Anisotropic magnetoresistance in an antiferromagnetic local-moment metal

To describe the layered arsenide antiferromagnetic local-moment metal Ba${}_{1\ensuremath{-}x}$K${}_{x}$Mn${}_{2}$As${}_{2}$, we propose a model Hamiltonian with the local moment Heisenberg superexchanges and the Hund's coupling between itinerant electrons and the local moments. The electric resistivity due to electron-magnon scattering is calculated by using the hydrodynamical approximation of the Kubo formula, leading to $\ensuremath{\rho}\ensuremath{\sim}{T}^{5}$ due to the small size of Fermi surface of the doped materials. When a magnetic field is applied along the crystallographic $c$ axis, which is the direction of the antiferromagnetic ordered moments, the resistivity increases indicating a positive magnetoresistance; while for a magnetic field applied perpendicularly to the $c$ axis, a negative magnetoresistance arises due to the partial suppression of local spin fluctuations.