Fundamental and harmonic susceptibilities of ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$

We have examined the complex harmonic magnetic susceptibilities ${\mathrm{\chi }}_{\mathrm{n}}$=${\mathrm{\chi }}_{\mathrm{n}}^{\prime }$-i${\mathrm{\chi }}_{\mathrm{n}}^{\mathrm{″}}$ (n=1,2,3,...,10) of the sintered high-critical-temperature (high-${\mathrm{T}}_{\mathrm{c}}$) superconductor ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. The experimental variables for the measurements of ${\mathrm{\chi }}_{\mathrm{n}}$ were the sample temperature T (10⩽T⩽110 K), the ac magnetic field amplitude ${\mathrm{H}}_{\mathrm{ac}}$ (1.4 μT⩽${\mathrm{\mu }}_0$ ${\mathrm{H}}_{\mathrm{ac}}$⩽8.5 mT), frequency f (7.3⩽f⩽1460 Hz), and the magnitude of a superimposed dc field ${\mathrm{H}}_{\mathrm{dc}}$ (|${\mathrm{\mu }}_0$ ${\mathrm{H}}_{\mathrm{dc}}$|⩽8.5 mT). As functions of temperature, ${\mathrm{\chi }}_1^{\prime }$ and ${\mathrm{\chi }}_1^{\mathrm{″}}$ depend on both ${\mathrm{H}}_{\mathrm{ac}}$ and ${\mathrm{H}}_{\mathrm{dc}}$. In particular, the ${\mathrm{\chi }}_1^{\prime }$ transition curve can shift to higher temperatures with increasing ${\mathrm{H}}_{\mathrm{dc}}$. Odd-harmonic susceptibilities were measured as functions of temperature below ${\mathrm{T}}_{\mathrm{c}}$ for zero ${\mathrm{H}}_{\mathrm{dc}}$; both even and odd harmonics were observed for nonzero ${\mathrm{H}}_{\mathrm{dc}}$. At fixed temperature, the odd-harmonic susceptibilities are even functions of ${\mathrm{H}}_{\mathrm{dc}}$, while the even-harmonic susceptibilities are odd functions of ${\mathrm{H}}_{\mathrm{dc}}$. We compared the experimental intergrain coupling characteristics of ${\mathrm{\chi }}_{\mathrm{n}}^{\prime }$ and ${\mathrm{\chi }}_{\mathrm{n}}^{\mathrm{″}}$ with theoretical susceptibility curves based on magnetization equations derived by Ji et al. from a simplified Kim model for critical current density. The theoretical curves are in good agreement with the temperature- and field-dependent features of ${\mathrm{\chi }}_{\mathrm{n}}^{\prime }$ and ${\mathrm{\chi }}_{\mathrm{n}}^{\mathrm{″}}$, and, therefore, the intergrain coupling component of a sintered high-${\mathrm{T}}_{\mathrm{c}}$ superconductor behaves as a type-II superconductor.