Nonlinear electrodynamics in granular ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$: Measurements and models of complex permeability

Measurements in ac and dc magnetic fields on a sintered rod of ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ at 77 K yield a clear distinction between inter- and intragranular contributions to the complex harmonic permeability μ̃=${\mathrm{\mu }}_{\mathrm{n}}^{\prime }$-i${\mathrm{\mu }}_{\mathrm{n}}^{\mathrm{″}}$: two peaks in ${\mathrm{\mu }}_1^{\mathrm{″}}$(${\mathrm{H}}_{\mathrm{ac}}$) are clearly observed. These data, together with harmonic-power ${\mathrm{P}}_{\mathrm{n}}$(${\mathrm{H}}_{\mathrm{dc}}$) measurements, are found to be well explained by a modified critical-state model, which, for fields ≲50 Oe, is dominated by intergranular critical currents ${\mathrm{J}}_{\mathrm{c}}$(H)∼${\mathrm{H}}_{\mathrm{loc}}^{\mathrm{-}2}$, a steeper field dependence than the original Bean-Anderson-Kim model.