[Wien] Hyperfine field

[Martin Pieper]

Dear Hideto Azuma,

the formula you cite (and Wien uses) gives the Fermi contact
contribution to the hyperfine field. This contribution is the one from
s-electrons, which are the only ones with significant probability in the
volume of and very near the nucleus. The difficulty with the classical
description is not their diverging spin density but the divergence of
the classical dipol-dipol interaction energy between nuclear and
electronic spin at zero distance. This divergence is just a breakdown of
the dipolar field approximation, not of Maxwell theory: if one
calculates the interaction energy of nuclear and electron spin starting
from the vector potential of the nuclear magnetic moment one arrives at
the Fermi contact term (see e.g. Kei Yosida, Theory of Magnetism,
Springer Series in Solid State Sciences Vol. 122, chapter 2 (I am fairly
sure this book has also been  published in Japanese :-) for the basics,
and perhaps S. Blügel et. al. Phys. Rev. B 35 (7), (1987), p. 3271 if
you are interested in the fully relativistic treatment ... or the
introduction to the orbital package from Pavel Novak here in the
Wien2k-pages).

Be aware that the Fermi contact term is only one contribution of several
possible in magnetic systems: dipolar fields from spin moments in
incompletely filled non-s shells, and from unquenched orbital moments
are treated with the ORB package of Wien, dipolar fields from
neighboring atoms and farther away by the dipol program.

Martin Pieper

Azuma, Hideto wrote:
>Hello, wien2k experts.
>
>Looking at the :HFF value in scf files, it seems that Wien2k program 
>gives us the hyperfine field as 
>
>:HFF = (8pi/3) x 'bohr magneton' x 'spin density at 1st radial point
>(:RTO)' ---(a).    (am i right?)
>
>In my recognition, wien2k's LCORE program treat the wave function
> in relativistic sentences even in the usual case ( LSDA or GGA without 
>orbital potential nor spin-orbit interaction), so, I am confusing;
>
>1. Does not the spin density diverge at nuclei?
>2. How about the validity of formula (a) ?
>3. Any good references?
>
>My interests is limited in light atoms like oxygen or lithium now, I
>hope
> relativistic effect is negligible in these case, and :HFF's are good
>value.
>Probably I should learn basic physics more, but I appreciate any
>suggestion.
>
>
>Hideto Azuma, sony corporation. 
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>Wien at zeus.theochem.tuwien.ac.at
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>  


-- 
Dr. Martin Pieper
Institut f. Physik, 
Karl-Franzens Universität Graz
Universitätsplatz 5, A - 8010 Graz, AUSTRIA
Tel.: +43-316-380-8564, Fax: +43-316-380-9816,
email: martin.pieper at ifp.tuwien.ac.at