High-Frequency Sound Propagation near Magnetic Phase Transitions

The results of ultrasonic attenuation and velocity experiments near the magnetic phase transitions in RbMn${\mathrm{F}}_3$ and Mn${\mathrm{F}}_2$ are presented. For $T>\mathrm{}{T}_N$, the data give additional evidence that the sound couples to the spin-energy-density fluctuations which decay via spin-lattice relaxation. The attenuation results for RbMn${\mathrm{F}}_3$ could be fitted with a single relaxation formula for the frequency range 90-930 MHz and for the temperature range of $\epsilon [=\frac{(T-T_N)}{T_N}]$ from ${10}^{-4\mathrm{}}$ to ${10}^{-2\mathrm{}}$. The spin-lattice relaxation time ${\tau }_L$ was found to vary from 4×${10}^{-10\mathrm{}}$ to 2×${10}^{-10\mathrm{}}$ sec in the same $\epsilon$ range. Furthermore, both the critical attenuation and velocity changes are independent of sound-wave propagation direction. In Mn${\mathrm{F}}_2$, we found from the critical velocity dispersion a constant relaxation time ${\tau }_L=(2.7\mathrm{}\pm 0.2)\times {10}^{-9\mathrm{}}$ sec for $\epsilon \ge {10}^{-3\mathrm{}}$, in good agreement with Kawasaki and Ikushima's quoted value. A small divergence was found for smaller $\epsilon$. For $T<\mathrm{}{T}_N$, it was found that the maxima of the attenuation and the minima of the velocity shifted to lower temperatures with increasing frequency in RbMn${\mathrm{F}}_3$. In addition, in RbMn${\mathrm{F}}_3$, a second attenuation peak was found below $T_N$ which shifted to lower temperatures with increasing frequency. This subsidiary attenuation peak was found to be strongly sample dependent. In Mn${\mathrm{F}}_2$, broad attenuation maxima and velocity minima are observed in the ordered region. Possible mechanisms for these effects are discussed.