High-resolution resonance spin-flip Raman spectroscopy of pairs of manganese ions in a CdTe quantum well

We report the observation of tens of minor lines of the combinational spin-flip Raman scattering in a CdTe:Mn quantum well by means of the high-resolution optical spectroscopy. Classification of this manifold leads to four characteristic values of energy, that correspond to four different types of pair clusters of Mn ions: the nearest, second, third, etc., neighbors. All the four energies show up in a single experiment with a very high precision, providing experimental grounds for a deeper understanding of the $d\ensuremath{-}d$ exchange interactions in a diluted magnetic semiconductor and demonstrating the capacity of the employed method. The major (nearest-neighbor) exchange constant ${J}_{1}=6.15\ifmmode\pm\else\textpm\fi{}0.05$ K was found to consent with its previously reported value. Other detected characteristic energies are as follows ($\ifmmode\pm\else\textpm\fi{}0.05$ K): ${J}_{(2)}=1.80$ K, ${J}_{(3)}=1.39$ K, ${J}_{(4)}=0.81$ K.