  We present a comprehensive experimental and theoretical studies of
photoluminescence of single CdMnTe quantum dots with Mn content x ranging from
0.01 to 0.2. We distinguish three stages of the equilibration of the exciton-Mn
ion spin system and show that the intermediate stage, in which the exciton spin
is relaxed, while the total equilibrium is not attained, gives rise to a
specific asymmetric shape of the photoluminescence spectrum. From an excellent
agreement between the measured and calculated spectra we are able to evaluate
the exciton localization volume, number of paramagnetic Mn ions, and their
temperature for each particular dot. We discuss the values of these parameters
and compare them with results of other experiments. Furthermore, we analyze the
dependence of average Zeeman shifts and transition linewidths on the Mn content
and point out specific processes, which control these values at particular Mn
concentrations.
