We identify the mechanism of energy dissipation relevant to
spin-sensitive nanomechanics including the recently introduced magnetic
exchange force microscopy, where oscillating magnetic tips approach
surface atomic spins. The tip-surface exchange couples spin and atom
coordinates, leading to a spin-phonon problem with Caldeira-Leggett-type
dissipation. In the overdamped regime, that can lead to a hysteretic
flip of the local spin with a large spin-dependent dissipation, even
down to the very low experimental tip oscillation frequencies,
describing recent observations for Fe tips on NiO. A phase transition to
an underdamped regime with dramatic drop of magnetic tip dissipation should in principle be possible by tuning tip-surface distance.
