Softening of low-energy anharmonic phonon modes in rutile TiO 2 investigated by inelastic x-ray and neutron scattering

Low-energy anharmonic phonons in rutile TiO 2 were investigated by inelastic x-ray and neutron scattering (IXS and INS) techniques. Owing to the different sensitivities of IXS and INS to phonon modes, the transverse optical branches corresponding to the B 1u and A 2u modes at the Γ point were selectively observed in the respective spectra. It was found that the lowest-energy B 1u mode exhibits pronounced softening with decreasing temperature, while the A 2u mode also shows softening, as previously reported. The observed temperature-dependent softening was well reproduced by density functional theory calculations based on the stochastic self-consistent harmonic approximation, although the magnitude of the softening was quantitatively underestimated. The pronounced softening of the B 1u mode, as well as its finite linewidth, is discussed in terms of possible higher-order phonon interactions between the B 1u and A 2u modes. The implications of this strong anharmonicity for lattice-related physicochemical properties, including dielectric response, thermal transport, Li-ion insertion, and polaron-related photocatalytic phenomena, are also addressed.