Magneto-optical investigations of diluted Cd 1 2x Mn x S magnetic semiconductors in the B -exciton region Yu. G. Semenov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine, Prospekt Nauki 45, Kiev 252028, Ukraine V. G. Abramishvili, A. V. Komarov, and S. M. Ryabchenko Institute of Physics, National Academy of Sciences of Ukraine, Prospekt Nauki 46, Kiev 252028, Ukraine ~Received 16 January 1997! The measurements of magnetoreflection spectra in the B -exciton region of diluted magnetic semiconductors ~DMS’s! Cd 12x Mn x 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 Cd 12x Mn x 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 Mn 21 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 D 1 , D 2 , D 3 and the hole-ion exchange constant J h in hex- agonal 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 magne- toreflection spectra of Cd 12x Mn x S crystals with different x . It is established that J h 521.7 eV and is inde- pendent 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 521.4 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 D 1 517.262 meV, D 2 525.660.7 meV, and D 3 521.760.3 meV. They differ from those known in the literature for pure CdS. @S0163-1829~97!01928-0# INTRODUCTION The investigations of giant spin splitting ~GSS! of exciton reflection spectra in Cd 1 2x Mn x S crystals show 1–5 a number of peculiarities as compared to other diluted magnetic semi- conductors ~DMS’s! of A 1 2x 2 Mn x B 6 type. The most widely discussed peculiarity is the sublinear concentration depen- dence of A -exciton GSS, which was interpreted in Refs. 1–3 to be a result of the effective dependence of the hole-band exchange constant J h 5J h ( x ) on the magnetic-component fractional content x . The measurements in Refs. 1–3 were performed on crystals with such small Mn 21 concentrations that the interaction between magnetic ions was negligible and could not be the reason for the dependence of J h ( x ). An explanation based on the mean-field approximation ~MFA!, acting on carrier spins has been suggested in Refs. 1–3. In that case the J h value reached 3–4 eV, several times larger than its value in the other DMS’s. This explanation, how- ever, cannot be regarded as a satisfactory one because the resulting J h value turn out to be greater than the CdS valence-band width. Due to this situation, attempts to explain GSS peculiari- ties of Cd 1 2x Mn x S A excitons beyond the MFA were made in Refs. 6–8. The result of the investigations was a qualita- tive understanding of observable peculiarities as a manifes- tation of multiple hole scattering on the magnetic ions. This scattering influences GSS; it is also important due to the large effective mass of A valence electrons. A quantitative description was carried out in the aforementioned works on the basis of a simplified band structure in the isotropic effective-mass approximation m h 51.3m 0 for the A subband of CdS crystal valence electrons. The ‘‘bare’’ exchange con- stant value J h 521.4 eV, obtained in the latter approach, is in agreement with the data for other A 1 2x 2 Mn x B 6 and seems to be reasonable. At the same time much less attention has been paid to magneto-optical investigations of the B band in Cd 1 2x Mn x S. One of the reasons was the absence of vivid effects, similar to those in A -band investigations. Moreover, the substantial splitting of B excitons was not observed in s 6 polarizations for the magnetic field H i c ~c is the hexago- nal axis of the crystal!. The latter circumstance, in fact, was explained in Ref. 9. The explanation was reduced to the re- consideration of the band parameters D 1 , D 2 , D 3 well known in the literature; the difference D 1 2D 2 turned out to have a different sign. The authors of Ref. 9 were not able to give a reliable value of the exchange constant J h along with sepa- rate band-parameter D 1 , D 2 , D 3 values due to the impossibil- ity of a joint description of A - and B -exciton GSS in the MFA framework. In the present paper we pay attention to the absence of a visible splitting of the B -exciton spectrum in s polarization for all magnetic fields and samples under investigation in a wide range of x values. This points to the equality between PHYSICAL REVIEW B 15 JULY 1997-II VOLUME 56, NUMBER 4 56 0163-1829/97/56~4!/1868~8!/$10.00 1868 © 1997 The American Physical Society