In this paper, we propose a concept of bilayer stacking 𝐴-type altermagnet (BSAA), in which two identical ferromagnetic monolayers are stacked with antiferromagnetic coupling to form a two-dimensional (2D) 𝐴-type altermagnet. By solving the stacking model, we derive all BSAAs for all layer groups and draw three key conclusions: (i) 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. (ii) It is impossible to connect the two sublattices of BSAA using 𝑆3⁢𝑧 or 𝑆6⁢𝑧, a constraint that is also applicable to all 2D altermagnets. (iii) 𝐶2⁢𝛼 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 (i), the bilayer NiZrCl6 is predicted to exhibit intrinsic 𝐴-type altermagnetism. Additionally, we use twisted-bilayer NiCl2 and CrOCl as supplementary examples of BSAA. Furthermore, utilizing symmetry analysis and first-principles calculation, we scrutinize their spin-momentum locking characteristic to substantiate their altermagnetic properties.

中文翻译：

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双层堆叠A 型互磁体：产生二维互磁体的一般方法


在本文中，我们提出了一个双层堆叠 A 型互电体 （BSAA） 的概念，其中两个相同的铁磁单层通过反铁磁耦合堆叠以形成二维 （2D） A 型互电体。通过求解堆叠模型，我们推导出了所有层组的所有 BSAA，并得出了三个关键结论：（i） 只有 17 个层组可以实现本征 A 型交替磁性。所有 2D A 型互交磁体都必须属于这 17 个层组，这将有助于搜索 2D A 型互交磁体。（ii） 不可能使用 S3z 或 S6z 连接 BSAA 的两个子晶格，这个约束也适用于所有二维交替磁体。（iii） C2α 是一种通用的堆叠操作，用于为任意单层生成 BSAA。我们的理论不仅可以解释以前报道的扭曲双层交替磁体，而且可以为产生 A 型交替磁体提供更多的可能性。我们的研究大大拓宽了 2D 交替磁体的候选材料范围。根据结论 （i），预测双层 NiZrCl6 表现出本征的 A 型交替磁性。此外，我们使用扭曲双层 NiCl2 和 CrOCl 作为 BSAA 的补充示例。此外，利用对称分析和第一性原理计算，我们仔细检查了它们的自旋动量锁定特性，以证实它们的交替磁性。