Bilayer stacking A -type altermagnet: A general approach to generating two-dimensional altermagnetism

In this article, we propose a new concept of bilayer stacking A-type altermagnet (BSAA), in which two identical ferromagnetic monolayers are stacked with antiferromagnetic coupling to form a two-dimensional A-type altermagnet. By solving the stacking model, we derive all BSAAs for all layer groups and draw three key conclusions: (1) Only 17 layer groups can realize intrinsic A-type altermagnetism. All 2D A-type altermagnets must belong to these 17 layer groups, which will be helpful to search for 2D A-type altermagnet. (2) It is impossible to connect the two sublattices of BSAA using $S_{3z}$ or $S_{6z}$, a constraint that is also applicable to all 2D altermagnets. (3) $C_{2\alpha}$ is a general stacking operation to generate BSAA for an arbitrary monolayer. Our theory not only can explain the previously reported twisted-bilayer altermagnets, but also can provide more possibilities to generate A-type altermagnets. Our research has significantly broadened the range of candidate materials for 2D altermagnets. Based on conclusion (1), the bilayer NiZrCl$_6$ is predicted to exhibit intrinsic A-type altermagnetism. Additionally, we use twisted-bilayer NiCl$_2$, previously reported in the literature, as the second example of BSAA. Furthermore, utilizing symmetry analysis and first-principles calculation, we scrutinize their spin-momentum locking characteristic to substantiate their altermagnetic properties.