  Based on micromagnetic simulation and analysis of Thiele's equation, in this
work we demonstrate that ratchet motion of skyrmion can be induced by a
biharmonic in-plane magnetic field hx(t) = h1sin(mwt) + h2sin(nwt + 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 degree. 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 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 of those found in
many soliton systems, and the facile controllability of both the skyrmion speed
and direction should be useful in practice.
