Strongly nonlinear magnetization above $T_c$ in $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$

Using high-resolution magnetometry we have investigated in detail the magnetization $M$ above the critical temperature $T_c$ in $\rm Bi_2Sr_2CaCu_2O_{8+\delta}$. In a broad range of temperature $T$ above $T_c$, we find that $M(T,H)$ is strongly non-linear in the field $H$. We show that as $T\to T_c$, the susceptibility $\chi(T,H)$ diverges to very large values ($\chi \to$ -1) if measured in weak $H$. In addition, $M(H)$ displays an anomalous non-analytic form $M\sim H^{1/\delta}$ in weak fields with a strongly $T$-dependent exponent $\delta(T)$. These features strongly support the proposal that, above $T_c$, the pair condensate survives to support significant London rigidity.