Experimental study of scaling laws for the complex susceptibility of type-II superconductors

Measurements of the nonlinear complex susceptibility $\chi ,$ taken as a function of amplitude h and frequency $\nu$ of the ac field, can collapse into a single universal curve if they are plotted against the scaling variable $hJ\left({\nu }_{\mathrm{ref}}\right)/J\left(\nu \right),$ where J is a shielding current density and ${\nu }_{\mathrm{ref}}$ is an arbitrary reference frequency. In this work we present $\chi (h,\nu )$ data for a large range of amplitudes and frequencies, measured in two Nb samples (one single crystal and one polycrystal) and one melt-textured ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ sample. The predicted scaling relation is verified for several sets of data taken at different temperatures below $T_c$ and applied magnetic fields well above the first critical field $H_{c1\mathrm{}}.$ Data taken closer to $T_c$ revealed a useful scaling applied directly to the critical current density, evaluated from the peak positions of the imaginary component ${\chi }^{″}.$ The occurrence of different regimes of collective vortex creep is also discussed for the ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ sample.