Band structure of diluted magnetic Pb1−xMnxTe: Magneto-optical investigations and four-wave-mixing spectroscopy

Abstract

Magneto-optical intraband and interband experiments on epitaxial ${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te samples with Mn contents x≤2% are reported. A direct observation of spin-flip transitions of electrons and holes is performed down to magnetic fields of less than 0.05 T by using coherent anti-Stokes Raman scattering experiments. g factors are determined as a function of magnetic field as well as a function of temperature. All experimental data are well accounted for by treating the exchange interaction between the mobile carriers and the localized 3d electrons of the ${\mathrm{Mn}}^{2+}$ ions in a mean-field approximation. In this many-valley semiconductor with conduction- and valence-band extrema at the L point of the Brillouin zone, four exchange integrals are relevant. These integrals have opposite influence for the conduction and valence bands, and the exchange-induced effects are much larger for holes than for electrons. The data and their interpretation yield conclusive evidence against the ‘‘zero-field splitting,’’ i.e., a finite energy difference of spin-split states in zero magnetic field (‘‘free magnetic polaron’’) in ${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te with x<0.02. The upper limit for the binding energy of a free magnetic polaron, if it exists at all, is less than 0.05 meV in ${\mathrm{Pb}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te, a value determined by the remaining experimental uncertainty. Although the experimental magneto-optical transition energies are perfectly fitted by the molecular-field approximation, their temperature dependence reveals the necessity for temperature-dependent exchange parameters, which is beyond a mean-field approach.