Magnus-induced ratchet effects for skyrmions interacting with asymmetric substrates

Abstract

We show using numerical simulations that pronounced ratchet effects can occur for ac driven skyrmions moving over asymmetric quasi-one-dimensional substrates. We find a new type of ratchet effect called a Magnus-induced transverse ratchet that arises when the ac driving force is applied perpendicular rather than parallel to the asymmetry direction of the substrate. This transverse ratchet effect only occurs when the Magnus term is finite, and the threshold ac amplitude needed to induce it decreases as the Magnus term becomes more prominent. Ratcheting skyrmions follow ordered orbits in which the net displacement parallel to the substrate asymmetry direction is quantized. Skyrmion ratchets represent a new ac current-based method for controlling skyrmion positions and motion for spintronic applications.

Reversible vector ratchets for skyrmion systems

“…In previous numerical work, it was shown that an individual skyrmion in a 2D system interacting with a quasi-1D asymmetric substrate exhibits a rocking ratchet effect when the ac drive is applied along the substrate asymmetry direction 40 . In this case, the resulting dc skyrmion velocity has components both parallel and perpendicular to the substrate asymmetry direction due to the Magnus term.…”

“…In this case, the resulting dc skyrmion velocity has components both parallel and perpendicular to the substrate asymmetry direction due to the Magnus term. A new type of ratchet effect, called a Magnus ratchet, was shown to occur when the ac drive is applied perpendicular to the substrate asymmetry direction 40 . Here, the Magnus term induces skyrmion velocity components both parallel and perpendicular to the ac drive.…”

Skyrmion ratchet effect driven by a biharmonic force

“…This is due to the fact that, for a driving force with a specific frequency, e.g., m, if one assumes that the an excited mode of D is at frequency, e.g., q, then a series of frequencies of the skyrmion coordinate R will be excited, including m, |m+q|, |m-q|, |m+2q|, |m-2q|, …. The In Table I, We emphasize that the ratchet effect revealed in this work should be distinguished in both the source application and the dynamics behind from those driven by oscillating driving forces as reported in previous works [33][34][35][36][37] . The ratchet motion, either driven by a biased oscillating magnetic field 33 or by oscillating drives in combination with substrate asymmetry 35,36 , is intrinsically due to a spatial symmetry-breaking, as introduced by the field or by the substrate.…”

“…The In Table I, We emphasize that the ratchet effect revealed in this work should be distinguished in both the source application and the dynamics behind from those driven by oscillating driving forces as reported in previous works [33][34][35][36][37] . The ratchet motion, either driven by a biased oscillating magnetic field 33 or by oscillating drives in combination with substrate asymmetry 35,36 , is intrinsically due to a spatial symmetry-breaking, as introduced by the field or by the substrate. For the ratchet motion driven by a tilted oscillating magnetic field 34 , while the dissipation force should also play an important role in the net motion, such a net dissipation force relies on the co-excitation of the gyration mode caused by the in-plane field and the breathing mode caused by the out-of-plane field.…”

Topological dynamics and current-induced motion in a skyrmion lattice

“…The relation between skyrmion and superconducting vortices was explored by Reichhardt et al [20] while Lin et al [21] treated the effects of a current pulse in the creation of a skyrmion. Reichhardt et al explored various aspects of skyrmion dynamics: effects of random quenched disorder [22], ac driven skyrmions over asymmetric quasi-one-dimensional substrates [23] and two-dimensional periodic substrates [24]. The effects of a small hole in a magnetic layer were explained by Muller and Rosch [25].…”