Interband faraday and kerr effects in germanium: Interrelations and dispersion relations

Abstract

Differential magneto‐optical (mo) spectra in the Faraday configuration for i‐Ge (111) in the energy range of the direct interband transitions from 0.78 to 4.6 eV are presented. These spectra are obtained using linear and circular polarization modulation, respectively. Measurements of the complex mo‐Kerr effect (Kerr ellipticity and rotation) in high magnetic fields (B = 12 T; T = = 300 K) are used to calculate the off‐diagonal component \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^\~ $\end{document} xy of the complex dielectric tensor requiring no Kramers‐Kronig transformation (KKT). Measurements of the complex Faraday effect (Faraday ellipticity and rotation) in the spectral region where the transmittance is sufficiently high, i.e., from 0.78 to 1.6 eV, yield good agreement between reflected and transmitted mo spectra. The possibility of converting both effects into each other is confirmed except for the region of discrete exciton transitions indicating dead layer effects. The KKT between the real and imaginary parts of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \varepsilon \limits^\~ $\end{document}xy is used to provide an overall check of the dielectric response in the presence of a magnetic field. It is impossible to derive KKT's between the directly measurable quantities themselves without restrictive approximations. The consequences of different approximations on the KKT are discussed using calculated and measured data.