  We predict a repulsive Casimir-Polder-type dispersion interaction between a
single neutron and a metal or dielectric surface. We consider a scenario where
a single neutron is subject to an external magnetic field. Due to its intrinsic
magnetic moment, the neutron then forms a magnetisable two-level system which
can exchange virtual photons with a nearby surface. The resulting dispersion
interaction between a purely magnetic object (neutron) and a purely electric
one (surface) is found to be repulsive, in contrast to the typical attractive
interaction between electric objects. Its magnitude is considerably smaller
than the standard atom--surface Casimir-Polder force due to the magnetic nature
of the interaction and the smallness of the electron-to-neutron mass ratio.
Nevertheless, we show that it can be comparable to the gravitational potential
of the same surface and should be taken into consideration in future neutron
interference experiments.
