Motivated by recent observations of unconventional out-of-plane dampinglike torque in ${\mathrm{WTe}}_2$/Permalloy bilayer systems, we calculate the spin-orbit torque generated in two-dimensional transition metal dichalcogenide (TMD)–ferromagnet heterostructures using first-principles methods and linear response theory. Our numerical calculation of spin-orbit torques in ${\mathrm{WTe}}_2/\mathrm{Co}$ and ${\mathrm{MoTe}}_2/\mathrm{Co}$ heterostructures shows both conventional and novel dampinglike torkances (torque per electric field) with comparable magnitude, around $100\hslash /2e{\left(\mathrm{\Omega }\mathrm{cm}\right)}^{-1}$, for an electric field applied perpendicular to the mirror plane of the TMD layer. To gain further insight into the source of dampinglike torque, we compute the spin current flux between the TMD and Co layers and find good agreement between the two quantities. This indicates that the conventional picture of dampinglike spin-orbit torque, whereby the torque results from the spin Hall effect plus spin transfer torque, largely applies to TMD/Co bilayer systems.

中文翻译：

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第一性原理计算的过渡金属二硫化物-铁磁体双层中的非常规自旋轨道扭矩

受到最近对非常规平面外阻尼类扭矩的观察的启发${\mathrm{钨碲}}_2$/坡莫合金双层系统，我们使用第一原理方法和线性响应理论计算二维过渡金属二硫属化物（TMD）-铁磁体异质结构中产生的自旋轨道扭矩。我们对自旋轨道扭矩的数值计算${\mathrm{钨碲}}_2/钴$和${\mathrm{钼碲}}_2/钴$异质结构显示出传统的和新型的阻尼类扭矩（每个电场的扭矩），其大小相当，大约$100\hslash /2e{（\mathrm{\Omega }\mathrm{厘米}）}^{-1}$，垂直于 TMD 层镜面施加的电场。为了进一步了解类阻尼扭矩的来源，我们计算了 TMD 和 Co 层之间的自旋电流通量，并发现这两个量之间具有良好的一致性。这表明阻尼类自旋轨道扭矩的传统图像，即由自旋霍尔效应加上自旋转移扭矩产生的扭矩，很大程度上适用于TMD/Co双层系统。