  We explore the inelastic electron scattering cross section off a quantum dot
close to the Stoner instability. We focus on the regime of strong Coulomb
blockade in which the scattering cross section is dominated by the cotunneling
processes. For large enough exchange interaction the quantum dot acquires a
finite total spin in the ground state. In this, so-called mesoscopic Stoner
instability, regime we find that at low enough temperatures the inelastic
scattering cross section (including the contribution due to an elastic electron
spin-flip) for an electron with a low energy with respect to the chemical
potential is different from the case of a magnetic impurity with the same spin.
This difference stems from (i) presence of a low-lying many-body states of a
quantum dot and (ii) the correlations of the tunneling amplitudes. Our results
provide a possible explanation for absence of the dephasing rate saturation at
low temperatures in recent experiment [N. Teneh, A. Yu. Kuntsevich, V. M.
Pudalov, and M. Reznikov, Phys. Rev. Lett. 109, 226403 (2012)] in which
existence of local spin droplets in disordered electron liquid has been
unraveled.
