Anomalous Hall Effect and Ferromagnetism in Altermagnets

The interplay between the anomalous Hall effect and ferromagnetism has played a central role in quantum materials. In altermagnets, which exhibit large momentum-dependent spin splitting and a vanishing net magnetization, density functional theory (DFT) calculations reveal that the anomalous Hall effect exists with a large or vanishing ferromagnetic spin moment depending on the specific material. In this work, we examine realistic minimal models for altermagnetism and uncover a general spin-orbit coupling enabled quasi-symmetry that provides a natural explanation for when ferromagnetism is large or vanishingly small depending on the specific altermagnetic symmetry.