Effect of quantum fluctuations of vortices on reversible magnetization in high-Tc superconductors

The field (B) and temperature dependence of reversible magnetization M in Bi (2:2:1:2) single crystals is measured for the orientation of the field along the c axis. The slope of the curve M vs lnB decreases remarkably with field below 70 K. In the mean-field approach this slope should be almost B independent. We explain this change of slope by the quantum fluctuations of vortices. We show that for magnetization quantum fluctuations are important at all temperatures except in a narrow region near Tc.