Bilayer altermagnets featuring layer-mediated spin-valley locking hold significant promise in spintronics and valleytronics. In this study, we perform a comprehensive symmetry analysis of bilayer altermagnets and identify seven spin point group candidates with spin-valley-layer coupling, including ²2, ²2²2¹2, ²4̅, ¹4²2²2, ²4̅²2¹m, ¹3²2, and ¹6²2²2. Focusing on the platform of bilayer metal–organic frameworks, we theoretically design materials with S₄ symmetry through chemical modification, achieving spin-splitting in the valence band. Furthermore, the spin valleys from different layers exhibit tunable responses to external static gate electric fields, enabling precise control of spin-splitting. Our findings presented a framework that integrates spin, valley, and layer degrees of freedom in bilayer altermagnets, paving the way for nanoscale spintronics and valleytronics applications.

中文翻译：

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双层金属-有机框架互磁体，具有电可调自旋分裂谷


具有层介导的自旋谷锁定的双层替代磁体在自旋电子学和谷电子学中具有重要前景。在这项研究中，我们对双层交替磁体进行了全面的对称分析，并确定了七个具有自旋谷耦合的自旋点组候选者，包括 ²2、²2^{22 1}2、²4̅、¹4^{22 2}2、²4̅²2 1 m、¹3²2 2 和 ¹6²2^{2 2}2. 以双层金属-有机框架为平台，通过化学修饰理论设计具有 S₄ 对称性的材料，实现价带的自旋分裂。此外，来自不同层的自旋谷对外部静态栅极电场表现出可调响应，从而能够精确控制自旋分裂。我们的研究结果提出了一个框架，该框架将自旋、谷和层自由度集成到双层替代磁体中，为纳米级自旋电子学和谷电子学应用铺平了道路。