DYNAMICAL NONLINEAR RESPONSES AND PHASE TRANSITION IN COMPLEX SYSTEMS

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Successive ordering processes in some complex systems such as graphite intercalation compounds (GIC) or ceramic superconductors have been studied in order to search a universal nature of the characteristic phase transitions introduced by the mesoscopic structure. For the experimental method, nonlinear response (X_2) analyzes are usefully employed in consideration of fluctuations of the mesoscopic clusters at very low frequencies. To this end, a new measuring system, which detects fundamental and highher harmonic responses in a wide frequency range of mHz-120Hz, was constructed.A divergent singularity of X_2 is observed for CoC1_2-GIC at the upper critical point where the intra-cluster long range order appears. This singularity changes from symmetric into antisymmetric when the excitation amplitude is reduced or the frequency is raised enough. Such a behavior indicates that the intra-cluster ferromagnetic critical phenomenon reflects on X_2 when the response of the cluster moment is restrained by the slow relaxation and some pinning field. From the results, some random energy barrier which causes the cluster moments to get into meta stable state can be suggested.As for a series of ceramic YBa_2Cu_4O_8 prepared under several sintering conditions, two step superconducting orderings are observed. The sharp lower critical points are almost independent of the applied field, whereas their locations distinctly depend on the sintering temperature. Considering the facts together with the mesoscopic grain structure, the critical behavior can be taken as a certain thermodynamic phase transition where inter-grain phase coherence is established cooperatively by weak junctions among the grains. The observed X_2 singularity at the critical point might be, therefore, a critical phenomenon of XY model with some randomness.