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

Recently discovered, altermagnetism represents a third class of collinear magnets. These materials exhibit zero net magnetization, similar to antiferromagnets, but display anomalous transport properties resembling those of ferromagnets. Altermagnetic materials manifest various anomalous electronic transport phenomena, including the anomalous Hall effect, anomalous Nernst effect, and anomalous thermal Hall effect. Additionally, they exhibit magneto-optical Kerr and Faraday effects, previously considered exclusive to ferromagnetic materials. These anomalous transport phenomena are constrained by symmetry, as revealed 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 $k\cdot p$ model for $d$-wave altermagnets CuX$_2$ (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.