纵横向交流驱动搓板势上Skyrmion运动的Shapiro步
Shapiro Steps for Skyrmion Motion on a Washboard Potential with Longitudinal and Transverse ac Drives
摘要：
我们用数值方法研究了在准一维正弦基底中，在外加直流和交流驱动的影响下，二维Skyrmions的行为。在过阻尼的限制，当直流和交流驱动器是在平行于基板调制的方向的纵向方向对齐，速度-力曲线表现出经典的夏皮罗阶跃功能时，交流驱动器的频率匹配的搓衣板频率是动态产生的运动的skyrmions在基板上，类似于以前的观察超导涡旋系统。在skyrmions的情况下，从非耗散马格努斯力的skyrmion运动的额外贡献转移的锁定步骤的位置，以更高的直流驱动器，我们发现，skyrmions移动在一个角度相对于直流驱动器的方向。对于一个纵向直流驱动器和一个垂直或横向交流驱动器，过阻尼系统没有夏皮罗步骤，但是，当一个有限的马格努斯力存在，我们发现明显的横向夏皮罗步骤随着复杂的二维周期轨道的skyrmions在相位锁定制度。纵向和横向交流驱动器都产生锁定台阶，其宽度随着交流驱动振幅的增加而振荡。我们研究集体skyrmion相互作用的作用，并发现额外的分数锁定步骤发生纵向和横向交流驱动器。在较高的skyrmion密度，该系统经历了一系列的动力学有序无序转变，与skyrmion形成一个移动的固体上的相位锁定步骤和波动的动态液体之间的步骤。
英文摘要：
We numerically study the behavior of two-dimensional skyrmions in the presence of a quasi-one-dimensional sinusoidal substrate under the influence of externally applied dc and ac drives. In the overdamped limit, when both dc and ac drives are aligned in the longitudinal direction parallel to the direction of the substrate modulation, the velocity-force curves exhibit classic Shapiro step features when the frequency of the ac drive matches the washboard frequency that is dynamically generated by the motion of the skyrmions over the substrate, similar to previous observations in superconducting vortex systems. In the case of skyrmions, the additional contribution to the skyrmion motion from a non-dissipative Magnus force shifts the location of the locking steps to higher dc drives, and we find that the skyrmions move at an angle with respect to the direction of the dc drive. For a longitudinal dc drive and a perpendicular or transverse ac drive, the overdamped system exhibits no Shapiro steps; however, when a finite Magnus force is present we find pronounced transverse Shapiro steps along with complex two-dimensional periodic orbits of the skyrmions in the phase-locked regimes. Both the longitudinal and transverse ac drives produce locking steps whose widths oscillate with increasing ac drive amplitude. We examine the role of collective skyrmion interactions and find that additional fractional locking steps occur for both longitudinal and transverse ac drives. At higher skyrmion densities, the system undergoes a series of dynamical order-disorder transitions, with the skyrmions forming a moving solid on the phase locking steps and a fluctuating dynamical liquid in regimes between the steps.
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