Magnon scattering modulated planar Hall effect in a ferromagnet/topological insulator heterostructure

We study in-plane magnetotransport for the interface of a ferromagnet insulator (FMI) and a topological insulator (TI), taking into account thermal fluctuation effect of the magnetization in the FMI. It is found that the planar Hall effect (PHE) can display complicated angular dependencies beyond the standard paradigm ${\ensuremath{\sigma}}_{xx}\ensuremath{\sim}({\ensuremath{\sigma}}_{\ensuremath{\parallel}}\ensuremath{-}{\ensuremath{\sigma}}_{\ensuremath{\perp}}){cos}^{2}\ensuremath{\theta}$ and ${\ensuremath{\sigma}}_{xy}=({\ensuremath{\sigma}}_{\ensuremath{\parallel}}\ensuremath{-}{\ensuremath{\sigma}}_{\ensuremath{\perp}})sin\ensuremath{\theta}cos\ensuremath{\theta}$, where ${\ensuremath{\sigma}}_{\ensuremath{\parallel}(\ensuremath{\perp})}$ is the longitudinal conductivity in the direction parallel (vertical) to the magnetic field and $\ensuremath{\theta}$ denotes the relative angle between the applied electric and magnetic fields. The rich structures in angular dependence of the conductivities can arise from the cooperation and competition effect between multiple coexisting mechanisms, e.g., impurity and magnon scattering, band anisotropy, as well as reconstruction of the electronic structure by magnetic fields. Consequently, in addition to the relative angle $\ensuremath{\theta}$, the actual direction of the external fields can be crucial to the PHE, dependent on the specific properties of a material. As a result, the planar Hall conductivity can be nonvanishing even for parallel construction of the applied electric and magnetic fields. Our findings are based on but not limited to the FMI/TI heterostructure, which would be helpful to understand the emergent PHEs in topological materials.