Muon spin relaxation $(\ensuremath{\mu}\mathrm{SR})$ measurements have been made on ${\mathrm{Cd}}_{0.85}{\mathrm{Mn}}_{0.15}\mathrm{Te}:\mathrm{In}$ and ${\mathrm{Cd}}_{0.86}{\mathrm{Mn}}_{0.14}\mathrm{Te}:\mathrm{Al}$. The spin glass transition region has been studied using $\ensuremath{\mu}\mathrm{SR}$ and low-temperature magnetic susceptibility measurements. Persistent photoconductivity (PPC) has been shown to exist only in the In-doped sample, the effect of PPC on the spin glass transition temperature using bulk magnetic susceptibility has also been studied, indicating the presence of bound magnetic polarons. $\ensuremath{\mu}\mathrm{SR}$ on the Al-doped sample clearly shows the spin glass transition, however, the presence of the DX center, which causes PPC when doping with In donors, perturbs the muon response. Particular attention is paid to the possibility of the DX center trapping muonium, preventing the detection of the spin glass transition. PPC does not induce a change in the muon response, however, we find continuous illumination of the sample allows the observation of the spin glass transition. We suggest that these results can be explained by assuming the presence of multiple DX centers. The muon acting as a local magnetic probe of the DX center also suggests the ground state is diamagnetic.
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