Experimental determination of the Fermi surface of thin ${\mathrm{Sc}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Er}}_{\mathit{x}}$As epitaxial layers in pulsed magnetic fields

High field magnetotransport measurements on thin ${\mathrm{Sc}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Er}}_{\mathit{x}}$As layers buried in GaAs have been performed to obtain a detailed description of the ${\mathrm{Sc}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Er}}_{\mathit{x}}$As Fermi surface. The Shubnikov–de Haas (SdH) oscillations observed in the magnetoresistance and in the Hall effect are attributed to electron ellipsoids at the X points of the first Brillouin zone, and two hole spheres at the zone center. The masses of the charge carriers are determined. The assignment of the SdH frequencies is confirmed by the analysis of the relative phases of the ${\mathrm{\rho }}_{\mathit{xx}}$ and the ${\mathrm{\rho }}_{\mathit{yx}}$ oscillations. A splitting of the SdH frequencies, due to the exchange interaction between the mobile charge carriers and the 4f Er spins, is observed for the holes as well as for the electrons. Strong evidence is presented for confinement of the charge carriers in the ${\mathrm{Sc}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Er}}_{\mathit{x}}$As quantum well. As a consequence of this confinement, the carrier densities decrease with decreasing thickness of the layers and the SdH oscillations show two-dimensional behavior. © 1996 The American Physical Society.