Domain wall mobility, stability and Walker breakdown in magnetic nanowires

We present an analytical calculation of the velocity of a single 180° 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 is defined. The threshold field and current density, stating the wall's internal structure stability, differ from those in thick films; both 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.