  Collapse models predict a tiny violation of energy conservation, as a
consequence of the spontaneous collapse of the wave function. This property
allows to set experimental bounds on their parameters. We consider an ultrasoft
magnetically tipped nanocantilever cooled to millikelvin temperature. The
thermal noise of the cantilever fundamental mode has been accurately estimated
in the range $0.03-1$ K, and any other excess noise is found to be negligible
within the experimental uncertainty. From the measured data and the cantilever
geometry, we estimate the upper bound on the Continuous Spontaneous
Localization (CSL) collapse rate in a wide range of the correlation length
$r_C$. Our upper bound improves significantly previous constraints for
$r_C>10^{-6}$ m, and partially excludes the enhanced collapse rate suggested by
Adler. We discuss future improvements.
