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/[email protected]/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 [[email protected]] im Auftrag von reyhaneh
ebrahimi [[email protected]]
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/[email protected]/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
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