Collinear Altermagnets and their Landau Theories

Collinear altermagnetism corresponds to a collinear, compensated magnetic order exhibiting alternating spin-splitting of electronic bands. The distinctive magneto-crystalline symmetries of altermagnets ensure that the spin-splitting has a characteristic anisotropy in crystal momentum space. 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 with and without 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.