Description of two-dimensional altermagnetism: Categorization using spin group theory

Altermagnetism, recently spotlighted in condensed matter physics, presents captivating physical properties and holds promise for spintronics applications. This study delves into the theoretical description and categorization of two-dimensional altermagnetism using spin group theory. Employing spin-group formalism, we establish seven distinct spin layer groups, extending beyond the conventional five spin Laue groups, to describe two-dimensional altermagnetism. Utilizing these findings, we classify previously reported two-dimensional altermagnets and identify different materials exhibiting altermagnetism. Specifically, monolayer ${\mathrm{MnTeMoO}}_{6}$ and ${\mathrm{VP}}_{2}{\mathrm{H}}_{8}{({\mathrm{NO}}_{4})}_{2}$ are predicted to be two-dimensional altermagnets. Furthermore, we scrutinize their spin-momentum-locking characteristics through symmetry analysis and density functional theory calculations, substantiating their altermagnetic properties.