Intrinsic anomalous and crystal Hall effects in altermagnets

We construct the tight-binding model of the altermagnet in the presence of a finite spin-orbit interaction. As a concrete example, we have studied the collinear FeSb₂. The Fe ions form two sublattices with opposite spin polarization. Inclusion of the intra-sublattice hopping amplitudes up to the next-to-nearest neighbor results in the generic model free of accidental degeneracies. The zero spin-orbit interaction limit is achieved by elimination of spin dependent hopping amplitudes. The additional band degeneracies in this limit are shown to coincide with the prediction of spin symmetry. The minimal one-orbital model gives rise to four bands due to two sublattices and two spin orientations. We have constructed a simplified two-band description valid in the limit of large exchange splitting. Close to the center of the Brillouin Zone, it reduces to the k· p-type Hamiltonian. Based on this Hamiltonian, we have computed the intrinsic contribution to the anomalous Hall conductivity. In a metallic limit, the result can be expressed analytically in terms of the two-kinds of spin splitting: one associated with the altermagnetism, and the other originating from the spin orbit interaction.