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Magnetization M and heat capacity C were measured around the first order vortex transition lines of two Bi 2 Sr 2 CaCu 2 O 8 + δ single crystals having different oxygen contents. The entropy jump per vortex per layer, Δs , at the transition was estimated from the step in M . The oxygen-content dependence of Δs was contradictory to the simple vortex lattice melting theory based on the Lindemann criterion. In both crystals, no anomalies in C were observed at the transition owing to both the small Δs and the broadening of the transition.

We have measured the magnetization and the heat capacity of over-doped (OVD) and optimally doped (OPD) Bi 2 Sr 2 CaCu 2 O y single crystals in the mixed state under magnetic fields applied along the c -axis. In both samples, a distinct magnetization step is observed in the magnetization curve at high temperatures and is found to change to a kink at low temperatures. At still lower temperatures, the peak effect dominates the magnetization curve and the kink vanishes. The origin of the step and the kink in the magnetization curve is considered to be the first-order phase transition in a quasi-three-dimensional vortex system although the heat capacity shows little anomalies at the transition because the latent heat is small. The first-order phase transition line of each sample is drawn on the H - T plane and it is found that the slope of the line of the OVD sample is steeper than that of the OPD sample. The entropy jump at the transition of the OVD sample is estimated to be larger than that of the OPD one at all temperatures and magnetic fields studied. This behavior is contradictory to the simple vortex-lattice melting picture.

We measured a bulk magnetization and heat capacity of Bi2Sr2CaCu2Oy single crystals with different oxygen stoichiometry in the mixed state. The samples show a magnetization step, indicating a first order transition in high temperature region. With lowering temperature, the step changes into some depression-and-kink structure, then vanishes when the second peak appears. The first order transition line is found to become steeper with increasing oxygen content. It is also found that the transition line seems to be terminated by the second peak field. We also measured heat capacity of the same samples. However, neither latent heat nor any other anomaly was detected, possibly because of the non-uniformity of the field distribution inside the plate-like samples.

The second peak effect in the magnetisation of Bi2Sr2CaCu2O8+δ has been investigated for both under-, near optimally-, and over-doped single crystals. The size and position of the peak depend strongly on the doping, and hence anisotropy, showing a large enhancement in the overdoped sample. For all states, though, the peak persists to high temperatures, with no evidence for an intersection of the curve describing peak position in the H-T plane with the irreversibility line. The temperature dependence can be described with recent theories of a 3D-2D transition in the vortex system, allowing derivation of values of the anisotropy γ. This interpretation is supported by μSR experiments on the same samples which indicate a reduction of vortex dimensionality at crossover fields matching the peak fields.

In Bi2Sr2CaCu2Oy under magnetic fields along the c-axis, both the local and the macroscopic magnetization show clear steps indicating the first order phase transition (FOPT) in the vortex lattice (VL). Local measurements have revealed that the FOPT occurs from the center of the sample owing to the field inhomogeneity originated from the geometrical effect. The heights of the steps are strongly suppressed in local measurements by the demagnetization effect. With decreasing temperature, the irreversibility in the magnetization just below the step begins to increase and is smoothly connected to the second peak at low temperatures.

The deviation of magnetic relaxation from the usual logarithmic decay in type-II superconductors was analyzed in terms of the first-order kinetic relaxation process. The theoretical and experimental results show that the relaxation of magnetic induction B obeys the power law equation, namely, B=B 0 +B 1 t -α, where B 0 is the \lq\lqequilibrium" value of the magnetic induction, and B 1 and α are field- and temperature-dependent constants. It was found that α, which is related to the pinning potential barrier, varies with temperature following the Arrhenius-type thermal activation behavior. Based on the present phenomenological theory, the current J dependence of the apparent activation energy U a is discussed by using the relaxation data of a Bi2.1Sr1.8Ca1.0Cu2.0O8+δ single crystal.