Altermagnetism and weak ferromagnetism

Using a realistic model relevant to La 2 CuO 4 and other altermagnetic perovskites, we study interrelations between weak spin ferromagnetism, anomalous Hall conductivity, σ x y , 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, σ x y 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 σ x y 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 σ x y and \({\mathcal{M}}\) .