Dimensional crossover in the magnetic phase diagram of crystals with different oxygen stoichiometry

We have performed muon-spin-rotation measurements on the high-temperature superconductor (Formula presented) for a range of oxygen stoichiometries. The low-temperature in-plane penetration depth (Formula presented) was determined as a function of oxygen content. In addition, for each sample the crossover field (Formula presented), separating the regime of three-dimensional and quasi-two-dimensional vortex behavior, was measured. It is found that (Formula presented) depends only on the penetration depth as (Formula presented) rather than on the superconducting anisotropy (Formula presented). This may be understood in terms of a system of vortices controlled predominantly by electromagnetic interactions. The results are contrasted with other materials, such as (Formula presented), where Josephson coupling plays a more significant role.