Comment on the physical mechanisms of the 37 K and 65 K anomalies in strontium titanate

We show that the relaxation mechanism for ultrasonic and dielectric anomalies at 65 K is due to long-wavelength (q=0) optical phonons that would be described at Γ25' (F2g) in the cubic Oh high-temperature phase whose frequency is known to be 62 meV (499 cm-1) at the R-point Brillouin zone boundary; for the anomaly at 37 K the interaction is also with a q=0 phonon, but it is with a different symmetry silent F2u branch of the Oh phase at 33 meV (268 cm-1). Since the eigenvector of this mode at 33 meV is known exactly (it is the only mode having the F2u irreducible representation) and since it involves only oxygen motion (by symmetry), we can conclude rigorously that only oxygen displacements contribute to the dielectric relaxation at 37 K. The other temperatures at which the dielectric loss exhibits maxima (namely, 8, 18 and 30 K) are all proportional to the known energies of q=0 transverse optical phonons (at 48, 110 and 171 cm-1), suggesting that the observed sequence of five relaxation peaks involves the same defect (polar clusters of oxygen vacancies?) interacting in turn with each phonon mode as temperature is increased. This provides a single mechanism for all relaxation peaks, which heretofore had received interpretation in terms of qualitatively different mechanisms. (author)