Figure 2
From: Topology dependence of skyrmion Seebeck and skyrmion Nernst effect
Skyrmionic spin structures driven by monochromatic magnon currents. (a) Skyrmion Nernst angle \(\theta\) versus absolute value of the wave vector \(\mathbf {k}\) of the monochromatic magnon current and strength of the temperature gradient \(|\mathbf {\nabla } T|\) for skyrmionic spin structures with different topological charges at \(\alpha =0.01\). Open symbols correspond to the simulated values and dotted lines are the predictions from Eq. (3) based on the differential cross sections. Note, that due to the lack of topological protection the chimera skyrmion gets destroyed more easily by a finite temperature as compared to the other skyrmions and it was found to be stable only at the lowest value for the temperature gradient that we simulated. (b) Illustration of magnons scattering at an antiskyrmion. The magnons are emitted from the left with momentum \(\mathbf {p}^\mathrm {in}\) and, after being scattered, leave the system with \(\mathbf {p}^\mathrm {out}\), giving rise to the force \(\mathbf {F}^\mathrm {mag}\) via Eq. (1). For finite Q and small \(\alpha\), Thiele’s Eq. (2) predicts that the velocity \(\mathbf {v}\) is perpendicular to the force. For the antiskyrmion, the direction of the velocity can hence be obtained by a clockwise rotation of \(\mathbf {F}^\mathrm {mag}\). (c) Differential cross sections as a function of spatial coordinates x, y obtained from simulation data for \(\omega ={8.56\times 10^{13}}{\mathrm{s}^{-1}}\) and \(\alpha =0.01\). The color coding has a cutoff value of \(\partial \sigma /\partial \chi ={3.2}{\mathrm{nm}}\) for the sake of visibility, because our method of calculating the differential cross section (see Supplemental Material) yields very large values in the vicinity of the skyrmion core, where it is not applicable anyway. (d) Differential cross sections as a function of the scattering angle \(\chi\) obtained from simulation data for \(\alpha =0.01\). They are obtained by selecting all values of \(\partial \sigma /\partial \chi\) within an annulus of width 10a with an outer diameter of 40a.
