The Dynamincs Of Magnetic Skyrmions

Skyrmion is a non-trivial topological spin texture in magnetic materials,and has attracted extensive attention in recent years.In addition,it has been theoretically and experimentally demonstrated that skyrmions can be driven by the current with an ultra-low current density,which is at least five orders of magnitude smaller than that typically applied in experiments on the currentdriven domain-wall dynamics.The topological protection,nanoscale structure,low energy cost and low Joule heating of skyrmions are very promising characteristics for future applications in advanced electronic and spintronic devices.As a novel topological excitation,the theoretical and experimental studies are very significant.Due to the complex interactions of skyrmions,it is difficult to study the dynamical behavior of the skyrmions.Especially,there exists the critical slowing down phenomenon near the phase transition,which makes the study of the phase transition of skyrmions more difficult.There are some novel phenomena,such as the driven-dependence skyrmion Hall effect and the anomalous skyrmion Hall effect at low temperature,have also been found experimentally near the phase transition,so the critical behavior is very important to explain these phenomena.Landau-Lifshitz-Gilbert(LLG)equation is the fundamental equation describing the microscopic configuration of skyrmion with high complexity.In this paper,based on nonstationary dynamics approach,the critical slow down is overcome,the current-driven critical dynamic behavior of skyrmion is simulated for the first time by particle model and LLG equation respectively,and the anisotropic critical behavior is found.We also simulate the creep motion of skyrmion induced by temperature in the full driving range.For the first time,we determine the two-stages dynamic behavior of skyrmions and the role of thermal effect in skyrmion motion.With the Thiele equation of the particle-based model,we investigate the dynamic depinning phase transition of skyrmions,the structure information and transport properties near depinning phase transition.However,the particle model is a phenomenological model,in which the detailed microscopic structure and distortion of skyrmion are not concerned.Therefore,in order to understand the effect of the microscopic structure of skyrmion and the complex interaction in system,the simulation base on Heisenberg model is necessary.Through numerical simulations of the nonstationary current-driven dynamics of skyrmions with the Landau-Lifshitz-Gilbert equation,the critical current,static and dynamic critical exponents of the depenning phase transition are accurately determined for both adiabatic and non-adiabatic spin-transfer torques and with different strengths of disorder,based on the dynamic scaling behavior far from stationary.The results show that the skyrmions exhibit very different universal class compared to the domain wall and vortices.Meanwhile,the transition from glassy state to liquid state is accompanied by the depinning transition.The theoretical analysis using the Thiele’ s approach is presented,and the critical current and the static exponents support the simulation results.Moreover,we find that the threshold current is insensitive to a small non-adiabatic coefficient of the spin-transfer torque,but dramatically reduced for a large one.This provides a guidance to find the materials with an appropriate non-adiabatic coefficient in the efficient manipulation of skyrmions.More importantly,the critical behaviors of skyrmions are anisotropic in directions perpendicular and parallel to the driving force,providing an understanding of the force-dependent Hall angle around the phase transition in experiment.Finally,we perform large-scale numerical simulations of the skyrmion dynamics with quench disorder at finite temperatures.Two universal creep behaviors are observed below the depinning transition current,and the creep exponents are accurately determined.Our results provide comprehensive understanding for the role of temperature in the current-driven skyrmion dynamics.