Signatures of electron-boson coupling in half-metallic ferromagnet Mn${}_5$Ge${}_3$: study of electron self-energy $\mathrm{\Sigma }(\omega )$ obtained from infrared spectroscopy

We report results of our infrared and optical spectroscopy study of a half-metallic ferromagnet Mn${}_5$Ge${}_3$. This compound is currently being investigated as a potential injector of spin polarized currents into germanium. Infrared measurements have been performed over a broad frequency (50 - 50000 cm${}^{-1}$) and temperature (10 - 300 K) range. From the complex optical conductivity $\sigma (\omega )$ we extract the electron self-energy $\mathrm{\Sigma }(\omega )$. The calculation of $\mathrm{\Sigma }(\omega )$ is based on novel numerical algorithms for solution of systems of non-linear equations. The obtained self-energy provides a new insight into electron correlations in Mn${}_5$Ge${}_3$. In particular, it reveals that charge carriers may be coupled to bosonic modes, possibly of magnetic origin.