Quadratic Field Dependence of Ultrasonic Attenuation Coefficient in Paramagnetic Holmium

The ultrasonic attenuation coefficient ${\alpha }_k$ has been measured in the paramagnetic phase of Ho in fields from 0 to 50 kG. ${\alpha }_k$ increased as the square of the field and decreased as the temperature increased. A model has been developed which ascribes this increase in ${\alpha }_k$ to the interaction of the longitudinal phonons, via modulation of the exchange interaction, with the spin fluctuations associated with the virtual phase transition at the paramagnetic Curie temperature. This theory also agrees with the velocity data obtained by Moran and Lüthi.