Stepwise Behavior of Vortex-Lattice Melting Transition in Tilted Magnetic Fields in Single Crystals of ${{\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_{2}O}_{8+\mathit{\delta }}$

The vortex-lattice melting transition in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ single crystals was studied using in-plane resistivity measurements in magnetic fields tilted away from the $c$ axis to the $\mathrm{ab}$ plane. In order to avoid the surface barrier effect which hinders the melting transition in the conventional transport measurements, we used the Corbino geometry of electric contacts. The complete $H^c-H^{\mathrm{ab}}$ phase diagram of the melting transition in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ is obtained for the first time. The $c$-axis melting field component $H_{\mathrm{melt}}^c$ exhibits the novel, stepwise dependence on the in-plane magnetic fields $H^{\mathrm{ab}}$ which is discussed on the basis of the crossing vortex-lattice structure. The peculiar resistance behavior observed near the $\mathrm{ab}$ plane suggests the change of phase transition character from first to second order.