Damping of a nanocantilever by paramagnetic spins

We compute damping of mechanical oscillations of a cantilever that contains flipping paramagnetic spins. This kind of damping is mandated by the dynamics of the total angular momentum, spin + mechanical. Rigorous expression for the damping rate is derived in terms of measurable parameters. The effect of spins on the quality factor of the cantilever can be significant in cantilevers of small length that have large concentration of paramagnetic spins of atomic and/or nuclear origin.