Ultrasound and vortex oscillations in high-temperature superconductors

An HTSC powder sample with grain (particle) diameter of 20–50 $\mu$m placed in a dc magnetic field $B_0$ and cooled to a temperature below the superconducting transition temperature was exposed to the radiofrequency (rf) pulsed magnetic field $B_\sim(B_\perp B_0)$ at a carrier frequency of 30.7 MHz. Stable echo signals were recorded which followed different rf-pulse trains. This phenomenon has the following mechanism. The rf magnetic field stimulates fluxoid oscillations on the HTSC grain surface, which are transformed into lattice oscillations through the pinning centers and induce a propagating sound wave. The second-order nonlinearity with respect to the gradient of the crystal lattice deviation from the equilibrium position taken into account in the sound wave equation yields the dependence of the crystal lattice natural frequency on the amplitude and length of the pulses which excite these oscillations. This dependence is responsible for the emergence of echo signals.