Vortex melting and decoupling transitions in YBa${}_2$Cu${}_4$O${}_8$ single crystals

The vortex correlation along the c-axis in high quality single crystals of YBa${}_2$Cu${}_4$O${}_8$ has been investigated as a function of temperature T in different magnetic fields, using the quasi-flux transformer configuration. A simultaneous sharp drop associated with the vortex lattice melting is observed in both the primary and secondary voltages(V${}_{top}$ and V${}_{bot}$). Just above the melting temperature, the vortices form three-dimensional line liquid with the correlation length along the c direction $L_c\le$ t, the sample thickness. The temperature where a resistive peak in R${}_{bot}$ develops corresponds to the decoupling temperature T${}_d$ at which the vortices loose their correlation along the c-direction and they dissolve into the two dimensional pancake vortices. The H-T phase diagram for the YBa${}_2$Cu${}_4$O${}_8$ single crystal is obtained.