Determination of the analytical and the nonanalytical part of the exchange interaction of InP and GaAs from polariton spectra in intermediate magnetic fields

Abstract

The isotropic analytical exchange interaction ${\ensuremath{\Delta}}_{a}$ of GaAs and InP is determined to be 0.02\ifmmode\pm\else\textpm\fi{}0.01 and 0.04\ifmmode\pm\else\textpm\fi{}0.015 meV, respectively, for the two materials from a comparison of theoretically generated and experimentally determined transverse exciton energies and oscillator strengths in magnetic fields up to 20 T. The calculation of the theoretical spectra is based on a recent intermediate-field theory including the analytical and nonanalytical part of the exchange interaction. The experimental values are determined from a two-oscillator line-shape analysis of ${\ensuremath{\sigma}}^{\ensuremath{-}}$,- ${\ensuremath{\sigma}}^{+}$-, and $\ensuremath{\pi}$-polarized magnetoreflection spectra. A newly developed model describing the exciton-free surface layer of a semiconductor by an exponentially decreasing damping of the exciton contribution to the dielectric constant is shown to improve strongly the quality of the line-shape fit. This improvement is achieved without increasing the number of fitting parameters as compared to the older model using a layer of finite thickness with infinite damping. From a similar comparison of theoretical and experimental values of the energies and oscillator strengths of longitudinal-transverse mixed-mode exciton spectra in magnetic fields which are found for the $\ensuremath{\sigma}$ polarization in Voigt configuration ($\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}\ensuremath{\perp}\stackrel{\ensuremath{\rightarrow}}{\mathrm{H}}$) the size of the nonanalytical exchange interaction ${\ensuremath{\Delta}}_{\mathrm{LT}}$ in GaAs is determined to be 0.08\ifmmode\pm\else\textpm\fi{}0.02 meV. For InP an upper limit of ${\ensuremath{\Delta}}_{\mathrm{LT}}<~0.1$ meV is derived.