Specific Heat and Paramagnetic Susceptibility of Stoichiometric and Reduced Rutile (TiO2) from 0.3 to 20 K

Abstract

The specific heat of rutile (Ti${\mathrm{O}}_{2}$) has been measured between 0.3 and 20 K in different magnetic fields, and for various degrees and types of reduction. In addition, the paramagnetic susceptibility has been measured below 4.2 K for three reduced samples. The parameters which characterize the specific heat of the stoichiometric boule include a Debye $\ensuremath{\Theta}$ at $T=0$ of 778 K, an optical mode of Einstein frequency 83 ${\mathrm{cm}}^{\ensuremath{-}1}$, and an impurity of 1.08 ppm ${\mathrm{Fe}}^{3+}$. The specific heat of all reduced samples indicates that there is a narrow intrinsic conduction band lying below the wider conduction band seen above 30 K. The electrons in this band have a density-of-states effective mass of $190{m}_{e}$. The specific heat of a vacuum-reduced sample in zero field and two magnetic fields is reproduced by a model which has 1.1\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$ impurity-related spin-degenerate levels 1.8\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV below the narrow band. In the more highly reduced samples, the defects are not impurity-related. Below 1.2 K, the specific heats and magnetic susceptibility of highly reduced rutile are characteristic of a paramagnetic ion with two energy levels about ${10}^{\ensuremath{-}4}$ eV apart. Hydrogen reductions result in interaction between the ions. The activation energy to the band is about 5\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ eV for rutile reduced highly without the use of hydrogen, but no activation energy is evident for hydrogen-reduced material. A decrease in the specific heat near 20 K is not understood. It may be explained as being due to a decrease in the lattice specific heat with reduction. It also may be due to electrons approaching the top of the band which then narrows with increasing temperature because of small polaron effects.