The vortex phase transition was systematically studied in twin-free ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$ for various δ. For $7-\delta >~6.94,$ the first order transition was evidenced by an abrupt jump and a hysteresis of magnetization in the field-cooled (FC) cooling-warming cycles, which indicates the coexistence of vortex crystallites and liquid. For $7-\delta <6.89\mathrm{}$ the jump was not sharp and FC magnetization was reversible, suggesting a second order transition. The first and the second order transitions merge at a critical point (CP) which goes to zero field for $7-\delta <\mathrm{6.89.}\mathrm{}$ Three-dimensional XY scaling satisfactorily fits the data at 1–7 T for $7-\delta <6.94\mathrm{}$ and for $7-\delta <6.89,$ but does not fit for $6.89<7-\delta <6.94,$ where the CP passes through this field range.

• Received 11 February 1999

DOI:https://doi.org/10.1103/PhysRevB.60.7601