Controllable and nondissipative inertial dynamics of skyrmions in a bosonic platform

It has been understood in the past decade or two that the dynamics of spin or magnetization in an ultrafast regime necessarily involves an inertial term that reflects the reluctance to follow abrupt or sudden changes in the spin or magnetization orientation. The role of inertial spin dynamics in governing the motion of the skyrmion, a topological spin texture, is elucidated. Using the nonequilibrium Green's function Keldysh formalism, an equation of motion is derived in terms of collective coordinates for a skyrmion coupled via a ``minimal coupling'' to a bath of harmonic oscillators of frequency $\ensuremath{\omega}$, modeling an optical phonon-like bosonic bath with its nearly flat energy spectrum, and a coupling to the phonon energy density that dominates under the resonance condition at the optical phonon frequency. A deterministic and nondissipative dynamics equation of motion is obtained with an explicit mass term for the skyrmion emerging due to the coupling, even within the rigid skyrmion picture. This results in a cyclotronic motion of the skyrmion, with a frequency that can go ultrafast, depending on that of the oscillator. Controlling the oscillator frequency can therefore guide the skyrmion dynamics. Our theory bridges inertial dynamics and topology in magnetism and opens a pathway to ultrafast control of topological spin textures.