  We analyze the magnetic dipole contribution to atom-surface dispersion
forces. Unlike its electrical counterpart, it involves small transition
frequencies that are comparable to thermal energy scales. A significant
temperature dependence is found near surfaces with a nonzero DC conductivity,
leading to a strong suppression of the dispersion force at T > 0. We use
thermal response theory for the surface material and discuss both normal metals
and superconductors. The asymptotes of the free energy of interaction and of
the entropy are calculated analytically over a large range of distances. Near a
superconductor, the onset of dissipation at the phase transition strongly
changes the interaction, including a discontinuous entropy. We discuss the
similarities with the Casimir interaction beween two surfaces and suggest that
precision measurements of the atom-surface interaction may shed new light upon
open questions around the temperature dependence of dispersion forces between
lossy media.
