Fractional-exponent behavior of magnetization near Tc in Bi2Sr2CaCu2O8

Using high-resolution torque magnetometry, we have investigated in detail how long-range phase coherence develops as the critical temperature T_c (88.7 K) is approached in optimally-doped Bi₂Sr₂CaCuO_8+δ with field H||c. Three distinct regimes are observed. Above ∼92 K, |M| increases rapidly as T->T_c in step with the vortex Nernst signal. M is strictly linear in H in weak H, but shows strong curvature at large H (5-14 T). The curvature provides a determination of the correlation length ξ_sc which grows as a power law, viz. ξ_sc∼1/t^ν. In the second regime, 86 < T < 92 K, M becomes nonlinear in H, viz. M∼H^α(T), where the exponent α(T) decreases from 1 to 0. This interesting fractional-exponent behavior is highly unusual and fits poorly with conventional pictures of `fluctuating diamagnetism.' As previously known, M is virtually H independent below 2 Tesla at the ``crossing temperature'' T_cr = 86 K. Below T_cr, M is a function of H. We compare this behavior with predictions of the 3DXY and Kosterlitz-Thouless theory. Supported by funds from the U.S. National Science Foundation under grant DMR 0213706.