Longitudinal ultrasonic attenuation in the spin spiral state of single crystal holmium

Ultrasonic attenuation experiments have been performed using 15–255 MHz longitudinal sound waves along the c-axis of single crystal holmium. Without an external magnetic field, the attenuation increases in the spin-spiral state. This anomalous increase originates, at least in part, from the spin-phonon relaxation mechanism we have proposed, which states that the attenuation coefficient Δα₁ ∞ ω²/(1+ω²τ²) where τ is the longitudinal spin phonon relaxation time. The frequency dependence of the attenuation varies from ω^1·0 to ω^1·5 which suggests a frequency-dependent character for the spin-phonon relaxation time τ. A broad longitudinal attenuation maximum, which presumably is due to the competing processes between $\overline{S}$, J and τ, is observed in the spin-spiral state, where $\overline{S}$ is the thermal average of the spin angular momentum per trivalent ion and J the Fourier transform of the exchange integral. An anomalous suppression of the longitudinal attenuation spike at T_N for frequencies higher than 165 MHz is unexplainable at present. The longitudinal attenuation spike at T_N for frequencies higher than 165 MHz is unexplainable at present. The longitudinal spin-phonon relaxation time for Ho has been determined using experimental data. It has a T^?3 temperature dependence. In the presence of an external magnetic filed in the basal plane the attenuation is decreased and a new peak and a plateau appear at the intermediate phase transitions.