Theory of bound magnetic polarons in cubic and uniaxial antiferromagnets

Motivated by a recent debate about the origin of remanent magnetization and the corresponding anomalous Hall effect in antiferromagnets and altermagnets, a theory of bound magnetic polarons (BMPs) in anisotropic magnetic semiconductors is developed. The theory describes quantitatively the experimentally observed magnitude of excess magnetization and its dependence on the magnetic field in cubic antiferromagnetic EuTe. In contrast to the cubic case, our theory predicts the presence of magnetization hysteresis below N\'eel temperature in antiferromagnets with uniaxial anisotropy. We show, employing material parameters implied by experimental and ab initio results, that the magnitudes of remanent magnetization and the coercive field are in accord with recent experimental observations for altermagnetic hexagonal MnTe. While the altermagnets have an intrinsic contribution to the remanent magnetization and the anomalous Hall effect, our theory explains the origin of an extrinsic contribution. Our findings address, therefore, a question about the relative contribution to the remanent magnetization of bound magnetic polarons and weak ferromagnetism driven by the antisymmetric exchange interaction, the latter weakened by the formation of antiferromagnetic domains. Furthermore, we provide the theory of BMP spontaneous spin splitting, which can be probed optically.