Magnon Superlattices around Skyrmions in Frustrated Magnets

TL;DR

The paper investigates magnon dynamics in frustrated magnets with atomic-scale skyrmions, showing that when magnon wavelength $l_{ ext{min}}$ is comparable to skyrmion size $\lambda$, strong magnon–skyrmion hybridization arises in centrosymmetric lattices. A 2D triangular-lattice model with competing exchanges $J_1$, $J_2$, single-ion anisotropy $K$, and field $h$ is analyzed via linear spin-wave theory and Landau-Lifshitz-Gilbert simulations, revealing crystal-like magnon localization patterns (magnon superlattices) formed by interference among six degenerate states at $|k_{ ext{min}}|$ on a Mexican-hat dispersion $(\omega_{\mathbf{k}})$; these patterns persist far from the skyrmion core. Helicity acts as an internal dynamical degree of freedom, enabling nonlinear phenomena such as helicity precession and second-order activation of breathing modes, while skyrmion lattices host dispersive magnon bands with nonzero Chern numbers $\mathcal{C}$ within the first magnon gap, whose sign follows the skyrmion charge. The work highlights frustrated magnets as a versatile platform for engineering topological spin excitations and suggests experimental pathways using nm-scale skyrmions and high-resolution probes.

Abstract

Dynamic and stable magnetic textures offer a powerful platform for controlling magnon states in the broader context of spin electronics. In this work, we uncover a novel class of dynamical, crystal-like localization patterns in real space, arising from the hybridization of magnons with topologically non-trivial spin textures that possess helicity as an internal degree of freedom. By tuning the magnon wavelength to match the size of these textures, specifically, atomic-scale skyrmions in centrosymmetric frustrated magnets, we achieve strong interference effects. This leads to the emergence of magnon superlattices, shaped by the internal skyrmion structure and the underlying Mexican-hat magnon dispersion. Furthermore, helicity-driven nonlinear dynamics give rise to dispersive magnon bands with nontrivial Chern numbers within the first magnon gap. These findings provide fundamental insights into magnon behavior in complex spin environments and establish frustrated magnets as a versatile platform for manipulating spin excitations at the atomic scale.

Figures (10)

• Figure 1: Finite-wavelength magnon excitations matching skyrmion size. (a) Isolated skyrmion of a frustrated magnet in a triangular lattice with $J_1 = 1$, $J_2 = 0.5$, $h = 0.225/S$, and $K = 0.15$. (b) Skyrmion profile calculated along a line passing through the skyrmion center as $\theta(r_i) = \arccos{S^z_i}$ for isolated skyrmions in frustrated (red line) and chiral magnets (black line), which illustrates the skyrmion tails, unique to frustrated magnets. (c) Low energy dispersion of magnon excitations around the uniformly magnetized state of a frustrated (red line) and chiral magnet (black line) along the $\Gamma$-M-K direction. The Mexican hat-like shape in frustrated magnets introduces complexity to the magnon dynamics around skyrmions. (d) Magnetic dipole moment $|\mathcal{M}|$ of the magnon modes around a single skyrmion.
• Figure 2: Observable magnon superlattices. Crystal-like localization patterns of magnon modes in the presence of a skyrmion. (a)-(d) Real-space deformation $\Delta S_z$ and $\Delta S_x$, probability density $\vert \Psi \vert$, and real-time dynamics $\mathcal{D} S_x(t)$ for the low-lying $\hbox{CCW1}$ hybridized with interference patterns of finite-wavelength extended states. (e)-(h) Same quantities for the $\hbox{CCW2}$ mode, exhibiting magnon crystals with shorter periodicity. (i)-(k) The symmetric localization patterns of the high in energy $\hbox{CCW3}$ mode with the largest $\mathcal{M}_x$. (m)-(p) The lowest lying breathing mode has a vanishing $\mathcal{M}_z$, but is dynamically activated due to a second-order effect. Here we use the parameters of Fig. \ref{['Isolated_Skyrmion']}.
• Figure 3: Helicity induced nonlinear dynamics. (a)-(d) Isolated skyrmion breathing mode from \ref{['Localization']} (m)-(p) involving coupled oscillation of skyrmion $z-$magnetization and helicity, $\varphi_0$, found at $\omega=0.028$. The average magnon number per lattice site is $\bar{n}/N^2 = 2^7/42^2 \approx 0.073$. Snapshots are taken at equally spaced time-steps and cover one full oscillation period. (e) Nonlinear dependence of helicity oscillations over one period on the magnon number $\bar{n}$. (f)-(i) Snapshots of the same breathing mode activated by an out-of-plane magnetic field $h_{\hbox{\scriptsize AC}} = 0.1$ due to second-order coupling. (j) Nonlinear dependence of helicity oscillations over one period on the drive amplitude.
• Figure 4: Magnon bands around skyrmion lattice.(a) Skyrmion lattice ground state at parameters: $J_1=1$, $J_2=0.5$, $h = 0.15/S$, $K=0.15$. (b)-(e) Snapshots of excited skyrmions calculated with $\bar{n}_{\mu, \mathbf{k}} = 3$ magnons per unit cell. The symmetry of multipolar modes is dependent on magnon momentum (b, c). A new band corresponding to helicity excitations emerges, and hybridizes with multipolar channels at large $\mathbf{k}$ (d, e). (f) Magnon band structure of the skyrmion lattice. Band gaps are highlighted in gold, with edges corresponding to frequencies of topologically-protected edge states (see Figure 5). Due to complex skyrmion-skyrmion interactions, multipolar bands are also dispersive in frustrated magnets.
• Figure 5: Topological magnon bands. Magnetic dipole moment $\boldsymbol{\mathcal{M}}_\mu$ and topological Chern numbers $\mathcal{C}$ of the lowest magnon bands shown in Fig. \ref{['Lattice_Bands']}. For antiskyrmion lattices, the sign of $\mathcal{C}$ flips, illustrating the dependence of edge state chirality on bulk topology. The neighboring elliptical and CCW bands touch, and have a total Chern number of $2$. Some topological edge states are observable via in-plane AC magnetic field excitation due to their finite magnetic dipole moment.