Spin-orbit torque (SOT) created by a spin current injected into a ferromagnet by an adjacent heavy metal or topological insulator represents an efficient tool for the excitation and manipulation of spin waves. Here we report the micromagnetic simulations describing the influence of SOT on the propagation of spin waves in the $\mathrm{W}/\mathrm{CoFeB}/\mathrm{MgO}$ nanostructure having voltage-controlled magnetic anisotropy (VCMA). The simulations show that two spin waves traveling in the opposite directions can be generated in the center of the $\mathrm{CoFeB}$ waveguide via the modulation of VCMA induced by a microwave voltage locally applied to the $\mathrm{MgO}$ nanolayer. The amplitudes of these waves exponentially decrease with the propagation distance with similar decay lengths of about $2.5\mu \mathrm{m}$. In the presence of a direct electric current injected into the $\mathrm{W}$ film beneath the waveguide center, the decay lengths of two spin waves change in the opposite way owing to different directions of the electric currents flowing in the underlying halves of the $\mathrm{W}$ layer. Remarkably, above the critical current density $J_{\mathrm{W}}\approx 2\times {10}^{10}\mathrm{A}{\mathrm{m}}^{-2}$, SOT provides the amplification of the spin wave propagating in one half of the waveguide and strongly accelerates the attenuation of the wave traveling in the other half. As a result, a long-distance spin-wave propagation takes place in half of the $\mathrm{CoFeB}$ waveguide only. Furthermore, by reversing the polarity of the dc voltage applied to the heavy-metal layer one can change the propagation region and switch the travel direction of the spin wave in the ferromagnetic waveguide. Thus, the $\mathrm{W}/\mathrm{CoFeB}/\mathrm{MgO}$ nanostructure can be employed as an electrically controlled magnonic device converting the electrical input signal into a spin signal, which can be transmitted to one of two outputs of the device.

中文翻译：

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铁磁波导中自旋波的自旋轨道扭矩控制

由相邻重金属或拓扑绝缘体注入铁磁体的自旋电流产生的自旋轨道扭矩 (SOT) 是激发和操纵自旋波的有效工具。在这里，我们报告了描述 SOT 对自旋波传播的影响的微磁模拟$\mathrm{宽}/\mathrm{钴铁硼}/\mathrm{氧化镁}$具有压控磁各向异性 (VCMA) 的纳米结构。模拟结果表明，两个方向相反的自旋波可以在中心产生$\mathrm{钴铁硼}$ 通过局部施加到波导的微波电压引起的 VCMA 调制 $\mathrm{氧化镁}$纳米层。这些波的振幅随着传播距离的增加呈指数下降，衰减长度类似$2.5\mu \mathrm{米}$. 在注入直流电的情况下$\mathrm{宽}$ 在波导中心下方的薄膜中，由于在下面的一半中流动的电流方向不同，两个自旋波的衰减长度以相反的方式变化 $\mathrm{宽}$层。值得注意的是，高于临界电流密度$J_{\mathrm{宽}}\approx 2\times {10}^{10}\mathrm{一种}{\mathrm{米}}^{-2}$, SOT 提供了在波导的一半中传播的自旋波的放大，并强烈加速了在另一半中传播的波的衰减。结果，长距离自旋波传播发生在一半$\mathrm{钴铁硼}$仅波导。此外，通过反转施加到重金属层的直流电压的极性，可以改变传播区域并切换铁磁波导中自旋波的行进方向。就这样$\mathrm{宽}/\mathrm{钴铁硼}/\mathrm{氧化镁}$ 纳米结构可以用作电控制的磁器件，将电输入信号转换为自旋信号，该信号可以传输到器件的两个输出之一。