Determination of magnetic penetration depth from the reversible magnetization inBi2Sr2CaCu2O8+δ:Dependence on weak disorder and interlayer coupling

Abstract

The reversible magnetization in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ is analyzed within existing theoretical models. The field-induced suppression of the empirical ``superfluid density'' $dM/d(\mathrm{ln}H)$ are compared for the fluctuation mechanism and for the suppression of the order parameter in the vortex core. The thermal fluctuation term is found to be essentially reduced compared to the theoretical prediction for decoupled pancake vortices. We suggest that the energy of Josephson and magnetic coupling between two-dimensional (2D) layers is at the origin of observed decrease in the entropy term. The interlayer coupling is best maintained in samples with reduced disorder. In the samples of the best quality, the fluctuation contribution to the reversible magnetization drops down to less than ${k}_{B}T/10s{\ensuremath{\Phi}}_{0}$ $(s\ensuremath{\approx}15.4\mathrm{\AA{}}\mathrm{}).$ Taking into account this reduction we obtain the curve ${\ensuremath{\lambda}}^{2}(0)/{\ensuremath{\lambda}}^{2}(T)$ versus T from the reversible magnetization similar to the one obtained from measurements of microwave surface impedance, which is also consistent with ${H}_{c1}$ derived from micro-Hall ac technique. The accuracy of determination of ${H}_{c1}$ from the scaled M vs T curves is found to be even better than that for ${\ensuremath{\lambda}}^{2}(0)/{\ensuremath{\lambda}}^{2}(T).$