Muon Spin Rotation Studies of the Vortex Matter in the High-T$\text{}_{c}$ Superconductor Bi$\text{}_{2}$Sr$\text{}_{2}$CaCu$\text{}_{2}$O$\text{}_{8+δ}$

We report muon spin rotation studies of the magnetic field distribution n(B) in the vortex state of the high-temperature superconductor Bi$\text{}_{2}$Sr$\text{}_{2}$CaCu$\text{}_{2}$O$\text{}_{8+δ}$. From our data on three sets of overdoped, nearly optimized and underdoped single crystals we obtain evidence for a two-stage melting process of the vortex matter under equilibrium conditions. In the irreversible regime well below the irreversibility line we observe a transition in the vortex state which we associate with an intra-planar melting transition. The resulting flux-line liquid phase persists over a sizeable temperature interval before the inter-planar decoupling of the individual vortex lines takes place in a second step at the irreversibility line, resulting in a pancake liquid phase