Phenomenology of altermagnets

Altermagnets have recently emerged as a new class of magnetic materials sharing properties of both antiferromagnets and ferromagnets. Despite very small net magnetization, they show phenomena usually associated with ferromagnetism, such as the Faraday, Kerr and Anomalous Hall effects, resulting from the relativistic spin-orbit coupling, as well as the spin splitting of electron bands and Spin Hall Effect of non-relativistic origin. Spin space groups and magnetic multipoles are used to explain symmetry properties of altermagnets. Here, I show that the conventional phenomenological description in terms of a vector antiferromagnetic order parameter can be applied to all effects observed in altermagnets with collinear and non-collinear spin orders. I also discuss non-relativistic effects in non-altermagnets.