Dynamical depinning of chiral domain walls

The domain wall depinning field represents the minimum magnetic field needed to move a domain wall, typically pinned by samples' disorder or patterned constrictions. Conventionally, such a field is considered independent on the Gilbert damping since it is assumed to be the field at which the Zeeman energy equals the pinning energy barrier (both damping independent). Here we analyze numerically the domain wall depinning field as a function of the Gilbert damping in a system with perpendicular magnetic anisotropy and Dzyaloshinskii-Moriya interaction. Contrary to expectations, we find that the depinning field depends on the Gilbert damping and that it strongly decreases for small damping parameters. We explain this dependence with a simple one-dimensional model and we show that the reduction of the depinning field is related to the finite size of the pinning barriers and to the domain wall internal dynamics, connected to the Dzyaloshinskii-Moriya interaction and the shape anisotropy.