Experimental evidence of a crossover in the vortex dimensionality in high-T_c superconductors

Quantum motion of vortices in high-temperature superconductors (HTSCs) was studied via magnetic relaxation measurements performed with a commercial superconducting quantum interference device magnetometer. At a fixed temperature, the field dependence of the time-logarithmic magnetic relaxation rate normalized to the first magnetization value, R =|d(M/M₀)/d In(t)|, was investigated in different polycrystalline HTSCs: TlBaCaCuO (2212 and 2223 single phases), YBaCuO (123 phase), and (Hg,Tl)BaCaCuO (1223 phase). The results obtained for TlBaCaCuO 2223 phase and (Hg,Tl)BaCaCuO show a common trend: R increases linearly with magnetic field up to a certain value, the dimensional crossover field H_3D-2D, above which it becomes field-independent. H_3D-2D is a characteristic field which depends on the anisotropy parameter and the interlayer spacing of the material. The field dependence of R can be ascribed to a crossover in the dimensionality of the object involved in the quantum process: above H_3D-2D, the longitudinal dimension of the tunneling object, L_c, is smaller than the interlayer distance, so the object is of two-dimensional (2D) nature (2D pancake vortices). Below H_3D-2D, 2D vortices in neighboring layers become coupled, so the tunneling object becomes three-dimensional (3D) in nature (3D flux-lines). The field dependences of R obtained for TlBaCaCuO 2212 phase and YBaCuO show only the 2D and 3D vortex regimes, respectively. Well agreement between theoretical estimates and experimental values for the dimensional crossover field and normalized relaxation rates is achieved.