Melting of vortex solid phase in irradiated Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$ single crystals in tilted magnetic fields

The boundary between the vortex-solid and the vortex-liquid in $H_{c} - H_{ab}$ phase plane for irradiated Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta }$single crystals is studied by measuring the local ac-magnetic permeability by using the miniature coils in tilted magnetic fields. It was found that the $c$-axis magnetic field component at the phase transition decreases linearly when increasing the in-plane magnetic field at high temperatures even in a wider angular range than in pristine samples. At lower temperatures, this linear decrease transforms to a concave (hyperbolic-like) curve that differs even stronger from the usual elliptical phase boundary derived from Ginzburg-Landau theory. A theoretical approach to this challenging problem is discussed.