Infrared spectroscopy of Cr and V doped Sb$_2$Te$_3$: dilute magnetic semiconductors*

Temperature dependent optical reflectance measurements on well characterized samples of non-intentionally doped, Cr-doped and V-doped Sb$_2$Te$_3$ show that both the parent compound and the Cr-doped version are narrow-gap semiconductors (E$_g\approx 0.25$ eV) with a conventional Drude free carrier absorption. The carrier density increases slightly with decreasing temperature while the scattering rate increases quadratically with temperature which is a sign of optical phonon scattering. Vanadium doping introduces a change in the temperature dependence of the scattering rate as well as higher electrical resistivity than Cr-doped Sb$_2$Te$_3$. An analysis of the literature values of the saturation magnetization for $H\parallel c$ suggests that V is in a mixed valence state V$^{3+}$/V$^{4+}$.