Transport Coefficients of Dirac Ferromagnet: Effects of Vertex Corrections

Abstract

As a strongly spin-orbit coupled metallic model with ferromagnetism, we have considered an extended Stoner model to the relativistic regime, named Dirac ferromagnet in three dimensions. In the previous paper~[Phys. Rev. B 90, 214418 (2014)], we studied the transport properties giving rise to the anisotropic magnetoresistance~(AMR) and the anomalous Hall effect~(AHE) with the impurity potential being taken into account only as the self-energy. The effects of the vertex corrections~(VCs) to AMR and AHE are reported in this paper. AMR is found not to change quantitatively when the VCs is considered, although the transport lifetime is different from the one-electron lifetime and the charge current includes additional contributions from the correlation with spin currents. The side-jump and the skew-scattering contributions to AHE are also calculated. The skew-scattering contribution is dominant in the clean case as can be seen in the spin Hall effect in the non-magnetic Dirac electron system.Comment: 21 pages, 7 figure