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 $1/c^2$, whereas the correct results obtained from the exact Kohn-Sham-Dirac equation are of order $1/c^4$ . We give a qualitative estimate of the order of magnitude of these spurious terms.

Cited by in corpus (18)

• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Calculating linear response functions for finite temperatures on the basis of the alloy analogy model
• Real-space calculation of the conductivity tensor for disordered topological matter
• Magneto-transport and magneto-optical properties of ferromagnetic (III,Mn)V semicondcutors: a review
• Coherent description of the intrinsic and extrinsic anomalous Hall effect in disordered alloys on an $ab$ $initio$ level
• Valley-Polarized Quantum Transport Generated by Gauge Fields in Graphene
• Manipulating Anomalous Hall Antiferromagnets with Magnetic Fields
• Ab initio investigation of light-induced relativistic spin-flip effects in magneto-optics
• Transport Properties of Dirac Ferromagnet
• Anomalous Hall conductivity: local orbitals approach
• First-principles evaluation of intrinsic, side-jump, and skew-scattering parts of anomalous Hall conductivities in disordered alloys
• Transport properties of doped permalloy via ab-initio calculations: effect of the host disorder
• Kubo formula for dc conductivity: generalization to systems with spin-orbit coupling
• Dynamics of the relativistic electron spin in an electromagnetic field
• Terahertz spin dynamics driven by an optical spin-orbit torque
• Spin-polarized current, spin-transfer torque and spin Hall effect in presence of an electromagnetic non-minimal coupling
• Anisotropy of the spin Hall effect in a Dirac ferromagnet
• Field-derivative torque induced magnetization reversal in ferrimagnetic Gd${}_{3/2}$Yb${}_{1/2}$BiFe${}_5$O${}_{12}$