Ultrasonic investigation of critical dynamics in KMnF3

Abstract

An extensive ultrasonic investigation of the cubic-tetragonal phase transition in KMn${\mathrm{F}}_3$ with respect to temperature, frequency, mode, and sample dependence has been carried out by means of wave-vector-reversed echo technique as well as conventional pulse reflections. All measurements of the attenuation $\alpha$ obey a dynamic scaling law $\alpha \sim {\omega }^2{t}^{-\rho }G\left(\omega \tau \right)$. We have measured $\rho =1.87\mathrm{}\pm 0.05$, in accord with the predictions of the three-dimensional Heisenberg model, a result which is consistent with the expected value $\phi \approx 1.26$ for the anisotropy cross-over exponent. The relaxation time $\tau$, governing the dynamics of ordered clusters, is found to be $\approx (9\mathrm{}\times {10}^{-13\mathrm{}})t^{-1.41\mathrm{}}$ s. The form of the scaling function $G$ is experimentally determined, and its expected limiting forms at low and high $\omega \tau$ values discussed.