  We study formation of local magnetic moments in strongly correlated Hubbard
model within dynamical mean field theory and associate peculiarities of
temperature dependence of local charge $\chi_c$ and spin $\chi_s$
susceptibilities with different stages of local moment formation. Local maximum
of temperature dependence of the charge susceptibility $\chi_c$ is associated
with beginning of local magnetic moments formation, while the minimum of the
susceptibility $\chi_c$ and double occupation, as well as low temperature
boundary of the plateau of effective local magnetic moment $\mu_{\rm
eff}^2=T\chi_s$ temperature dependence are connected with full formation of
local moments. We also obtain interaction dependence of the Kondo temperature
$T_K$, which is compared to the fingerprint criterion of Phys. Rev. Lett. 126,
056403 (2021). Near the Mott transition the two criteria coincide, while
further away from Mott transition the fingerprint criterion somewhat
overestimates Kondo temperature. The relation of the observed features to the
behavior of eigenvectors/eigenvalues of fermionic frequency-resolved charge
susceptibility and divergences of irreducible vertices is discussed.
