Thermal effects in domain wall motion: Micromagnetic simulations and analytical model

Micromagnetic simulations are used to study the effect of thermal fluctuations in domain wall motion driven by either an external field or an in-plane spin-polarized current in ferromagnetic nanowires of rectangular cross section. For wires with no edge roughness, simulations reveal that thermal effects do not significantly modify field-driven and current-driven domain wall dynamics at $T=0$ if nonadiabatic contributions are taken into account in the latter. If the perfect adiabatic approximation is assumed, however, no-null velocities are obtained for currents smaller than the critical value below which there is no domain wall propagation in the deterministic case. In order to mimic experimental conditions and carry out more realistic simulations, we have introduced some edge roughness in the nanowire, which leads into a characteristic pinning force for domain walls. If the driving force, either field or current, is large enough to overcome the roughness pinning force, the wall velocities are found to be similar to those at $T=0$. However, finite positive velocities are obtained for fields and currents smaller than the deterministic depinning threshold when thermal perturbations are included. In this thermally activated regime, the velocity increases exponentially with both field and current. Moreover, our results are found to be in good quantitative agreement with some experimental data. In the last part of this work, the one-dimensional model for domain wall motion derived by Li et al. [J. Appl. Phys. 99, 08Q702 (2006)] is extended to include thermal perturbations following the Langevin formalism of the Brownian motion. The predictions of the model are compared with those of micromagnetic simulations finding good agreement between them.