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 anomali es at 65 K is due to long-wavelength (q = 0) optical phonons that would be described at Gamma(25)' (F-2g) in the cubic O-h high-temperature phase whos e frequency is known to be 62 meV (499 cm(-1)) at the R-point Brillouin zon e boundary; for the anomaly at 37 K the interaction is also with a q = 0 ph onon, but it is with a different symmetry silent F-2u branch of the O-h pha se at 33 meV (268 cm(-1)). Since the eigenvector of this mode at 33 meV is known exactly tit is the only made having the F-2u irreducible representati on) and since it involves only oxygen motion (by symmetry), we can conclude rigorously that only oxygen displacements contribute to the dielectric rel axation at 37 K. The other temperatures at which the dielectric loss exhibi ts maxima (namely, 8, 18 and 30 K) are all proportional to the known energi es of q = 0 transverse optical phonons (at 48, 110 and 171 cm(-1)), suggest ing that the observed sequence of five relaxation peaks involves the same d efect (polar clusters of oxygen vacancies?) interacting in turn with each p honon mode as temperature is increased. This provides a single mechanism fo r all relaxation peaks, which heretofore had received interpretation in ter ms of qualitatively different mechanisms.