Controllable and Non-Dissipative Inertial Dynamics of Skyrmion in a Bosonic Platform

TL;DR

This work demonstrates that a Skyrmion immersed in a bosonic bath of harmonic oscillators acquires a deterministic inertial mass through a quadratic (minimal) spin-phonon coupling, realized within a Keldysh framework. The effective action reveals a non-dissipative, velocity-squared term, yielding a Skyrmion mass \\(m_{Sk} = A \\frac{\\hbar \\omega \\tau^2}{8\\pi} \\Lambda^4\\) and a gyrotropic force that drives cyclotron-like motion with frequency \\Omega = \\frac{8\\pi N_{Sk}\\rho_s}{m_{Sk}} = \\frac{64\\pi^2 N_{Sk}\\rho_s}{A\\Lambda^4 \\hbar \\omega \\tau^2}". The oscillator (phonon) frequency thus controls ultrafast Skyrmion dynamics, enabling tunable high-frequency motion without dissipation, and the results bridge inertial spin dynamics with topology. The analysis further connects to inertial Landau-Lifshitz-Gilbert behavior at the spin level, contrasts with magnetoelastic couplings that add dissipation and confinement, and outlines pathways to realize coherent control via coherent phonons. Extending to full phonon models, including both optical and acoustic branches, suggests versatile routes to engineer Skyrmion dynamics in inversion-symmetric magnets, with NiGa_2S_4 as a promising platform.

Abstract

It has been understood in the past a decade or two that the dynamics of spin or magnetization in ultrafast regime necessarily involves inertial term that reflects the reluctance to follow abrupt or sudden change in the spin or magnetization orientation. The role of inertial spin dynamics in governing the motion of Skyrmion, a topological spin texture, is elucidated. Using 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 $ω$, modeling an optical phonon-like bosonic bath with its nearly-flat energy spectrum, and a coupling to the phonon energy density that dominates under resonance condition at the optical phonon frequency. A deterministic and non-dissipative dynamics equation of motion is obtained with an explicit mass term for the Skyrmion emerging due to the coupling, even within rigid Skyrmion picture. This results in a cyclotronic motion of 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.

Figures (3)

• Figure 1: Illustrative profile of a Skyrmion on a two-dimensional (2D) lattice (arylide yellow plane). The spins sit on a lattice whose vibration is modeled by harmonic oscillators whose displacement field is coupled to the Skyrmion. The axes are labeled in dimensionless coordinates; $x=\tilde{x}/(2a),y=\tilde{y}/(2a)$ where $\tilde{x},\tilde{y}$ are dimensioned coordinates while $a$ is the lattice spacing. The inset schematically illustrates the coupling between the spin and the lattice harmonic oscillator, modeled as a bob carrying spin (arrow) connected to the spring attached to the lattice site.
• Figure 2: (a)The dependence of the Skyrmion cyclotron frequency $\Omega$(Hz) on the oscillator frequency $\omega$(Hz) and spin dynamics characteristic time $\tau$(s). Pertinent parameters are given in the text; the paragraph before Eq.(\ref{['NetStaticForce']}). The log is in base 10 and reference quantities are $\Omega_0=\omega_0=1$Hz, $\tau_0=1$s.(b)The dependence of the perturbation parameter $\xi=\omega\tau$ and its validity regime $\omega\tau\leq 1$(or $\mathrm{log}(\omega\tau)\leq 0$). The resulting frequency $\Omega$ clearly enters ultrafast regime (beyond GHz (log$(\Omega/\Omega_0)\geq 9$)) for small $\omega\tau$.
• Figure 3: Typical profile of optical phonon spectrum (upper) and acoustic phonon spectrum (lower).