General Stacking Theory for Altermagnetism in Bilayer Systems.

Two-dimensional (2D) altermagnetism was recently proposed to be attainable in twisted antiferromagnetic bilayers providing an experimentally feasible approach to realize it in 2D materials. Nevertheless, a comprehensive understanding of the mechanism governing the appearance of altermagnetism in bilayer systems is still absent. In the present Letter, we address this gap by introducing a general stacking theory (GST) as a key condition for the emergence of altermagnetism in bilayer systems. The GST provides straightforward criteria to predict whether a bilayer demonstrates altermagnetic spin splitting, solely based on the layer groups of the composing monolayers. According to the GST, only seven point groups of bilayers facilitate the emergence of altermagnetism. It is revealed that, beyond the previously proposed antiferromagnetic twisted Van der Waals stacking, altermagnetism can even emerge in bilayers formed through the symmetrically restricted direct stacking of two monolayers. By combining the GST and first-principles calculations, we present illustrative examples of bilayers demonstrating altermagnetism. Our work establishes a robust framework for designing diverse bilayer systems with altermagnetism, thereby opening up new avenues for both fundamental research and practical applications in this field.