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Newton's second law in spintronics: role of spin-force in spin-orbit torque

机译:牛顿自旋电子学的第二定律:自旋力在自旋轨道中的作用   扭矩

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摘要

We introduced concept of force in describing spin-orbit torque (SOT) inspin-orbit coupling systems. We showed that the damping-like torque is inducedwhen the system is not in steady state, i.e., when the electron spin is stillprecessing ($d{\bf s}/dt\ne 0$) and the electron being accelerated by, e.g., anelectric field. The damping-like SOT can be expressed as ${\bfT}^\mathrm{SO}=({\bf R}\times {\bf F}^{{\mathrm {SO}}})$, which is similar tothe torque-force relation in classical mechanics, where ${\bfF}^{{\mathrm{\mathrm {SO}}}}$ is the spin-force acting on electron, and ${\bfR}\propto \hat{{\bf z}}$ is some effective radius vector. Furthermore, we alsodemonstrated that under the damping SOT, the magnetic energy is transferred toconduction electrons, which dissipates into Joule heating at a rate of $({\bfj}_e\cdot {\bf F}^{\mathrm {SO}})/e$, with $j_e$ being the applied current.Finally, we propose an experimental verification of our findings viameasurement of the anisotropic magnetoresistance effect.
机译:我们在描述自旋轨道转矩(SOT)自旋轨道耦合系统时引入了力的概念。我们表明,当系统不稳定时,即当电子自旋仍然进动($ d {\ bf s} / dt \ ne 0 $)且电子通过例如电场。类似于阻尼的SOT可以表示为$ {\ bfT} ^ \ mathrm {SO} =({{bf R} \ times {\ bf F} ^ {{\ mathrm {SO}}})$$到经典力学中的扭力关系,其中$ {\ bfF} ^ {{\ mathrm {\ mathrm {SO}}}}} $是作用在电子上的自旋力,而$ {\ bfR} \ propto \ hat { {\ bf z}} $是一些有效的半径向量。此外,我们还演示了在阻尼SOT下,磁能被转移到导电电子,该电子以$({{\ bfj} _e \ cdot {\ bf F} ^ {\ mathrm {SO}})的速率消散到焦耳加热中。 / e $,其中$ j_e $为施加电流。最后,我们建议通过各向异性磁阻效应的测量对我们的发现进行实验验证。

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