[Wien] MMINT

[Fecher, Gerhard]

This is basic calculus,
in an antiferromagnet the total magnetic moment in the cell has to vanish, that is: Mcell = 0
in case of say 2 atoms in the cell (e.g.: Cr) you have M1=m and M2=-m
The total mament in the cell is the sum of the moment in the interstitial region Mint that does NOT belong to any of the two atoms and the magnetic moments in the MT spheres that define atom1 and atom2
           Mcell = Mint + M1  + M2  
           ==>  Mint = Mcell - (M1+M2) = Mcell - (m-m)  = 0 - 0 = 0, q.e.d.
This has to be the similar for more atoms as always the moment of a pair of atoms has to vanish, otherwise you have a ferrimagnet. The muffin tin radii of the atoms of each cancelling pair have to be identical by symmetry.
The situation is different if you have a compensated ferrimagnet, that is a system were the moments of DIFFERENT atoms cancel such that the total moment is also Zero.

Your misconcept is that you try to assign the interstitial region to a particular atom, which is not correct. To distribute the magnetic moment onto "atoms" you have to use a SPACEFILLING partitioning without any interstial. 

The effect that the "atomic" moment depends on the muffin tin radius is nicely shown in the PHYSICAL REVIEW B 102, 024407 (2020) of Fabien

PS.: the link " “https://www.mailarchive.com/wien@zeus.theochem.tuwien.ac.at/msg11651.html”" does not work for me.

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 reyhaneh ebrahimi [reyhanehebrahimi52 at gmail.com]
Gesendet: Samstag, 25. Juni 2022 08:45
An: A Mailing list for WIEN2k users
Betreff: [Wien] MMINT

Dear WIEN2k users;
Would you please let me know why for an antiferromagnetic system, as stated in “https://www.mailarchive.com/wien@zeus.theochem.tuwien.ac.at/msg11651.html”, we compare MMI00X with the experimental data? Although we know that MMINIT is always zero for an antiferromagnetic system, but this does not mean that the contribution of the magnetic moment of an atom in the interstitial region is zero. Zero MMINT may be due to the cancellation of MMINIT of an atom with up spin states and another atom with down spin states. Therefore, an atom may have the non-zero MMINT in the interstitial region. In this case, MMINT should be summed with the MMI00X and then compared with experimental data. For example, MMTOT is always zero for antiferromagnetic systems, but this does not mean that the magnetic moment of an atom is zero.
Thank you very much;
Sincerely yours