Is it possible to use the ATK to calculate the ferroelectric polarization?

[rosen]

Dear developer,
Some software via Berry Phase to calculate the polarization of ferroelectric material, such as PbTiO3, is it possible to use the ATK to such calculation to solve the problem in the ferroelectric material?

[Anders Blom]

In principle, this is possible, meaning that the formalism allows it, and all quantities required are present in the code. It is, however, not implemented in ATK yet.

[rosen]

Is it the code complicated, can you put the script on the "Scripts, Tutorials and Applications" section?

[Anders Blom]

Unfortunately, it's complicated. First of all you need access to internal quantities, and second it involves some relatively complex surface integrals. I suppose by the time implement it, we will take a lot of inspiration from SIESTA (see http://www.uam.es/departamentos/ciencias/fismateriac/siesta/manual-2.0/node18.html, scroll down to "PolarizationGrids").

[1ight0ne]

Do you plan to realize calculation of the polarization of ferroelectric materials in ATK ?

[Anders Blom]

We have added it to ATK, but it's not a well tested feature yet. Also, in version 13.8 (out in beta now) you can in principle perform this calculation using Abinit.

[1ight0ne]

We have added it to ATK, but it's not a well tested feature yet. Also, in version 13.8 (out in beta now) you can in principle perform this calculation using Abinit.

That is great! But i want to ask you few questions about calculating polarization.
Today exists many publications about polarization of multiferroic tunnel junctions (MFTJ) (for example: Effects of ferroelectricity and magnetism on electron and spin transport in Fe/BaTiO3/Fe multiferroic tunnel junctions, DOI:10.1063/1.2828512) and I dont understand how they get ferroelectric (FE) and paraelectric (PE) states ? I only know that state is sets after optimization, but how exactly ?
1.Can you tell me how to set electric state in MFTJ (in ATK) ?
2. If this calculation may perform by Abinit, then can you give me some instructions ?

[1ight0ne]

can anyone answer my question please

[Anders Blom]

First of all, we are perhaps talking about two different things. I initially understood the question as related using the Berry phase to compute the polarization of a piezoelectric material. Here, the feature exists in ATK but is not well tested, and also exists in Abinit and you can find many publications on such calculations.

But the ferroelectric junction calculation you refer to is not related to that, but is a more normal transport calculation, of a type that can definitely be carried out in ATK, and does not require any new features implemented lately. In fact, there are at least 4 articles of similar nature to the one you mention, and which are based on ATK:

DOI:10.1063/1.3462070
DOI:10.1021/nn1031438
DOI:10.1103/PhysRevB.85.064105
DOI:10.1063/1.3698503

You could in principle use Abinit in the same way Tsymbal et al. used VASP, but in that case it's only possible to get a rough estimate of the transport properties, whereas with ATK you can truly compute them.

As you can see from all these articles, the electric states are not really something you set in the calculation as a parameter (like the spin for magnetic tunnel junctions) but rather a consequence of the internal polarization arising from small asymmetries or charge transfer at the surface to the electrodes. Specifically, the paraelectric (PE) or non-ferroelectric state (NFE) is obtained by a geometry optimization at zero bias, and the ferroelectric state (FE) by an optimization at a small electric field.

I find the discussion in PRB 85, 064105 (2012) (one of the articles in the list above) particularly enlightening and very detailed.

[1ight0ne]

Thank you Anders! Now i see that is two different things.

• Can you say why authors in publication above are used VASP for geometry optimization and ATK only for transport characteristics. Why they dont use ATK for optimization ?
• You say:

  the ferroelectric state (FE) by an optimization at a small electric field.

  Does it mean that for FE state I must set small bias ?

[Anders Blom]

It's hard to guess but one reason could be that VASP licensing works a bit different so it's easier for people to run multiple VASP calculations simultaneously. Also, to be open and honest, ATK had a reputation in the past for being inaccurate in relaxations. Part of this was unfortunately true, there was a bug in the 2007 and 2008 versions of the code, but these have been fixed since long. One can argue that a plane-wave code is always more accurate, and it is usually, but there is also the question of using the optimized results from one code to run the calculation, transport in this case, in another code, because it may not be precisely the optimal geometry of that method. And neither is probably exactly the "experimental optimum" anyway.

So I would generally recommend (naturally ) to use ATK also for the optimization - unless you clearly can see that the results are not physically correct. There are some situations to be extra careful about, like large vacancy voids and particular surfaces where it may be necessary to use ghost atoms or basis sets of longer range to get an accurate description of the electron density in the region between atoms. Cf. for instance http://arxiv.org/abs/1306.2731.

[1ight0ne]

Many thanks for your answer, but I still not quite understand how to set FE and NFE state.
Can you correct me if I do this wrong:
1. To set NFE state I must do zero-bias optimization with freezing atoms in xy plane (how set artificial freezing in ATK ?)
2. To set FE state I must set finite bias (? V) at one of electrodes ?

[Anders Blom]

Oh I forgot to answer that point.

1) I don't think it's necessary to constrain the atoms in XY, that will more less happen by itself due to symmetry (at least if you consider similar structures as in the papers we have discussed). So I'm a bit surprised at this point in the PRB referenced above, esp. since Tsymbal's article instead talks about mirror symmetry in the Z direction as the key to getting the NFE state...
2) A small bias should do it, say 1 mV. You are just looking for break the symmetry.

I haven't done these simulations myself, so you might want to check with the authors.