Altermagnetism and weak ferromagnetism

Using a realistic model relevant to La2CuO4 and other altermagnetic perovskites, we study interrelations between weak spin ferromagnetism, anomalous Hall conductivity, σxy, and net orbital magnetization $${\mathcal{M}}$$. All of them are intertwined with the vector of Dzyaloshinskii-Moriya interactions. Nevertheless, while weak spin ferromagnetism is induced by interactions having the same sign in all equivalent bonds, σxy and $${\mathcal{M}}$$ are related to sign-alternating interactions, which do not contribute to any canting of spins. The microscopic model remains invariant under the symmetry operation $$\{{\mathcal{S}}| {\bf{t}}\}$$, combining the shift t of antiferromagnetically coupled sublattices to each other with the spin flip $${\mathcal{S}}$$. Thus, the band structure remains spin-degenerate, but the time-reversal symmetry is broken, providing a possibility to realize σxy in antiferromagnetic substances. The altermagnetic splitting of bands, breaking $$\{{\mathcal{S}}| {\bf{t}}\}$$, does not play a major role in the problem. More important is the orthorhombic strain, responsible for finite σxy and $${\mathcal{M}}$$.