Effect of carbon doping on optical constants of half-metallic ferromagnet Mn$_{5}$Ge$_{3}$

Mn$_{5}$Ge$_{3}$ is an intermetallic ferromagnetic compound with the high Curie temperature ($T_{C}$ = 296 K), a high spin polarization ($P$ = 42{\%}), and a good lattice match to germanium. Doping of Mn$_{5}$Ge$_{3}$ with carbon increases $T_{C}$ above room temperature and makes these compounds promising candidates for spin injectors for potential spintronics applications. In this study we employ optical spectroscopy to measure near-normal reflectance in the frequency range from far-infrared to ultraviolet (70 -- 50000 cm$^{-1})$ at temperatures between 10 and 300 K. In particular, we study the effect of carbon doping on the optical constants to gain a better insight into how it affects the electronic properties of the parent compound.