Magnetic properties and superconducting-fluctuation diamagnetism above ${\mathit{T}}_{\mathit{c}}$ in ${\mathrm{Bi}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ (x=0.0, 0.1, 0.2, 0.3, 0.5) and ${\mathrm{Bi}}_{2\mathrm{-}\mathit{x}}$${\mathrm{Pb}}_{\mathit{x}}$${\mathrm{Sr}}_2$${\mathrm{Ca}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_{10+\mathrm{\delta }}$ (x=0.2, 0.25)

The magnetic susceptibilities χ(T) of the title compounds above and below ${\mathit{T}}_{\mathit{c}}$ are reported. For the ${\mathrm{Bi}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Pb}}_{\mathit{x}}$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$ (Bi 2:2:1:2) system, optimization of the phase purity and superconducting properties is found between x=0.2 and 0.3. The χ(T) data for these Bi 2:2:1:2 and for the two Bi 2:2:2:3 samples increase monotonically with temperature from ${\mathit{T}}_{\mathit{c}}$ up to at least 400 K, exhibiting strong negative curvature below ∼200 K. From theoretical fits to the data in the two-dimensional regime above ${\mathit{T}}_{\mathit{c}}$ using the static Lawrence-Doniach model as modified by Klemm, we conclude that the negative curvature in χ(T) for each sample arises from superconducting-fluctuation diamagnetism (SFD). The data are thus consistent with a superconducting order parameter of s-wave symmetry. From the fits to the data, the Ginzburg-Landau coherence lengths in the ${\mathrm{CuO}}_2$ planes were obtained and found to be ${\xi }_{\mathit{a}\mathit{b}}$(0)=20.4(2) Å for Bi 2:2:1:2 and 11.8(4) Å for Bi 2:2:2:3. The value for Bi 2:2:1:2 is comparable to those calculated from upper critical magnetic-field data for this compound (23.5–27.1 Å). Our ${\xi }_{\mathit{a}\mathit{b}}$(0) values for Bi 2:2:1:2 and Bi 2:2:2:3 are also comparable with that (13.6 Å) found from our previous similar analysis of the SFD in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$. The possible role of the bridging oxygens out of the ${\mathrm{CuO}}_2$ plane in Bi 2:2:2:3 and the influence of the dynamics in the fits to the SFD in the Bi-based compounds remain to be addressed.