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.
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