Dimensional crossover in the fluctuation magnetization in   YBa_2Cu_3O_{7-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} 
S. Salem-Sugui Jr., A.D. Alvarenga, B. Veal, and A.P. Paulikas