Crossover from paramagnetic to diamagnetic ac-susceptibility in Bi₂Sr₂CaCu₂O${}_{8+\delta }$ superconductor for $H||c\text{-}axis$

Ac-susceptibility measurements of the superconducting Bi₂Sr₂CaCu₂O${}_{8+\delta }$ single crystal for $H||c$-axis are presented. In low frequency measurements the first harmonic ac-susceptibility, ${\chi }_1={\chi }_1^{\prime }-i{\chi }_1^{\prime \prime }$, is real and independent of the amplitude of the ac-magnetic field (linear behavior) and positive, implying that it represents the slope of the magnetization curve as the temperature changes below T _c2. The positive ac-susceptibility before becoming negative, at low temperatures, forms a positive local maximum arising from the melting transition of the Abrikosov vortex lattice. For higher frequencies the response becomes diamagnetic due to the eddy currents. The signature of the discontinuous change of the magnetization, at the melting transition in higher frequency measurements, is a sharp shoulder near the complete screening. The presence of second harmonic susceptibility in the liquid regime implies nonlinear variation of the equilibrium magnetization. (paper)