[Wien] MMINT

Fecher, Gerhard fecher at uni-mainz.de
Fri Jun 24 12:15:47 CEST 2022 

If one does an AIM analysis, one has no interstitial anymore and the question "What is the sign of interstitial magnetic moment (MMINT) per atom?" does not make much sense.
If one has an interstitial, it is just nowhere defined to which atom that belongs or is distributed about the atoms. 
The magnetic moment of the interstitial is just the difference between the total magnetic moment in the cell and the magnetic moments in the Muffin Tin (MT) spheres.
The latter depend on the size of the MT spheres (note: the smaller the MT spheres the larger is the interstitial region) and thus the sign of the moment in the interstitial has no meaning at all (e.g.: in anti-ferromagnets the moment of the interstitial is always Zero)
(Indeed the moments from the AIM should not depend on the MT spheres, which might be used as a kind of convergence test)

PS.: Instead of a Bader AIM analysis one can principally use any other space filling (!) partitioning of the cell (say a Wigner Seitz type construction), which will result in different moments per atom.

PSS.: Measuring "atom resolved" magnetic moments with XMCD will also have other results, because one finds the magnetic moment averaged over the extend of the core level wave functions, which covers not necessarily the same volume and region as a Wigner Seitz cell or a Bader AIM basin. 

As Peter told, use a plot of the spin density. To have more insight into the problem draw also the MT spheres, the Wigner Seitz cell and the AIM basins, to see the differences. In complicated cases you may wish to use a non-collinear spin method.

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Physics
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: Wien [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Peter Blaha [peter.blaha at tuwien.ac.at]
Gesendet: Donnerstag, 23. Juni 2022 20:31
An: wien at zeus.theochem.tuwien.ac.at
Betreff: Re: [Wien] MMINT

As stated in the UG, for an integration of the spin.density in the
atomic basins you should use:

x aim -dn

Of course, the inaim file must contain the integration directives.

You do not need to run   x aim and   x aim -dn  and take some
difference. Just    x aim -dn  is enough.

Whether the "interstitial" moments are positive or negative depends a
lot on the system and also on the chosen RMT values.
For instance for 3d elements, the delocalized 4s states have opposite
polarization than the 3d electrons. Thus basically the interstital
moment is "negative". However, when you select very small spheres, the
3d moments are not fully confined inside spheres and may contribute to a
positive interstitial moment.

Plot a spin-density to get more insights about its distribution.

Am 23.06.2022 um 16:50 schrieb Laurence Marks:
> I do not think that there is a unique definition of interstitial
> magnetic moments for each atom -- in APW+lo methods the interstitial
> states extend over the whole cell.
>
> The best I can think of is to use the Bader charge, i.e. use "x aim" and
> "x aim -dn", take the difference (to spin resolve) then compare to the
> :MM for the relevant atom.
>
> (N.B., "x aim -up" does not look right.)
>
> WRT your other questions, the sign of the spin without -so or a magnetic
> field is not well defined, you can multiply all by -1 and nothing in the
> density/energy will change.
>
> The interstitial components do not have to have the same sign, and often
> do not. Sometimes one spin state is more delocalized, hence more in the
> interstitial.
>
> --
> Professor Laurence Marks
> Department of Materials Science and Engineering, Northwestern University
> www.numis.northwestern.edu <http://www.numis.northwestern.edu>
> "Research is to see what everybody else has seen, and to think what
> nobody else has thought" Albert Szent-Györgyi
>
> On Thu, Jun 23, 2022, 9:26 AM shahrbano rahimi
> <shahrbanorahimi60 at gmail.com <mailto:shahrbanorahimi60 at gmail.com>> wrote:
>
>     Dear WIEN developers and users:
>
>     Please let me know:
>
>     How I can find the interstitial magnetic moment (MMINT) per atom in a ferromagnetic system with two kinds of magnetic atoms? What is the sign of interstitial magnetic moment (MMINT) per atom? Is it similar to the sign of the MMI of that atom?
>
>     Best Regards,
>     Shahrbano Rahimi
>
>
>
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