Abrupt Change of Josephson Plasma Frequency at the Phase Boundary of the Bragg Glass in ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{O}_{8+\delta }$

We report the first detailed and quantitative study of the Josephson coupling energy in the vortex liquid, Bragg glass, and vortex glass phases of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }$ by the Josephson plasma resonance. The measurements revealed distinct features in the $T$ and $H$ dependencies of the plasma frequency ${\omega }_{\mathrm{pl}}$ for each of these three vortex phases. When going across either the Bragg-to-vortex glass or the Bragg-to-liquid transition line, ${\omega }_{\mathrm{pl}}$ shows a dramatic change. We provide a quantitative discussion on the properties of these phase transitions, including the first order nature of the Bragg-to-vortex glass transition.