Topology-Dependent Brownian Gyromotion of a Single Skyrmion

Abstract

Non-interacting particles exhibiting Brownian motion have been observed in many occasions of sciences, including spin textures in magnetic materials. Skyrmions are particle-like topological spin textures stabilized by the Dzyaloshinskii-Moriya interaction (DMI), with their topological properties being governed by the skyrmion number Q, which can also be thermally activated and behave like Brownian particles. In the present report, the Brownian dynamics of skyrmion is firstly discussed through performing micromagnetic simulation based on stochastic Landau-Lifshitz-Gilbert equation. More interestingly, a topology-dependent gyromotion from being clockwise (Q = +1) to counterclockwise (Q = -1) can be identified, as shown in Figs. 1(a) and 1(b), respectively. We subsequently utilized a polar magneto-optic Kerr effect (MOKE) microscopy to experimentally examine the Brownian motion of a single isolated skyrmion in the Ta/CoFeB/TaOx multilayer. The diffusion coefficient of skyrmion is found to exhibit an exponential dependence on temperature, instead of simple linear temperature dependence as Einstein predicted, as shown in Fig.1(c). Further, a topology-dependent Brownian gyromotion is confirmed by revealing the clockwise and counterclockwise rotations for Q = +1 and Q = -1 skyrmions, as shown in Figs. 2(a) and 2(b), respectively. Average rotation angle 〈θsr〉 is systematically calculated and shown in Fig.2(c), in which a clear difference in the whole temperature range can be seen. The experimental results are consistent with the analytical calculations from the stochastic Thiele equation, suggesting the Brownian gyromotion of a single skyrmion is captured.