Magnetoacoustic Attenuation in High-Field Superconductors

A phenomenological model for the magnetic-field variation of the ultrasonic attenuation in the mixed and normal states of a high-field superconductor is developed. It is shown that the attenuation in the mixed state is related to the motion of the Abrikosov flux lines and is greatly affected by the strength of the pinning forces which inhibit this motion. The pinning forces are characterized by the "depinning frequency" ${\omega }_0$. At frequencies well above ${\omega }_0$ the attenuation is directly related to the dc flow resistivity. A method for determining ${\omega }_0$, and hence the strength of the pinning forces, from ultrasonic data is outlined. Ultrasonic-attenuation measurements were carried out on five different high-field superconducting alloys, viz., annealed Nb-25 at.% Zr, Nb-32 at.% Ti, V-42 at.% Ti, V-21 at.% Ti, and unannealed Nb-25 at.% Zr. These measurements were performed at liquid-helium temperatures and in steady magnetic fields up to 100 kG. Shear and longitudinal sound waves, with frequencies ranging from 8 to 56 Mc/sec, were used. The data are compared in detail with the predictions of the phenomenological model. It is found that in all cases there is good agreement between experiment and theory. In particular, it is shown that estimates of the depinning frequency obtained from the ultrasonic data agree with those derived from critical-current measurements carried out on the same materials.