Characterizing breathing dynamics of magnetic skyrmions and antiskyrmions within the Hamiltonian formalism

Abstract

We derive an effective Hamiltonian system describing the low energy dynamics of circular magnetic skyrmions and antiskyrmions. Using scaling and symmetry arguments we model (anti-)skyrmion dynamics through a finite set of coupled, canonically conjugated, collective coordinates. The resulting theoretical description is independent of both micromagnetic details as well as any specificity in the ansatz of the skyrmion profile. Based on the Hamiltonian structure we derive a general description for breathing dynamics of (anti-)skyrmions in the limit of radius much larger than the domain wall width. The effective energy landscape reveals two qualitatively different types of breathing behavior. For small energy perturbations we reproduce the well-known small breathing mode excitations, where the magnetic moments of the skyrmion oscillate around their equilibrium solution. At higher energies we find a breathing behavior where the in-plane angle of the skyrmion continuously precesses, transforming Néel to Bloch skyrmions and vice versa. For a damped system we observe the transition from the continuously rotating and breathing skyrmion into the oscillatory one. We analyze the characteristic frequencies of both breathing types, as well as their amplitudes and distinct energy dissipation rates. For rotational (oscillatory) breathing modes we predict on average a linear (exponential) decay in energy. We argue that this stark difference in dissipative behavior should be observable in the frequency spectrum of excited (anti-)skyrmions.

Oscillations of skyrmion clusters in Co/Pt multilayer nanodots

“…In the same direction, in recent years, different research groups have faced several problems related to the oscillations of skyrmions, such as the breathing modes of individual skyrmions 8 under the action of an alternating external magnetic field 9 , as well as oscillations and rotation of arrays of skyrmions (called clusters) under in-plane external magnetic fields 10 . In all these works the nature of the stimulation, the coupling of the magnons 11 with the breathing modes of the skyrmions 12 , and the geometry and nature of the skyrmions themselves seem to be relevant.…”

Statistical Properties and Configurational Entropy of a Two-Dimensional Néel Magnetic Skyrmions Population

“…The passage from the 3D to the 2D description does not avoid the unphysical divergent result as T→0 K. This confirms that this result does not depend on the dimensionality but on the fact that the configurational entropy was computed according to a classical approach showing the same limits of the Sackur-Tetrode entropy equation for the ideal gas and that, as T→0 K, a quantum approach would be necessary to remove the divergent behavior. Numerically, analogously to the 3D model, the calculations performed according to Equations (6), (9) and (15) for the average diameter, the standard deviation and the configurational entropy, respectively, within the 2D model are well reproduced by the corresponding low-temperature expansions to the first-order of Equations (17)- (19), respectively for 1 K ≤ T ≤ 50 K. The curve of < D 2D sky (T) > T→ 0 K is almost superimposed to that of < D 3D sky (T)…”

“…Recently, several efforts were done to study static properties, such as skyrmion stability in low-dimensional magnetic systems [7], and dynamic properties (see e.g., [8,9]). However, until recently, not much attention has been paid to the investigation of statistical and statistical thermodynamic properties of magnetic skyrmions.…”

Statistical Thermodynamics of Chiral Skyrmions in a Ferromagnetic Material

“…The tilting of edge moments in nanostructures hosting skyrmions [25], the evolution of single chiral skyrmions under an applied magnetic field [26], the current induced motion of different types of chiral skyrmions [27,28,29,30], the current-induced rotational torques in skyrmion lattices [31], and the current-dependent skyrmion Hall angle [32] were also studied. In addition, the breathing dynamics [33] and the skyrmion state stability [34,35] were also investigated.…”