The control of the spin degree of freedom is at the heart of spintronics, which can potentially be achieved by spin-orbit coupling or band topological effects. In this paper, we explore another potential controlled mechanism under debate: the spin-deformation coupling (SDC)—the coupling between intrinsic or extrinsic geometrical deformations and the spin degree of freedom. We focus on polar-deformed thin films or two-dimensional compounds, where the Rashba spin-orbit coupling (SOC) is considered as an SU⁡(2) non-Abelian gauge field. We demonstrate that the dynamics between surface and normal electronic degrees of freedom can be properly decoupled using the thin-layer approach by performing a suitable gauge transformation, as introduced in the context of many-body correlated systems. Our work leads to three significant results: (i) gauge invariance implies that the spin is uncoupled from the surface's extrinsic geometry, challenging the common consensus; (ii) the Rashba SOC on a curved surface can be included as an SU⁡(2) non-Abelian gauge field in curvilinear coordinates; and (iii) we identify a previously unnoticed scalar geometrical potential dependent on the Rashba SOC strength. This scalar potential, independent of spin, represents the residual effect remaining after decoupling the normal component of the non-Abelian gauge field. The outcomes of our paper open alternative pathways for exploring the manipulation of spin degrees of freedom through the use of the SDC.

中文翻译：

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二维极性材料中的自旋-变形耦合


自旋自由度的控制是自旋电子学的核心，这可以通过自旋轨道耦合或能带拓扑效应来实现。在本文中，我们探讨了另一种正在争论的潜在受控机制：自旋-变形耦合 （SDC） — 内禀或外禀几何变形与自旋自由度之间的耦合。我们专注于极化变形薄膜或二维化合物，其中 Rashba 自旋轨道耦合 （SOC） 被认为是 SU（2） 非阿贝尔规范场。我们证明，表面和法向电子自由度之间的动力学可以通过执行适当的规范变换，使用薄层方法适当地解耦，就像在多体相关系统的背景下引入的那样。我们的工作导致了三个重要的结果：（i） 规范不变性意味着自旋与表面的外在几何解耦，挑战了普遍共识;（ii） 曲面上的 Rashba SOC 可以作为曲线坐标中的 SU（2） 非阿贝尔规范场包含在内;（iii） 我们确定了一个以前未被注意到的标量几何势，具体取决于 Rashba SOC 强度。这个标量势与自旋无关，表示与非阿贝尔规范场的法向分量解耦后剩余的残余效应。我们论文的结果为通过使用 SDC 探索自旋自由度的操纵开辟了替代途径。