2000/11/30 by A. Crépieux, P. Bruno · 1 citation
Physics and Astronomy · #cond-mat
paper · pdf · doi:10.1103/physrevb.64.094434
published as Phys. Rev. B 64, 094434 (2001)
arxiv created 2001/08/16 · arxiv updated 2016/08/15
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 1/c2, whereas the correct results obtained from the exact Kohn-Sham-Dirac equation are of order 1/c4 . We give a qualitative estimate of the order of magnitude of these spurious terms.