Skyrmion Jellyfish in Driven Chiral Magnets

Chiral magnets can host topological particles known as skyrmions, which carry an exactly quantised topological charge $Q=-1$. In the presence of an oscillating magnetic field ${\mathbf{B}}_1(t)$, a single skyrmion embedded in a ferromagnetic background will start to move with constant velocity ${\mathbf{v}}_{\text{trans}}$. The mechanism behind this motion is similar to the one used by a jellyfish when it swims through water. We show that the skyrmion’s motion is a universal phenomenon, arising in any magnetic system with translational modes. By projecting the equation of motion onto the skyrmion’s translational modes and going to quadratic order in ${\mathbf{B}}_1(t)$, we obtain an analytical expression for ${\mathbf{v}}_{\text{trans}}$ as a function of the system’s linear response. The linear response and consequently ${\mathbf{v}}_{\text{trans}}$ are influenced by the skyrmion’s internal modes and scattering states, as well as by the ferromagnetic background’s Kittel mode. The direction and speed of ${\mathbf{v}}_{\text{trans}}$ can be controlled by changing the polarisation, frequency and phase of the driving field ${\mathbf{B}}_1(t)$. For systems with small Gilbert damping parameter $\alpha$, we identify two distinct physical mechanisms used by the skyrmion to move. At low driving frequencies, the skyrmion’s motion is driven by friction, and $v_{\text{trans}}\sim \alpha$, whereas at higher frequencies above the ferromagnetic gap, the skyrmion moves by magnon emission, and $v_{\text{trans}}$ becomes independent of $\alpha$.