Abstract
The exchange interactions between excitons and manganese ions in wide (80 nm) quantum wells of Cd${}_{1\ensuremath{-}x}$Mn${}_{x}$Te ($x\ensuremath{\approx}0.0015$ and $x\ensuremath{\approx}0.00027$) have been measured for states with center of mass quantum numbers up to 10. The corresponding translational wave vectors are in the range up to $4\ifmmode\times\else\texttimes\fi{}{10}^{6}\phantom{\rule{2.84526pt}{0ex}}$cm${}^{\ensuremath{-}1}$ and in this range we detect no systematic variation of the exchange parameter ${N}_{0}(\ensuremath{\alpha}\ensuremath{-}\ensuremath{\beta})$, which remains constant to within $\ifmmode\pm\else\textpm\fi{}3%$. The result is consistent with previous studies of the wave vector dependence of the electron contribution ${N}_{0}\ensuremath{\alpha}$ but differs from previous observations of the wave vector dependence of exciton exchange interaction in quantum wells with much higher concentrations of manganese.
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