  We measure the dissipation and frequency shift of a magnetically coupled
cantilever in the vicinity of a silicon chip, down to $25$ mK. The dissipation
and frequency shift originates from the interaction with the unpaired
electrons, associated with the dangling bonds in the native oxide layer of the
silicon, which form a two dimensional system of electron spins. We approach the
sample with a $3.43$ $\mu$m-diameter magnetic particle attached to an ultrasoft
cantilever, and measure the frequency shift and quality factor as a function of
temperature and the distance. Using a recent theoretical analysis [J. M. de
Voogd et al., arXiv:1508.07972 (2015)] of the dynamics of a system consisting
of a spin and a magnetic resonator, we are able to fit the data and extract the
relaxation time $T_1=0.39\pm0.08$ ms and spin density $\sigma=0.14\pm0.01$
spins per nm$^2$. Our analysis shows that at temperatures $\leq500$ mK magnetic
dissipation is an important source of non-contact friction.
