Dielectric tensor for magneto-optic NiMnSb

The diagonal component ${\varepsilon }_{\mathrm{xx}}$ and off-diagonal component ${\varepsilon }_{\mathrm{xy}}$ of the complex dielectric tensor for the ferromagnetic compound NiMnSb are determined using ex situ spectroscopic ellipsometry and magneto-optic analysis over the spectral range from 0.7 to 6.2 eV. The effects of the overcoat on the raw data are removed by the analysis. First, the complex ${\varepsilon }_{\mathrm{xx}}$ of thin-film NiMnSb were determined by ex situ spectroscopic ellipsometry; then ${\varepsilon }_{\mathrm{xy}}$ was determined by analyzing Kerr rotation and ellipticity data using the determined ${\varepsilon }_{\mathrm{xy}}$ data. Lorentz oscillators were used to model peaks seen in the ${\varepsilon }_{\mathrm{xx}}$ spectra. The diagonal dielectric component ${\varepsilon }_{\mathrm{xx}}$ is dominated by free-carrier effects below 1.15 eV, and dominated by interband transitions above 2.0 eV. The center energies of the Lorentz oscillators are consistent with the calculated band structure and minority-spin optical conductivity of NiMnSb. Joint density of states and optical conductivity calculated from ${\varepsilon }_{\mathrm{xx}}\mathrm{}\left(2\right)\mathrm{}$ data with free-carrier effects removed shows onset energies at ∼0.6 and ∼0.2 eV, respectively. From a study of the ${\varepsilon }_{\mathrm{xx}}$ and ${\varepsilon }_{\mathrm{xy}}$ spectra, the Kerr rotation peak at lower energy is determined to be due to combined contributions from: (1) a crossover between the free-carrier effect and interband transitions, and (2) transitions involving spin-orbit coupling. The high-Kerr rotation peaks at higher energies result exclusively from transitions involving spin-orbit coupling.