Equilibrium magnetization of a ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{\mathit{x}}$ single crystal measured up to 20 T

The reversible magnetization of a high quality ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{\mathit{x}}$ crystal has been measured by torque magnetometry at fields up to 20 T and temperatures ranging from 40 to 100 K. For fields above 7 T the superconducting diamagnetic moment follows a simple London-like behavior (${\mathit{M}}_{\mathit{S}}$∝lnB). For lower fields, we observe a strong dependence of ${\mathit{dM}}_{\mathit{S}}$/dlnB on the magnetic field B. The results are discussed in terms of quantum and classical fluctuations of pancake vortices.