Josephson Plasma Resonance in Solid and Glass Phases of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$

Vortex matter phases and phase transitions are investigated by means of Josephson plasma resonance in under-doped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ single crystals in a microwave frequency range between 19 and 70 GHz. Accompanied by the vortex lattice melting transition, a jump of the interlayer phase coherence extracted from the field dependence of the plasma frequency was observed. In the solid phase, the interlayer coherence little depends on field at a temperature region well below $T_c$ while it gradually decreases as field increases toward the melting line up to just below $T_c$. As a result, the magnitude of the jump decreases with increasing temperature and is gradually lost in the vicinity of $T_c$. This indicates that the vortex lines formed in the vortex solid phase are thermally meandering and the phase transition becomes weak especially just below $T_c$.