We consider a magnetic skyrmion driven by a spin-polarized electrical current that is periodic in time, and is periodic and asymmetric in a direction different from that of the current itself. We study its classical stochastic transport in a finite temperature, by using the Fokker-Planck equation of the probability distribution, derived from the stochastic equation of motion, the Langevin equation. We also perform numerical simulation of the original Landau-Lifshitz-Gilbert equation describing the spins constituting the skrymion. The probabilistic average velocity of the skyrmion is along the direction of the periodicity. When the thermal energy is much lower than the potential energy, and their ratio is also much smaller than that between the time periodicity and the diffusion time, the time and probabilistic average velocity is the ratio between the spatial and temporal periodicities multiplied by topological integer called the Chern number. This result provides a practical way of realizing topological numbers in classical stochastic systems and suggests a convenient way of manipulating skyrmions at finite temperatures.

中文翻译：

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棘轮状自旋极化电流在有限温度下驱动的磁天窗的经典随机传输的拓扑量化

我们考虑由自旋极化电流驱动的磁天文子，该自旋极化电流在时间上是周期性的，并且在不同于电流本身的方向上是周期性且不对称的。通过使用概率分布的Fokker-Planck方程（从运动随机方程Langevin方程派生），我们研究了其在有限温度下的经典随机传输。我们还对原始的Landau-Lifshitz-Gilbert方程进行了数值模拟，描述了组成Skrymion的自旋。天敌的概率平均速度沿周期性的方向。当热能远低于势能，并且它们的比率也远小于时间周期和扩散时间之间的比率时，时间和概率平均速度是空间和时间周期之间的比率乘以称为Chern数的拓扑整数。该结果提供了一种在经典随机系统中实现拓扑数的实用方法，并提出了一种在有限温度下操纵Skyrmion的便捷方法。