Polar Kerr effect studies ofGa1−xMnxAsepitaxial films

Abstract

The ferromagnetic state of thin ${\mathrm{Ga}}_{1\ensuremath{-}x}{\mathrm{Mn}}_{x}\mathrm{As}$ layers ($d=300\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$; $x=0.014$, $p=6.7\ifmmode\times\else\texttimes\fi{}{10}^{19}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, ${T}_{C}=40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, easy axis in plane; $x=0.03$, $p=9.5\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.3em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$, ${T}_{C}=60\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, easy axis out of plane) on GaAs substrates is investigated by polar magneto-optical Kerr effect (MOKE) and reflectance magnetocircular dichroism (MCD) studies in the temperature range between $1.6\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ and $100\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, in magnetic fields normal to the layer plane ranging from $\ensuremath{-}5\phantom{\rule{0.3em}{0ex}}\text{to}\phantom{\rule{0.3em}{0ex}}+5\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$. A magnetic field of $70\phantom{\rule{0.3em}{0ex}}\mathrm{kOe}$ is applied in those cases when truly saturated magnetization has to be determined. A parabolic interband dielectric function model that includes the relevant (heavy-hole, light-hole, and split-off) valence bands, as well as the finite Moss-Burstein shift, was developed for analyzing both the MOKE and MCD. The occupation of the spin-split valence bands is taken into account by explicitly including the Fermi level for holes in analytic form. The samples were sufficiently different in their Curie temperatures, easy axis directions, magnetic ion contents, and hole concentrations to demonstrate experimentally the versatility of the proposed model. Superconducting quantum interference device measurements carried out on the samples demonstrated the validity of the dilute-magnetic-semiconductor (DMS) mean-field approach for the contact exchange interaction between manganese spins and hole carriers, reflected by a more or less fixed conduction-band exchange parameter ${N}_{0}\ensuremath{\alpha}=0.22--0.29\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ and a hole exchange parameter ${N}_{0}\ensuremath{\beta}$ varying between 0.9 and $2.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, depending on the hole concentration and on the Mn content. Note that the magnitudes are close to those familiar from II-VI DMS's, but the sign of ${N}_{0}\ensuremath{\beta}$ is reversed from the II-VI case---i.e., from antiferromagnetic to ferromagnetic local exchange. The quantitative wavelength-dependent $(\ensuremath{\lambda}=550--950\phantom{\rule{0.3em}{0ex}}\mathrm{nm})$ analysis of MOKE and MCD spectra for both samples and the imposed requirement that the band parameters should not deviate significantly from the GaAs-related band alignment and from exchange-induced spin multiplicities lead us to the introduction of a dispersionless level superimposed in the conduction band of GaMnAs (fitted energy gaps $1.50--1.57\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$). The physical nature of such a level could not be identified by our simplified model, but we note that a high-density-of-states level in the conduction band of GaMnAs has been predicted recently by Sandratskii and Bruno [Phys. Rev. B 66, 134435 (2002)]. The hysteresis measurements are presented without deeper analysis. The hole concentration fitted to MOKE and MCD spectra deviates for the $x=0.014$ sample by a factor of 0.8 from the data obtained by anomalous Hall effect measurements, but this inconsistency should probably be viewed as a result of the difficulty in interpreting experimental magnetotransport measurements, rather than a shortcoming of our theoretical treatment.