Magneto-optical properties of diluted magnetic PbSe/Pb1−xMnxSe superlattices

Abstract

PbSe/${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se superlattices (x0.02, periods: 40 nm) were grown by molecular-beam epitaxy on (111) oriented substrates. They were investigated by interband absorption in Faraday geometry (B\ensuremath{\parallel}k\ensuremath{\parallel}[111]) and by coherent anti-Stokes Raman scattering in the mid-infrared range with B\ensuremath{\parallel}[11\ifmmode\bar\else\textasciimacron\fi{}0] (i.e., in the plane of the layers) up to 7 T at temperatures in the range of 1.7--20 K. The latter method yields precise information on the spin splittings of valence and conduction bands as a function of applied magnetic field and of temperature. The experimental results yield a staggered band alignment with the conduction-band edge of the wider gap ${\mathrm{Pb}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Mn}}_{\mathit{x}}$Se layers below that of the PbSe layers. A detailed theoretical analysis is made on the basis of a four-band envelope-function approximation taking into account the exchange interaction between the localized electrons of the half-filled ${\mathrm{Mn}}^{2+}$ 3d shell and the mobile carriers in mean-field approximation. Energy eigenstates and eigenfunctions have been calculated as well as interband selection rules. For the Voigt geometry, where the electric and magnetic motions are not decoupled, the center coordinate of the Landau orbits remains a good quantum number, albeit that the corresponding degeneracy of eigenstates is lifted. The dependence of the eigenstates and of the g values on the value of the center coordinate along the superlattice growth direction is investigated in detail. A normalized conduction-band offset \ensuremath{\Delta}${\mathit{E}}_{\mathit{c}}$/\ensuremath{\Delta}${\mathit{E}}_{\mathit{g}}$ of -0.4 is obtained. \textcopyright{} 1996 The American Physical Society.