Vortex dynamics near melting in layered superconductors: Theory versus NMR rerlaxation experiments in organic and HTSC matherials.

The plasticity of vortex crystals, their melting at the line T_m (B) or the corresponding freezing of the vortex liquid are on agenda in current studies of layered superconductors. We analyze the NMR experiments (S.M.De Soto et al.), Phys. Rev. Lett., 70,2956 (1993). (S. Brazovskii, H. Mayaffre, P. Wzietek, D. Jérome, P. Batail, Phys. Rev. Lett., 76) (1996) 4951. and present a detailed related theory of the NMR relaxation by defects and critical fluctuations. We prove the quasi 2D regime with an unexpectedly large concentration of highly diffusive thermally activated defects: interstitials and vacancies below T_m and indicate a presence of unbound 2D dislocations above T_m. Also we interpret the critical 2D regime of freezing above T_m. The picture is based on the analysis of the longitudinal relaxation rate γ (T,B) of the NMR in the layered organic superconductor with respect to a developed theory. The high magnitude of the peak in γ at T_m, its sharpening at lower fields and the "muster curve" structure in the family of lines γ (T, B=const) at the low T slope of the peak lead to above conclusions.