Optical nonreciprocity and hyperbolicity in altermagnetic MnF₂

Altermagnets have zero net magnetization but possess time-reversal symmetry breaking and non-relativistic spin-split band structures. Such materials may exhibit anomalous Hall conductivities without applying static magnetic fields. In this paper, we investigate the optical properties of the altermagnet MnF_2. The full conductivity tensor has been calculated using density functional theory and then converted into permittivities. The off-diagonal terms may slightly affect the optical responses, but the main optical properties are determined by the diagonal ones. Due to intrinsic time-reversal symmetry breaking, optical nonreciprocity has been found by polarization conversion during reflection. After hole doping, altermagnetic MnF_2 exhibits hyperbolic responses. Numerical simulations based on the finite element method have been used to confirm such hyperbolicity. Our investigations have revealed that some altermagnets may be more easily verified through optical detection and have fascinating applications in optics, which might lead to nonmagnetic material-based magneto-optical devices without external magnetic fields.