Intrinsic small polarons in rutile TiO2

Abstract

Electron paramagnetic resonance (EPR) is used to identify the intrinsic electron small polaron in TiO${}_{2}$ crystals having the rutile structure. These self-trapped electrons are produced at very low temperature with 442 nm laser light. The defects form when a Ti${}^{4+}$ ion at a regular lattice site traps an electron and converts to a Ti${}^{3+}$ (3${d}^{1}$) ion. They become thermally unstable above \ensuremath{\sim}15 K. An activation energy of 24 meV describes this ``release'' of the electrons (either by a hopping motion or directly to the conduction band). The $g$ matrix is obtained from the angular dependence of the EPR spectrum. Principal values are 1.9807, 1.9786, and 1.9563 and principal axes are along high-symmetry directions in the crystal. The unpaired electron occupies an $|{x}^{2}\ensuremath{-}{y}^{2}\ensuremath{\rangle}$ orbital where $x$ and $y$ are in the equatorial plane of the TiO${}_{6}$ unit and $y$ is the [001] direction. These intrinsic small polarons serve as a prototype for many of the defect-associated Ti${}^{3+}$ ions often observed in this material. They also can be used as a computational test case to evaluate the validity of different approximations presently being employed in density-functional-theory modeling of point defects in TiO${}_{2}$ and other transition-metal oxides.