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Anisotropic magnetoresistance of spin-orbit coupled carriers scattered from polarized magnetic impurities

Anisotropic magnetoresistance (AMR) is a relativistic magnetotransport phenomenon arising from combined effects of spin-orbit coupling and broken symmetry of a ferromagnetically ordered state of the system. In this work we focus on one realization of the AMR in which spin-orbit coupling enters via specific spin-textures on the carrier Fermi surfaces and ferromagnetism via elastic scattering of carriers from polarized magnetic impurities. We report detailed heuristic examination, using model spin-orbit coupled systems, of the emergence of positive AMR (maximum resistivity for magnetization along current), negative AMR (minimum resistivity for magnetization along current), and of the crystalline AMR (resistivity depends on the absolute orientation of the magnetization and current vectors with respect to the crystal axes) components. We emphasize potential qualitative differences between pure magnetic and combined electro-magnetic impurity potentials, between short-range and long-range impurities, and between spin-1/2 and higher spin-state carriers. Conclusions based on our heuristic analysis are supported by exact solutions to the integral form of the Boltzmann transport equation in archetypical two-dimensional electron systems with Rashba and Dresselhaus spin-orbit interactions and in the three-dimensional spherical Kohn-Littinger model. We include comments on the relation of our microscopic calculations to standard phenomenology of the full angular dependence of the AMR, and on the relevance of our study to realistic, two-dimensional conduction-band carrier systems and to anisotropic transport in the valence band of diluted magnetic semiconductors.