Interaction between a magnetic domain wall and a superconductor

The interaction between a magnetic thin film and a superconductor is studied. In particular, the equilibrium width of a Bloch wall is estimated with and without the superconductor. It is shown that the Bloch wall experiences a small shrinkage on cooling through the critical temperature of the superconductor. Furthermore, the interaction between the Bloch wall and a single vortex is estimated, and a simple expression for the force is found.