Dimensional Crossover Field Research Articles

Dimensional Crossover in the Fluctuation Magnetization in YBa2Cu3O7- x and its Evolution with the Content of Oxygen

We have studied the field-induced dimensional crossover in the fluctuation magnetization of three single crystals of $YBa_2Cu_3O_{7-x}$, with superconducting transition temperatures, $T_c$= 62.5, 52, and 41 K. The dimensional crossover is observed by studying the diamagnetic vortex fluctuations of the lowest-Landau-level type which occur in isochamps magnetization curves, $MvsT$, for temperatures close to the transition temperature $T_{c}(H)$. The study was accomplished by obtaining isochamps magnetization curves as a function of temperature for fields in the range of 0.4 T to 5 T. Magnetization curves for each sample when plotted together show two distinct well resolved crossing points, one formed by low field curves and located at a higher temperature than the other formed by high field curves. A lowest-Landau-level scaling analysis is applied to the curves forming the crossing points and it is verified that lower field curves obey the three-dimensional form of this scaling while the higher field curves obey the two-dimensional form. The results allow to observe the evolution of the dimensional crossover field $H_{cross}$, 3D-2D, with the content of oxygen in $YBa_2Cu_3O_{7-x}$. It is observed that the evolution of the field $H_{cross}$ with the content of oxygen in each sample qualitatively agrees with theoretical predictions and allow us to estimate the ratio of the anisotropy among the studied samples. \\pacs{74.40.+k}

The interpretation of improved flux pinning behaviour and second magnetization peaks observed in overdopedCu-rich Bi2Sr2CaCu2O8+x single crystals

The irreversibility line and second magnetization peak of heavily overdoped Cu-richBi2Sr2CaCu2O8+x (Bi2212) single crystals are studied by accurate magnetization measurements with a field. Compared with optimally-doped and Pb-doped Bi2212 single crystals, the present systemexhibits an enhanced pinning behaviour and higher dimensional crossover field. Thetemperature dependences of the critical current densities at the first and thesecond peaks exhibit different behaviour before and after the dimensional crossover.Above the crossover field, the irreversibility line obeys an exponential temperaturedependence. Our results suggest that the second peak is caused by the switch of the fluxpinning from three-dimensional flux line pinning to two-dimensional (2D) collectivepinning, and the irreversibility line is the depinning line of the 2D vortex lattice.

Anisotropy of iodine intercalated Bi2212 single crystals by magnetic torque

The magnetic torque of iodine intercalated Bi2Sr2CaCu2O8+δ (I-Bi2212) single crystals has been measured under magnetic fields up to 8 kOe in the temperatures from 4.2 to 100 K. The anisotropy parameter for the 1-Bi2212 determined by London model is smaller than that for the pure Bi2Sr2CaCu2O8+δ (Bi2212). A sharp peak C1 due to the intrinsic pinning and an extra peak C2 due to the dimensional crossover of the pancake vortex are observed in the magnetic field direction dependence of the torque. The reduced temperature at which the peak C1 appears with decreasing temperature is T/Tc=0.82, which is lower than T/Tc=0.97 for the pure Bi2212. The dimensional crossover field for the I-Bi2212 obtained from the peak C2 is larger than that for the pure Bi2212. According to these results, it is concluded that the iodine intercalation causes the enhancement of interlayer coupling.

Dimensional crossover of vortex state and peak effect in magnetization in organic superconductors

Magnetization measurements on the single crystals of the organic superconductor κ-(BEDT-TTF) 2Cu(NCS) 2 are performed in the magnetic field perpendicular to the conducting layers. We find an anomalous second peak on magnetization curves which is almost independent of the temperature, similar to the case of high- T c superconductor Bi 2Sr 2CaCu 2O 8+ y . The peak field H p-150 Oe well coincides with the dimensional crossover field B cr = φ 0/(γ s) 2. The temperature dependence of the irreversibility field in the quasi two dimensional (2D) region above B cr is different from those in the three dimensional (3D) region below B cr. At the 3D region, the irreversibility field is described by H irr (1− t) n with n = 1.9, however H irr increases exponentially with 1/ T at the 2D region. The dimensionality of the vortex state and the vortex pinning property are discussed.

Anomalous magnetization and dimensional crossover of the vortex system in the organic superconductor kappa -(BEDT-TTF)2Cu(NCS)2.

Magnetization measurements on high-quality single crystals of $\ensuremath{\kappa}$-${(\mathrm{B}\mathrm{E}\mathrm{D}\mathrm{T}\ensuremath{-}\mathrm{T}\mathrm{T}\mathrm{F})}_{2}$Cu${(\mathrm{NCS})}_{2}$ [where BEDT-TTF denotes bis(ethylenedithio)tetrathiafulvalene] are performed in the magnetic field perpendicular to the conducting layers. An anomalous second peak on magnetization curves observed at ${H}_{p}$ (\ensuremath{\approx} 150 Oe) is attributed to the dimensional crossover in the vortex system. At the dimensional crossover field ${B}_{2\mathrm{D}}=\frac{{\ensuremath{\varphi}}_{0}}{({\ensuremath{\gamma}}^{2}{s}^{2})}$, the temperature dependence of the irreversibility field changes from the power-law dependence in the three-dimensional (3D) regime below ${B}_{2\mathrm{D}}$ to the exponential dependence with $\frac{1}{T}$ in the quasi-2D regime above ${B}_{2\mathrm{D}}$. It is also found that the different magnetic field dependence of the critical current density above and below ${B}_{2\mathrm{D}}$ is well described by the collective pinning theory.

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 ln(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 H3D-2D, above which it becomes field-independent. H3D-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 H3D-2D, the longitudinal dimension of the tunneling object, Lc, is smaller than the interlayer distance, so the object is of two-dimensional (2D) nature (2D pancake vortices). Below H3D-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.

Dimensional crossover field as a function of oxygen stoichiometry inYBa2Cu3O7−δthin films

The magnetic phase diagram of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ thin films was studied as a function of anisotropy by systematically changing the oxygen stoichiometry (\ensuremath{\delta} value). For small \ensuremath{\delta} values the vortex-solid phase transition boundary ${\mathit{H}}_{\mathit{g}}$(T) is observed over the full accessible field range (50 kOe) to follow the (1-T/${\mathit{T}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{\sim}}1.5}$ dependence that is expected for an anisotropic superconductor in the three-dimensional regime. As \ensuremath{\delta} increases, a portion of the phase boundary no longer follows the (1-T/${\mathit{T}}_{\mathit{c}}$${)}^{\mathrm{\ensuremath{\sim}}1.5}$ dependence making it possible to identify the anisotropy-dependent dimensional crossover field ${\mathit{H}}_{0}$ at which the system begins to behave quasi-two-dimensionally. Plotting ${\mathit{H}}_{\mathit{g}}$(T) normalized by ${\mathit{H}}_{0}$ as a function of (1-T/${\mathit{T}}_{\mathit{c}}$) results in a collapse of the phase boundaries onto a single universal curve. Using published values of the anisotropy \ensuremath{\gamma}=8.5 and the upper critical field slope ${\mathit{dH}}_{\mathit{c}2}$/dT=-20 kOe/K it is possible to determine the specific relation ${\mathit{H}}_{0}$\ensuremath{\approxeq}1.2${\mathrm{\ensuremath{\varphi}}}_{0}$/(${\mathit{d}}^{2}$${\ensuremath{\gamma}}^{2}$), where d is the multilayer spacing, which can be used to determine the \ensuremath{\delta} dependence of \ensuremath{\gamma}.