Anisotropic skyrmion liquid phase

Abstract

The nature of the melting transition in two-dimensional systems of particles has attracted considerable research attention since the development of Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory. The hexatic phase proposed by this theory has been recently identified experimentally in ensembles of magnetic skyrmions, quasiparticles formed in a magnetically ordered crystal. Here, we use quasiparticle dynamical simulations to study how the anisotropy of the skyrmion-skyrmion interactions induced by the atomic lattice influences the melting transition. For isotropic interactions, we find a transition from a solid phase through a hexatic phase stable in a narrow temperature range to an isotropic liquid phase. However, if the interactions between skyrmions are forced to be anisotropic by the atomic lattice, then a direct solid-liquid transition can be observed with orientational order persisting up to temperatures of 30 K in the liquid phase.

Figures (8)

• Figure 1: Interaction potential between two skyrmions in the (Pt$_{0.95}$Ir$_{0.05}$)/Fe/Pd(111) system at $B= 1 \ \mathrm{T}$ along the $[2\overline{1}\overline{1}]$ and $[1\overline{1}0]$ directions. Dots denote simulation data points, whereas lines indicate fits according to Eq. \ref{['eq:PotentialFit']}.
• Figure 2: Interaction potentials between two skyrmions in the (Pt$_{0.95}$Ir$_{0.05}$)/Fe/Pd(111) system at $B= 1 \ \mathrm{T}$. (a) Anisotropic interaction potential obtained by interpolating between the fits along the high-symmetry directions in Fig. \ref{['fig:Potential_Fit']} using the function in Eq. \ref{['eq:interpolation']}. (b) Isotropic potential obtained from the fit along the $[2\overline{1}\overline{1}]$ direction in Fig. \ref{['fig:Potential_Fit']}. Arrows indicate the forces in the potential landscape.
• Figure 3: Examples of simulations of skyrmion ensembles. (a),(c),(e) System with isotropic interactions. (b),(d),(f) System with anisotropic interactions. The simulation temperatures are indicated in each panel. Skyrmions with five and seven neighbors forming lattice defects are colored orange and yellow, respectively. Skyrmions with six neighbors, where the orientational order parameter $|\Psi_{6}(\bm{r}_{i})|$ is close to unity, are colored according to the local lattice orientation $\arg\Psi_{6}(\bm{r}_{i})$ as shown in the colorbar.
• Figure 4: Average number of topologically non-trivial defects as a function of temperature. Solid lines show results for a system with isotropic interactions, dashed lines for a system with anisotropic interactions.
• Figure 5: Structure factor $S(\bm{q})$ calculated via Eq. \ref{['eq:structure_factor']}. (a),(c),(e) System with isotropic interactions. (b),(d),(f) System with anisotropic interactions. Simulation temperatures are indicated in each panel.