Altermagnets (AMs) are recently classified as a distinct class of collinear magnets that exhibit characteristics of both ferromagnetism and antiferromagnets. AMs are characterized by unconventional d, g, and i-wave spin momentum cou-pling with net zero magnetization. While the spin order parameter is strictly defined in the non-relativistic limit, it is still unclear to what extent spin-orbit coupling (SOC) modifies the alter magnetic behavior. Here, we understand the effect of SOC on the alter magnetic phenomena by performing first-principles density functional theory and symmetry analysis on prototypical AMs. We show that only two of the seven nontrivial spin layer groups exhibit an unconventional in-plane AHE in which the Néel vector lies within the plane of the Hall current. Although AHE is a relativistic effect, we find that the spin group symmetry is successful in determining the linear and cubic dependence of anomalous Hall conductivity in Néel vector space.

Hall Effect, Conductivity, Semiconductor