Interplay between magnetic structures, domain physics, and transport properties in a family of triangular layered materials

The triangular layered magnet PdCrO2 has attracted interest due to the interplay between its antiferromagnetic order and high in-plane conductivity, widely believed to be the key to understanding an unconventional anomalous Hall effect (AHE) in the material. More recent experiments reveal that the domain physics in the material may also play an important role on its electronic transport. Motivated by these experimental findings, we study the interplay between magnetic structures, domain physics, and transport properties of a layered triangular lattice with alternating layers of hopping electrons and localized spins. We analyze the possible magnetic orders of the most general symmetry allowed spin Hamiltonian at nearest neighbor level. Assuming appropriate intralayer exchange parameters and treating the interlayer exchange perturbatively, we show that threefold rotation symmetry breaking domains can emerge, in accordance with the experiments. We further show that, under certain conditions the Kondo lattice Hamiltonian possesses a particular symmetry that forbids contribution from the electron band topology to the Hall conductance. Finally we study various other effects including magnetic breakdown and spin-orbit coupling and comment on their contribution to the unconventional AHE.