Relativistic corrections in magnetic systems
Abstract
We present a weak-relativistic limit comparison between the Kohn-Sham-Dirac equation and its approximate form containing the exchange coupling, which is used in almost all relativistic codes of density-functional theory. For these two descriptions, an exact expression of the Dirac Green's function in terms of the non-relativistic Green's function is first derived and then used to calculate the effective Hamiltonian, i.e., Pauli Hamiltonian, and effective velocity operator in the weak-relativistic limit. We point out that, besides neglecting orbital magnetism effects, the approximate Kohn-Sham-Dirac equation also gives relativistic corrections which differ from those of the exact Kohn-Sham-Dirac equation. These differences have quite serious consequences: in particular, the magnetocrystalline anisotropy of an uniaxial ferromagnet and the anisotropic magnetoresistance of a cubic ferromagnet are found from the approximate Kohn-Sham-Dirac equation to be of order , whereas the correct results obtained from the exact Kohn-Sham-Dirac equation are of order . We give a qualitative estimate of the order of magnitude of these spurious terms.
Cite
@article{arxiv.cond-mat/0011426,
title = {Relativistic corrections in magnetic systems},
author = {A. Crépieux and P. Bruno},
journal= {arXiv preprint arXiv:cond-mat/0011426},
year = {2016}
}