Domain wall mobility, stability and Walker breakdown in magnetic nanowires

We present an analytical calculation of the velocity of a single 180 degree domain wall in a magnetic structure with reduced thickness and/or lateral dimension under the combined action of an external applied magnetic field and an electrical current. As for the case of field-induced domain wall propagation in thick films, two motion regimes with different mobilities are obtained, below and far above the so-called Walker field. Additionally, for the case of current induced motion, a Walker-like current density threshold can be defined. When the dimensions of the system become comparable to the domain wall width, the threshold field and current density, stating the wall's internal structure stability, are reduced by the same geometrical demagnetising factor which accounts for the confinement. This points out the fact that the velocity dependence over an extended field/current range and the knowledge of the Walker breakdown are mandatory to draw conclusions about the phenomenological Gilbert damping parameter tuning the magnetisation dynamics.