We have studied the lattice dynamics of crystalline ${\text{TiO}}_2$ using density-functional perturbation theory and the local-density approximation in a plane-wave pseudopotential formalism at equilibrium and uniaxially strained geometries. We present well-converged calculations of the dispersion curves, which sample a more complete volume of the Brillouin zone than in previous studies. We find an anomalously soft TA mode in a region of reciprocal-space previously unexplored either by any previous calculation or experiment. This is quite separate from the ${\text{A}}_{2\text{u}}$ mode which becomes soft at the $\mathbf{\Gamma }$ point and is responsible for the incipient ferroelectric behavior. The harmonic frequency of the soft TA mode around $q=\left(\frac{1}{2},\frac{1}{2},\frac{1}{4}\right)$ decreases to zero under an isotropic expansion with a strain slightly above 0.5% and we suggest that it may be possible to observe anomalous diffuse inelastic scattering corresponding to a dynamical instability using neutron scattering. In addition to the softening under isotropic strain, the frequency of this mode goes to zero under uniaxial strain along the [110] direction in both compression and expansion (at close to $-0.5\mathrm{\%}$ and $+1.0\mathrm{\%}$, respectively), which offers new possibilities for experimental tests of softening under compressional strain. We further suggest that the soft TA mode may help explain the anomalously long-ranged convergence observed in previous calculations on slab models of the ${\text{TiO}}_2$ (110) surface by providing a mechanism for small changes in bonding at the surface to propagate deep into the bulk. The behavior of other modes under strain was also studied. The ferroelectric ${\text{A}}_{2\text{u}}$ mode frequency is nearly independent of [110] strain, which contrasts with the behavior in response to [001] strain reported in the literature of a strong dependence. However, the frequency of the Raman-active ${\text{B}}_{2\text{g}}$ mode does decrease to zero frequency under 1.3% strain, which should be observable using Raman spectroscopy.

• Received 4 December 2009

DOI:https://doi.org/10.1103/PhysRevB.81.134303