Anisotropic critical behavior of current-driven skyrmion dynamics in chiral magnets with disorder

Abstract

The dynamic pinning effects are significant in manipulating skymions in chiral magnetic materials with quenched disorder. Through numerical simulations of the non-stationary 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. 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. The critical exponents indicate that the critical dynamic behavior is robust for different spin-transfer torques in the perpendicular component of the Hall motion, while exhibits a weak universality class in the direction of the driving current. The anisotropic behavior around the depinning phase transition provides a quantitative analysis of the drive-dependent skyrmion Hall effect in experiments. Further, the theoretical analysis using the Thiele's approach is presented, and the critical current and the static exponents support the simulation results.

Thermally activated dynamics of current-driven skyrmions in random media

“…The critical current u c = 0.024 for the set of parameters in this paper has been reported in ref. [19]. In fig.…”

“…In order to obtain the initial spin configurations of the perfect skyrmion crystal in our parameters, the replica Monte Carlo simulation is used to generate a spin configuration at a low temperature, to avoid the computational complexity of the LLG equation. It is then updated with the LLG equation without the driving current and temperature, i.e., u = 0, T = 0, until the sufficient convergence of the spin configuration [13,19]. With such initial configurations, a steady electric current is applied in the x-direction, starting the numerical simulation of the relaxation dynamics with the LLG equation at a finite temperature.…”

“…At zero temperature, the collective motion of skyrmions driven by a current exhibits a dynamic depinning phase transition. To study the thermal rounding behavior at the depinning phase transition, we focus on the nonstationary dynamic relaxation starting from a skyrmion crystal state [19]. Based on the renormalization group arguments, there should exist a dynamic scaling form already in the macroscopic short-time region [34][35][36].…”

“…In the absence of distortion of the skyrmion, D is typically diagonal, i.e., D xy = D xy = D, otherwise, D μν = 0. In our analysis, G and D are regarded as constants in the stationary state, and D = 6.976πQ can be evaluated at h/J = 0.04 without quenched disorder [19].…”

“…( 7), there exist deviations in early times. Therefore, a correction to scaling, ṽ⊥ (t, T ) = v ⊥ (t, T )(1 + cT /t 1/z ⊥ )/v ⊥ (t, 0), is introduced, with z ⊥ = 1.79 measured in the depinning transition at zero temperature [19]. Based on the above ansatz, the data collapse with ψ ⊥ = 0.48(2) in the perpendicular direction is shown in fig.…”