Skyrmion ratchet effect driven by a biharmonic force

Based on micromagnetic simulation and analysis of Thiele's equation, in this work we demonstrate that ratchet motion of a skyrmion can be induced by a biharmonic in-plane magnetic field h(x)(t) = h(1) sin(m omega t) + h(2) sin(n omega t + phi), provided that integers m and n are coprime and that m + n is odd. Remarkably, the speed and direction of the ratchet motion can be readily adjusted by the field amplitude, frequency, and phase, with the maximum speed being over 5 m/s and the direction rotatable over 360 degrees. The origin of the skyrmion ratchet motion is analyzed by tracing the excitation spectra of the dissipation parameter D and the skyrmion position R, and it shows that the dissipative force plays a key role in the appearance of ratchet motion. Such a ratchet motion of a skyrmion is distinguished from those caused by single-frequency ac drives reported in the literature, and from that driven by pulsed magnetic fields as also predicted in this work. Our results show that skyrmion ratchet effect under biharmonic forces shares some common features with those found in many soliton systems, and the facile controllability of both the skyrmion speed and direction should be useful in practice.