Interaction of a magnetic monopole with a ferromagnetic domain

We calculate the interaction energy of a magnetic monopole with a single ferromagnetic domain, taking into account the ferromagnetic exchange interaction in a linear approximation. In vacuum at 400 Å from the surface a monopole of strength $\frac{137e}{2}$ is bound by 35 eV in magnetite, and for iron at 300 Å from the surface the binding energy is 50 eV. We expect the binding energy to increase at smaller distances. The attractive force on a slow monopole approaching the surface of a ferromagnet from the vacuum differs, at these large distances, only slightly from that computed by simple classical image methods treating the magnet as a medium with an isotropic and wavelength-independent permeability equal to the long-wavelength transverse permeability of the ferromagnetic material. We consider the apparent contradictions with energy and momentum conservation in the problem of a monopole in the field of an electron. The exclusion of $s$- wave scattering largely resolves the contradictions. The effective field on a monopole in a ferromagnet is $\overrightarrow{\mathbf{H}}$ and not $\overrightarrow{\mathbf{B}}$.