Symmetry-Constrained Anomalous Transport in the Altermagnetic Material CuX₂ (X = F, Cl)

Altermagnetism, a recently identified class of collinear magnetism, combines key features of antiferromagnets and ferromagnets. Despite having zero net magnetization, altermagnetic materials exhibit anomalous transport effects, including the anomalous Hall, Nernst, and thermal Hall effects, as well as magneto-optical Kerr and Faraday effects. These phenomena, previously thought unique to ferromagnets, are dictated by symmetry, as confirmed by density functional theory (DFT) calculations. However, an effective model-based approach to verify these symmetry constraints remains unavailable. In this Letter, we construct a k ⋅ p model for d-wave altermagnets CuX₂ (X = F, Cl) using spin space group representations and apply it to calculate the anomalous Hall effect. The symmetry-imposed transport properties predicted by the model are in agreement with the DFT results, providing a foundation for further investigation into symmetry-restricted transport phenomena in altermagnetic materials.