Collapse of the vortex-lattice inductance and shear modulus at the melting transition in untwinned $\rm YBa_2Cu_3O_7$

Abstract

The complex resistivity $\hatρ(ω)$ of the vortex lattice in an untwinned crystal of 93-K $\rm YBa_2Cu_3O_7$ has been measured at frequencies $ω/2π$ from 100 kHz to 20 MHz in a 2-Tesla field $\bf H\parallel c$, using a 4-probe RF transmission technique that enables continuous measurements versus $ω$ and temperature $T$. As $T$ is increased, the inductance ${\cal L}_s(ω) ={\rm Im} \hatρ(ω)/ ω$ increases steeply to a cusp at the melting temperature $T_m$, and then undergoes a steep collapse consistent with vanishing of the shear modulus $c_{66}$. We discuss in detail the separation of the vortex-lattice inductance from the `volume' inductance, and other skin-depth effects. To analyze the spectra, we consider a weakly disordered lattice with a low pin density. Close fits are obtained to $ρ_1(ω)$ over 2 decades in $ω$. Values of the pinning parameter $κ$ and shear modulus $c_{66}$ obtained show that $c_{66}$ collapses by over 4 decades at $T_m$, whereas $κ$ remains finite.