Theory of magnetocrystalline anisotropy
The direction of a magnetization relative to body that supports it is determined mainly by two effects, shape anisotropy and magnetocrystalline anisotropy. The first arises from magnetostatic effects and the second from spin-orbit coupling between the spins and the lattice of the material. The magnetostatic effects can be calculated from micromagnetic calculations, but the magnetocrystalline anisotropy must be computed from the electronic structure of the material. This is an important quantity because it determines whether a magnetic material can be made into a good hard magnet, a good soft magnet or neither. Hard magnets are an essential component of electromagnetic motors and soft magnets are an essential component of transformers.
Unfortunately, the electronic structure calculations used for solids
cannot accurately predict the magnetocrystalline anisotropy of the
simplest systems, the 3d transition metals, Fe, Co, and Ni. The
figure above shows the results of several calculations in comparison
with experiment.
We have carried out well converged numerical calculations of the
anisotropy for these systems. We have investigated the possibility
that the error in previous calculations arose from an approximate
treatment of the spin-orbit interaction. We improved the description
of this interaction and found very little improvement in the
comparison with experiment. In addition, we carried out the first
numerically converged calculations for Co in its ground state
hexagonal-close-packed structure. It is "common lore" that
these types of calculations work better for low symmetry systems like
Co. We found that the disagreement between calculation and experiment
for Co is much larger in magnitude that that for either Fe or Ni.
The Spin-Other-Orbit Interaction and Magnetocrystalline Anisotropy
A Gradient Search Method for Orbital-Dependent Charge-Density and Current Density Functional Calculations
Mark D. Stiles
Andrew Zangwill - Georgia Institute of Technology
Ross Hyman - DePaul University
Samed Halilov - Naval Research Laboratory
Online: February 2002
Last Updated: February 2008
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