Experimental evidence for a three-dimensional–two-dimensional crossover for magnetic fields parallel to the $\mathrm{ab}$ plane in oxygen-deficient single crystals of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$

Resistive measurements on oxygen-deficient ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7-\delta }$ single crystals of varying anisotropy $\gamma$ $(22\mathrm{}<~\gamma <~36)$ have been used for investigations of the transition into a glassy vortex state for magnetic fields $0<~B<~12\hspace{0.5em}\mathrm{T}$ parallel to the $\mathrm{ab}$ plane. When B is accurately aligned parallel to the $\mathrm{ab}$ plane there is a remarkable change in behavior to a field-independent vortex solid-to-liquid transition at high magnetic fields. A possible explanation is suggested for the vertical transition involving a complete decoupling of the superconducting planes that leads to a two-dimensional system where the resistivity is given by nucleation of vortex-antivortex pairs.