Electromagnetic generation and detection of ultrasound in superconductors

Abstract

The magnetic field dependence of electromagnetically generated and detected acoustic waves has been measured in single crystals of two type-II superconducting alloys, Pb-In and Nb-Mo. Measurements span the complete field region in the mixed state, temperatures range from 1.5 to 4.2 K, and frequencies cover the 3-90-MHz region. At frequencies where the classical skin depth ${\ensuremath{\delta}}_{c}\ensuremath{\gtrsim}\ensuremath{\lambda}$, the acoustic wavelength, the acoustic amplitude increases as the field is decreased into the mixed state, reaches a maximum at some field below ${H}_{c2}$ and then goes continuously to zero as $H\ensuremath{\rightarrow}0$. These observations can be explained very well by a local model based upon the Lorentz force acting upon currents induced within the electromagnetic skin depth. With decreasing static magnetic field, the electromagnetic screening of the mixed state becomes increasingly more effective; the skin depth decreases from the classical skin-effect value in the normal state just above ${H}_{c2}$ (${\ensuremath{\delta}}_{c}\ensuremath{\sim}100$ \ensuremath{\mu}m) to the London penetration depth (${\ensuremath{\lambda}}_{L}\ensuremath{\ll}1$ \ensuremath{\mu}m) at zero field. Using the surface resistance as a relative measure of the skin depth, good agreement is obtained between the observed and predicted values for electromagnetic acoustic-wave detection. Thus, it appears that the general features of theories used to explain electromagnetic detection of acoustic waves in normal metals are valid even when superconductive screening currents are involved.