder , J.-P. Rivera & H. Schmid
(1994) Magnetoelectric effect of Cr 2 O 3 in strong static magnetic fields, Ferroelectrics, 162:1,
141-146, DOI: 10.1080/00150199408245099, http://dx.doi.org/10.1080/00150199408245099

Starting from the antiferromagnetic configuration and an external field along the z-axis, when Bsf is reached the spin-flop transition happens and the spins do not exhibit a ferromagnetic configuration afterwards. Instead, they are rotated by 90° into the plane perpendicular to the external field and otherwise almost keep their antiferromagnetic layout. Depending on the actual field they are slightly canted towards following the external field. To make this more clear I created this little illustration:

spin-flop.png

As you can see there is now a small "ferromagnetic contribution" because the spins do not point exactly in the opposite direction any more. However, this configuration does not correspond to the ferromagnetic configuration depicted on the right. This would happen only at much higher magnetic fields (Bsat >> Bsf).

With this in mind I think we cannot expect to see the ferromagnetic configuration (which is the one you provided in your INCAR files) with Bext set to 20T.

Now you could argue: "fine, so it cannot go to the FM configuration but why is there no transition to spin-flop"? At this point I am merely speculating but I believe that it is almost impossible for the optimizer to find a path from one configuration to the other during the SCF cycle because this would require a concerted "movement" of the spins. Or, in other words, the minima corresponding to AFM and spin-flop are separated by a high barrier in the energy landscape and if you start close to one of the minima you cannot expect the algorithm to always find the other one. If one wants to confirm that the spin-flop transition is actually present another approach would be better: For a given spin-flop configuration scan different values of the external field and check whether above Bsf the energy is actually lower than the one of the AFM configuration (which is independent of the external field value because of symmetry as you already found). Of course this is maybe not trivial to do because there may be preferred orientations within the plane (see also the publication above).

I hope this helps a little, I am sorry if there are any mistakes or inaccuracies in my reasoning. I will still ask my colleague whether the implementation of BEXT follows the formulae in the publication you mentioned.

All the best,
Andreas Singraber