Title: The description of two-dimensional altermagnetism

Abstract: 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 novel materials exhibiting altermagnetism. Specifically, monolayer MnTeMoO$_6$ and VP$_2$H$_8$(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.