Brillouin spectroscopy of the incommensurate phase of BaMnF4

The first determination of quantitative values characterizing relaxation near an incommensurate-normal phase transition is reported. Also, the first Brillouin scattering data near such a transition are presented. A frequency-dependent elastic anomaly in BaMn${\mathrm{F}}_4$ is attributed to interaction of the acoustic mode with a soft overdamped excitation which may be a "phason." Phasons are predicted as a result of an incommensurate crystal structure, and available theories indicate that they are overdamped. The elastic anomaly is approximately 26% at ultrasonic frequencies, but decreases to under 1% above 4 GHz. Because of this dispersion, the anomaly was only observable with the unusual technique of small-angle Brillouin scattering. A linear interaction model is found to fit the data, with the phason relaxation time following the dependence $\frac{1}{\left(2\mathrm{}\pi \tau \right)}=(6.7\mathrm{}\pm 0.4)\times {10}^8+(1.7\mathrm{}\pm 0.7)\times {10}^{11} \left[\frac{(T_0-T)}{T_0}\right]$ Hz, where $T_o=249\mathrm{}\pm 1°$K is the incommensurate-normal transition temperature for the sample used. The intensity and linewidth of the central mode are measured near $T_0$ and found to agree with theory.