The low-temperature vortex liquid in $\rm La_{2-x}Sr_xCuO_4$ and $\rm Bi_2Sr_{2-y}La_yCuO_6$

Diamagnetism in lightly-doped crystals of $\rm La_{2-x}Sr_xCuO_4 $ (LSCO)with doping $x$ = 0.03 to 0.09 has been investigated by torque magnetometry, which resolves weak 2D supercurrents against a nearly isotropic paramagnetic spin response.By carefully subtracting the large paramagnetic susceptibilities of the van Vleck and spin terms, we observe the diamagnetic signal of vortices in fields up to 45 T, even for $x$ as low as 0.03. The torque results allow the $x$ dependence of both the melting field $H_{irr}$ and upper critical field $H_{c2}$ to be measured. We find that $H_{c2}$ extends smoothly across the critical doping value $x_c\simeq 0.055$. Below $x_c$, the pair condensate survives as a vortex liquid in intense fields, but long-range phase coherence is absent down to our lowest temperature $T$ = 0.35 K. We discuss the interesting differences between the vortex liquid and solid phases, and the collapse at low $T$ of phase coherence at the boundary. The close correlation of $T_{onset}$ to $H_{c2}$ in LSCO and Bi 2201 will also be reported. Resarch supported by NSF grant DMR 0213706.