  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.
