Abstract
We propose a model ferromagnet based on the Dirac Hamiltonian in three spatial dimensions, and study its transport properties which include anisotropic magnetoresistance (AMR) and anomalous Hall (AH) effect. This relativistic extension allows two kinds of ferromagnetic order parameters, denoted by and , which are distinguished by the relative sign between the positive- and negative-energy states (at zero momentum) and become degenerate in the nonrelativistic limit. Because of the relativistic coupling between the spin and the orbital motion, both and induce anisotropic deformations of the energy dispersion (and the Fermi surfaces) but in mutually opposite ways. The AMR is determined primarily by the anisotropy of the Fermi surface (group velocity), and secondarily by the anisotropy of the damping; the latter becomes important for , where the Fermi surfaces are isotropic. Even when the chemical potential lies in the gap, the AH conductivity is found to take a finite nonquantized value , where is the (effective) fine structure constant. This offers an example of Hall insulator in three spatial dimensions.
- Received 18 April 2014
- Revised 21 November 2014
DOI:https://doi.org/10.1103/PhysRevB.90.214418
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