The stochastic nature of the domain wall motion along high perpendicular anisotropy strips with surface roughness.

The domain wall dynamics along thin ferromagnetic strips with high perpendicular magnetocrystalline anisotropy driven by either magnetic fields or spin-polarized currents is theoretically analyzed by means of full micromagnetic simulations and a one-dimensional model, including both surface roughness and thermal effects. At finite temperature, the results show a field dependence of the domain wall velocity in good qualitative agreement with available experimental measurements, indicating a low field, low velocity creep regime, and a high field, linear regime separated by a smeared depinning region. Similar behaviors were also observed under applied currents. In the low current creep regime the velocity-current characteristic does not depend significantly on the non-adiabaticity. At high currents, where the domain wall velocity becomes insensitive to surface pinning, the domain wall shows a precessional behavior even when the non-adiabatic parameter is equal to the Gilbert damping. These analyses confirm the relevance of both thermal fluctuations and surface roughness for the domain wall dynamics, and that complete micromagnetic modeling and one-dimensional studies taking into account these effects are required to interpret the experimental measurements in order to get a better understanding of the origin, the role and the magnitude of the non-adiabaticity.