Evidence for flux-lattice melting and a dimensional crossover in single-crystal ${\mathrm{Bi}}_{2.15}$${\mathrm{Sr}}_{1.85}$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$ from muon spin rotation studies

The microscopic magnetic field distribution in the mixed state of single-crystal ${\mathrm{Bi}}_{2.15}$ ${\mathrm{Sr}}_{1.85}$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$ has been measured using the muon spin rotation technique. A study of the line shapes as a function of temperature and magnetic field gives evidence for an abrupt change of flux-lattice structure which is attributed to the presence of a flux-lattice melting line in the B-T phase diagram. In addition, the data suggest the existence of a crossover field above which the flux structure is more 2D in nature.