The objective of this research is to explore, under the effective mass approximation (EMA) framework and employing the variational method, how hydrostatic pressure (HP), non-parabolicity (NP) and polaronic mass (PM) influence the binding energy ( \({\mathrm{E}}_{\mathrm{b}}\) ) and the diamagnetic susceptibility ( \({\upchi }_{\mathrm{dia}}\) ) of a magnetic impurity \({(\mathrm{Mn}}^{2+})\) in the ground state \(\left(1\mathrm{s}\right)\) and low-lying excited states \((2\mathrm{s}\) and \({2\mathrm{p}}_{\mathrm{z}})\) in a semimagnetic \(\mathrm{CdTe}/{\mathrm{Cd}}_{1-\mathrm{x}}{\mathrm{Mn}}_{\mathrm{x}}\mathrm{Te}\) double quantum well (DQW). Furthermore, the \({\mathrm{E}}_{\mathrm{b}}\) and the corresponding \({\upchi }_{\mathrm{dia}}\) for the impurity states were determined as a function of the barrier thickness \(\left({\mathrm{L}}_{\mathrm{b}}\right)\) and the impurity position \(\left({\mathrm{z}}_{\mathrm{i}}\right)\) , while keeping the well width \(\left({\mathrm{L}}_{\mathrm{w}}\right)\) fixed. Additionally, the polaronic correction \(\left({\mathrm{E}}_{\mathrm{sp}}\right)\) , arising from the strong coupling between the magnetic moment of the \({\mathrm{Mn}}^{2+}\) ion and the spin of the confined electron, has been calculated for the aforementioned states under the same effects. We hope that these numerical results will make a significant contribution to the advancement of optoelectronic devices based on semimagnetic semiconductors.
