Topology and dynamics in ferromagnetic media

A direct link between the topological complexity of ferromagnetic media and their dynamics has recently been established through the construction of unambiguous conservation laws as moments of a topological vorticity. In the present paper we carry out this program under completely realistic conditions, with due account of the long-range magnetostatic field and related boundary effects. In particular, we derive unambiguous expressions for the linear and angular momentum in a ferromagnetic film which are then used to study the dynamics of magnetic bubbles under the influence of an applied magnetic-field gradient. The semi-empirical golden rule of bubble dynamics is verified in its gross features but not in its finer details. A byproduct of our analysis is a set of virial theorems generalizing Derrick's scaling relation as well as a detailed recalculation of the fundamental magnetic bubble.