Nonlinear electrodynamics in the granular superconductor Y${\mathrm{Ba}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$: Experiments and interpretation

For bulk samples of superconducting Y${\mathrm{Ba}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ powder and pellets subject to a dc magnetic field $H_0$ and a parallel ac magnetic field $H_1$ at frequency $f\sim {10}^3 \mathrm{to} {10}^5$ Hz, we report data on the generated harmonic power $P\left(\mathrm{nf}\right)\mathrm{}$ up to harmonic $n\approx 40$, finding: (1) If $H_0=0\mathrm{}$, only odd harmonics; (2) if $H_0\ne 0$, even harmonics are additionally generated; (3) for $H_1$ sufficiently large (≳ 10 Oe) and $n$ large, then $P\left(\mathrm{nf}\right)\mathrm{}$ vs $H_0$ displays sharp and deep periodic dips, revealing a remarkably consistent and reproducible macroscopic flux quantization for the bulk sample. These data, as well as the relative intensities of the harmonic power, are found to be in semiquantitative agreement with detailed numerical predictions of a dynamical model of the material as a suitably averaged ensemble of prototype flux quantized loops with weak links. At lower values of $H_1$ additional structure is observed, related to fluxon pinning and depinning.