Magneto-optical investigations of dilutedCd1−xMnxSmagnetic semiconductors in theB-exciton region

Abstract

The measurements of magnetoreflection spectra in the $B$-exciton region of diluted magnetic semiconductors (DMS's) ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$ are carried out for the magnetic-field directions both along and across the crystal c axis. It is pointed out that giant spin splitting (GSS) of the $B$ exciton does not demonstrate a nonlinear dependence on the magnetic-component fractional content $x,$ contrary to the $A$-exciton GSS situation. It is supposed that the effects of multiple scattering of valence electron on the magnetic ions, which lead to a sublinearity of the $A$-exciton GSS $x$ dependence in ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S},$ are different for the $A$ and $B$ valence-electron subbands. In particular, due to a smaller effective mass of valence electrons in the $B$ subband, the multiple scattering of this electron on ${\mathrm{Mn}}^{2+}$ ions may be not important and the GSS of $B$ excitons can be described by the mean-field approximation (MFA) with the ``bare'' exchange constant ${J}_{h}$ for $B$-hole interactions with magnetic ions. The approach to the determination of band parameters ${\ensuremath{\Delta}}_{1},{\ensuremath{\Delta}}_{2},{\ensuremath{\Delta}}_{3}$ and the hole-ion exchange constant ${J}_{h}$ in hexagonal DMS's is suggested. This approach is based only on the $B$-exciton GSS MFA description and data of energy distances between $A,$ $B,$ and $C$ excitons. The method is applied for the treatment of exciton magnetoreflection spectra of ${\mathrm{Cd}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{S}$ crystals with different $x.$ It is established that ${J}_{h}=\ensuremath{-}1.7\mathrm{eV}$ and is independent of $x.$ This value ${J}_{h}$ turns out to be several times smaller than that obtained from MFA for $A$-exciton GSS. However, this value is in good agreement with ${J}_{h}=\ensuremath{-}1.4\mathrm{eV},$ the value obtained earlier from the $A$-exciton GSS treatment beyond the MFA. In the limiting case of small $x,$ we obtained the band parameter values ${\ensuremath{\Delta}}_{1}=17.2\ifmmode\pm\else\textpm\fi{}2\mathrm{meV},$ ${\ensuremath{\Delta}}_{2}=25.6\ifmmode\pm\else\textpm\fi{}0.7\mathrm{meV},$ and ${\ensuremath{\Delta}}_{3}=21.7\ifmmode\pm\else\textpm\fi{}0.3\mathrm{meV}.$ They differ from those known in the literature for pure CdS.