Interplay of Symmetry, Spin Textures, and Hall Effects in Altermagnets with Spin-Orbit Coupling

Altermagnets (AMs) are a newly discovered class of collinear magnets that combine characteristics of ferromagnets with those of antiferromagnets. In particular, AMs display momentum-dependent spin splitting of electronic bands, along with a net zero magnetization. Since the spin order parameter is strictly defined in the nonrelativistic limit, it is unclear to what extent spin-orbit coupling (SOC) modifies the altermagnetic behavior. Although the relativistic SOC energy scale is much smaller than the energy scale for the altermagnetic exchange fields, it is expected that the former can play a pivotal role in dictating the physical properties of AMs, resulting in noncollinear spin textures and anomalous Hall conductivity. Here, we explore the effect of SOC on the altermagnetic phenomena by performing first-principles density functional theory and symmetry analysis on prototypical AMs.