  We study bound magnetic polarons (BMP) in a very diluted magnetic
semiconductor CdMnTe by means of site selective spectroscopy. In zero magnetic
field we detect a broad and asymmetric band with a characteristic spectral
width of about 5 meV. When external magnetic fields are applied a new line
appears in the emission spectrum. Remarkably, the spectral width of this line
is reduced greatly down to 0.24 meV. We attribute such unusual behavior to the
formation of BMP, effected by sizable fluctuations of local magnetic moments.
The modifications of the optical spectra have been simulated by the Monte-Carlo
method and calculated within an approach considering the nearest Mn ion. A
quantitative agreement with the experiment is achieved without use of fitting
parameters. It is demonstrated that the low-energy part of the emission spectra
originates from the energetic relaxation of a complex consisting of a hole and
its nearest Mn ion. It is also shown that the contribution to the narrow line
arises from the remote Mn ions.
