Vortex-chain state in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$: Experimental evidence for coexistence of two vortex orientations

A detailed study is reported by the Bitter decoration technique of the mixed vortex chain–vortex lattice phase found in tilted magnetic fields in single crystals of the highly anisotropic ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathit{x}}$ (BSCCO). From the field and tilt-angle dependencies of the vortex periods in this structure we conclude that the vortex chains in BSCCO are qualitatively different from those in the moderately anisotropic and well-studied ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{\mathit{x}}$. In particular, the intrachain vortex period is independent of the tilt angle cphi for a given perpendicular component of the field while the vortex period in the intervening flux-line lattice (FLL) shows a maximum vs cphi. In addition, the ratio of the number of the FLL vortices to the total number of vortices decreases rapidly for cphi>70°. Proceeding from these dependencies, we show that the observed mixed vortex phase can be explained consistently by the chain and the FLL vortices having different orientations, neither parallel to the applied field, as suggested by recent theoretical calculations.