Title:

Phase transitions in spinphonon systems

General symmetry arguments show that an elastic constant should vanish when a crystal undergoes a second order structural phase transition. A detailed theory of the elastic anomaly is developed for DyVO_{4}, TbVO_{4}, and TmVO_{4}, which have crystallographic phase changes caused by the JahnTeller effect at 14, 34 and 2.1Â°K respectively. The theory predicts that the elastic constant ½(c_{11}c_{12}) should fall to zero at the transition temperature T_{D} for DyVO_{4}, and that c_{66} should vanish for TbVO_{4}, and TmVO_{4}. These conclusions have been verified experimentally. For DyVO_{4} the electron lattice interaction is predominantly of short range and a cluster theory has been used to interpret the results. For the other crystals a molecular field theory has been used to calculate the elastic constants under different thermodynamic regimes and the random phase approximation has been used in a treatment of the elementary excitations. In TbVO_{4} and TmVO_{4}, the theory predicts that the elastic constant only falls to zero at T_{D} when measured at a sufficiently low frequency. This frequency dependence has been observed in TbVO_{4}, and is satisfactorily described by the theory. At the first order 95Â°K phase change in DySb the elastic constant ½(c_{11}c_{12}) is observed to soften but not to vanish, consistent with general symmetry arguments. A theory of this anomaly has been developed within the molecular field approximation. Satisfactory agreement with experiment is obtained for T>T_{D} but there are large unresolved discrepancies in the low temperature phase. A theory for the elastic constant and spontaneous polarization of the ferroelectric KH_{2}PO_{4} has been developed. One of the lattice vibrational modes is written in a pseudcspin formalism and four spin interactions have been included in the model. Although the theory gives a reasonable account of the data some discrepancies still remain. Coupling between pairs of phonons and the soft mode in hydrogen bonded ferroelectrics has been investigated in the pseudospin model. An anomalous dielectric response is predicted similar to earlier work on the anharmonic phonon theory [71]. A frequency dependence of the elastic constants is expected but this has not yet been observed. An analysis of Raman scattering data shows that the low frequency anomaly is a small effect in KDP, KDA and CsDA contrary to an earlier analysis of the data [70]. When a magnetic field is applied in the hard direction of an anisotropic ferromagnet qualitative arguments show that an elastic constant should vanish when the moments line up parallel to the hard axis. These conclusions have been verified for a particular model of the ferromagnetic phase of Dy and Tb metal.
