A modified phenomenological description of the exchange interactions in dilute magnetic semiconductors

Magnetoreflectivity spectroscopy has been conducted on a series of Cd 1-x Mn x Te epilayers (x<0.2) in magnetic fields up to 45 T. For Mn concentrations greater than a fraction of one per cent, the electronic sp-d exchange interactions do not saturate for B>10 T at 4.2 K, as predicted by the widely used mean spin model of Gaj et al. (1979), but continue to decrease with increasing magnetic field. This is because of a field-dependent increase in the total resultant spin of the dilute magnetic sublattice, due to a reduction in the antiferromagnetic interactions between the Mn 2+ ions. We present a modified phenomenological description of the exchange interactions, which simply and efficiently accounts for this field-induced increase in spin, necessary for an accurate description of the high-field (B>10 T) regime. This is achieved semi-empirically within the mean spin formalism, without requiring solution of the complex spin Hamiltonians for double, triple and higher order clusters.