Magnetic penetration depth and flux dynamics in single-crystal ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_{8+\mathrm{\delta }}$

The muon-spin-relaxation technique has been used to study vortex dynamics in single-phase superconducting single crystals of ${\mathrm{Bi}}_2$ ${\mathrm{Sr}}_2$ ${\mathrm{CaCu}}_2$ ${\mathrm{O}}_{8+\mathrm{\delta }}$ (${\mathit{T}}_{\mathit{c}}$≊90 K). The data indicate motional narrowing of the internal field distribution due to vortex motion (on a time scale comparable to the muon lifetime). A field-dependent lattice transition is also observed at ${\mathit{T}}_{\mathit{x}}$∼30 K, as evidenced by the onset of an asymmetric line shape below ${\mathit{T}}_{\mathit{x}}$. Narrowing arising from disordering of the vortices along [001] is also discussed with reference to its effect on the measured penetration depth.