The heterostructures composed of an ultrathin ferromagnetic metal (FM) and a material hosting strong spin-orbit (SO) coupling are the principal resource for SO torque and spin-to-charge conversion nonequilibrium effects in spintronics. The key quantity in theoretical description of these effects is {}, which can appear on any monolayer of the heterostructure through which the current is flowing while the monolayer bands are affected by the native or proximity induced SO coupling. Here we demonstrate how hybridization of wavefunctions of Co layer and a monolayer of transition metal dichalcogenides (TMDs)—such as semiconducting MoSe${}_2$ and WSe${}_2$ or metallic TaSe${}_2$—can lead to {} of electronic and spin structure of Co within some distance away from its interface with TMD, when compared to the bulk of Co or its surface in contact with a vacuum. This is due to proximity induced SO splitting of Co bands encoded in the spectral functions and spin textures on its monolayers, which we obtain using noncollinear density functional theory (ncDFT) combined with equilibrium Green function (GF) calculations. In fact, SO splitting is present due to structural inversion asymmetry of the bilayer—i.e., just the presence of the interface—even if SO coupling within TMD monolayer is artificially switched off in ncDFT calculations, but switching it on makes the effects associated with proximity SO coupling within Co layer about five times larger. Injecting spin-unpolarized charge current through SO-proximitized monolayers of Co generates nonequilibrium spin density over them, so that its cross product with the magnetization of Co determines SO torque. The SO torque computed via first-principles quantum transport methodology, which combines ncDFT with nonequilibrium GF calculations, can be used as the screening parameter to identify optimal combination of materials and their interfaces for applications in spintronics. In particular, we identify heterostructure two-monolayer-Co/monolayer-WSe${}_2$ as {} one, at least in the clean limit.

中文翻译：

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单层过渡金属二硫化锡自旋轨道近似的铁磁金属：Co / MoSe2，Co / WSe2和Co / TaSe2异质结构中的光谱函数，自旋织构和自旋轨道转矩图集

由超薄铁磁金属（FM）和具有强自旋轨道（SO）耦合的材料组成的异质结构是自旋电子学中SO转矩和自旋至电荷转换非平衡效应的主要资源。这些作用的理论描述中的关键量是{}，它可以出现在电流流过的异质结构的任何单层上，而单层带受本征或邻近感应的SO耦合的影响。在这里，我们演示了Co层和过渡金属二卤化物（TMDs）（例如半导体MoSe）单层的波函数如何杂交${}_2$ 和WSe${}_2$ 或金属TaSe${}_2$与大量的Co或与真空接触的表面相比，－可能导致{}的Co的电子和自旋结构{}。这是由于在光谱函数中编码的Co波段的邻近感应SO分裂以及单层的自旋纹理，这是我们使用非共线密度函数理论（ncDFT）与平衡格林函数（GF）计算结合得出的。实际上，由于双层的结构反型不对称（即仅存在界面），所以存在SO分裂，即使在ncDFT计算中人为关闭了TMD单层内的SO耦合，但将其打开也会导致与邻近度相关的影响Co层内的SO耦合大约大五倍。通过SO刺激的Co单层注入自旋非极化电荷电流会在其上产生非平衡自旋密度，因此其与Co磁化的叉积决定了SO转矩。通过第一原理量子传输方法计算的SO扭矩，将ncDFT与非平衡GF计算相结合，可以用作筛选参数，以确定在自旋电子学中应用的材料及其界面的最佳组合。特别是，我们确定了异质结构两层单层Co /单层WSe 可以用作筛选参数，以确定在自旋电子学中应用的材料及其界面的最佳组合。特别是，我们确定了异质结构两层单层Co /单层WSe 可以用作筛选参数，以确定在自旋电子学中应用的材料及其界面的最佳组合。特别是，我们确定了异质结构两层单层Co /单层WSe${}_2$ 作为{}之一，至少在无限制的范围内。