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We develop a theory of the anisotropic magnetoresistance (AMR) effects ofarbitrary directions of current and magnetization for ferromagnets. Here, weuse the electron scattering theory with the $s$--$s$ and $s$--$d$ scatteringprocesses, where $s$ is the conduction electron state and $d$ is the localizedd states. The resistivity due to electron scattering is expressed by theprobability density of the d states of the current direction. The d states arenumerically obtained by applying the exact diagonalization method to theHamiltonian of the d states with the exchange field, crystal field, andspin--orbit interaction. Using the theory, we investigate the transverse AMR(TAMR) effect for strong ferromagnets with a crystal field of cubic ortetragonal symmetry. The cubic systems exhibit the fourfold symmetric TAMReffect, whereas the tetragonal systems show the twofold and fourfold symmetricTAMR effect. On the basis of the above results, we also comment on theexperimental results of the TAMR effect for Fe$_4$N.

journal of the physical society of japan

Theoretical Study on Anisotropic Magnetoresistance Effects of Arbitrary  Directions of Current and Magnetization for Ferromagnets: Application to  Transverse Anisotropic Magnetoresistance Effect