Planar Hall Effect in Antiferromagnetic MnTe Thin Films

We show that the spin-orbit coupling (SOC) in $\ensuremath{\alpha}$-MnTe impacts the transport behavior by generating an anisotropic valence-band splitting, resulting in four spin-polarized pockets near $\mathrm{\ensuremath{\Gamma}}$. A minimal $k\ifmmode\cdot\else\textperiodcentered\fi{}p$ model is constructed to capture this splitting by group theory analysis, a tight-binding model, and ab initio calculations. The model is shown to describe the rotation symmetry of the zero-field planer Hall effect (PHE). The PHE originates from the band anisotropy given by SOC, and is quantitatively estimated to be 25%--31% for an ideal thin film with a single antiferromagnetic domain.