Magneto-optical investigations of Eu-based diluted magnetic lead chalcogenides

MBE grown ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ and ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Se}$ films with Eu contents up to 7% were investigated by various magneto-optical methods as interband absorption, photomodulated reflectivity, photoluminescence, and coherent anti-Stokes Raman scattering (CARS) in the midinfrared. The observed interband and intraband transition energies were interpreted in the framework of the Mitchell and Wallis band-structure model with the exchange interaction taken into account in mean-field approximation. The interband matrix elements of the selenide are independent of the Eu concentration up to $x=0.07,$ whereas in the telluride they are reduced by about a factor of 2 between $x=0\mathrm{}$ and 0.05. The signs and the magnitudes of the exchange parameters for the exchange interaction between the free carriers in the conduction and valence band, respectively, and the localized magnetic moments of the ${\mathrm{Eu}}^{2+}$ ions are similar in ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ and ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Se}.$ This implies that in ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Te}$ the exchange interaction decreases the spin splitting of the valence band as it is known from ${\mathrm{Pb}}_{1-x}{\mathrm{Eu}}_x\mathrm{Se}.$ The sign and magnitude of the exchange parameters are different from the Mn-based compounds indicating that the effect is dominated by the hybridization of the band states with the localized wave functions of the $4f$ or $3d$ electrons, respectively. The minima of the magnetoabsorption spectra exhibit a strong line broadening with increasing Eu concentration. Weaker transitions are no longer observable. Thus for higher Eu contents CARS turned out to be important not only for the determination of exchange parameters but also for the precise determination of the anisotropy of the interband matrix elements. With increasing $x$ a strong decrease of the matrix elements is observed in the telluride, whereas the matrix elements in the selenide are less influenced.