Collinear Altermagnets and their Landau Theories

Collinear altermagnetism corresponds to compensated magnetic order exhibiting alternating and anisotropic spin splitting of electronic bands, due to distinctive magneto-crystalline symmetries. These systems have attracted interest because of their potential for spintronics applications. We provide a general Landau theory that encompasses all three-dimensional altermagnets, assuming the magnetic order does not enlarge the unit cell. We identify all crystal structures admitting altermagnetism, and reduce to a smaller set of possible Landau theories characterized both with and without spin-orbit coupling (SOC). In the zero SOC limit we determine the possible local multipolar orders that are tied to the spin splitting of the band structure. Importantly, we clarify the bridge between "ideal" SO-free altermagnets and real altermagnets with SOC, and we distinguish the measurable properties and response functions of SOC altermagnets from collinear Néel antiferromagnets.