It is shown that spin-spin interactions rather than spin-lattice coupling control the dynamics of the magnetization formation visible in time-resolved luminescence and SQUID magnetometry of bulk and layered diluted magnetic semiconductors. A numerical solution of a nonlinear Schr\"odinger equation is applied to find the relation between formation time of the exciton magnetic polaron and relaxation time of the spin subsystem.
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Dietl et al. (1995) studied this question.
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