Mesoscopic fluctuating domains in strontium titanate
Benoît Fauqué, P. Bourges, Alaska Subedi, Kamran Behnia, Benoı̂t Baptiste, B. Roessli, T. Fennell, S. Raymond, P. Steffens
Abstract
Spatial correlations between atoms can generate a depletion in the energy dispersion of acoustic phonons. Two well-known examples are rotons in superfluid helium and the Kohn anomaly in metals. Here we report on the observation of a large softening of the transverse acoustic mode in quantum paraelectric $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ by means of inelastic neutron scattering. In contrast to other known cases, this softening occurs at a tiny wave vector implying spatial correlation extending over a distance as long as 40 lattice parameters. We attribute this to the formation of mesoscopic fluctuating domains due to the coupling between local strain and ferroelectric fluctuations. Thus, a hallmark of the ground state of insulating $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_{3}$ is the emergence of hybridized optical-acoustic phonons. Mesoscopic fluctuating domains may play a role in quantum tunneling, which impedes the emergence of a finite macroscopic polarization.