Relating the ac complex resistivity of the pinned vortex lattice to its shear modulus

We propose a way to determine the shear rigidity of the pinned vortex lattice in high-purity crystals from the dependence of its complex resistivity (Formula presented) on frequency (Formula presented). The lattice is modeled as an elastic medium pinned by a sparse, random distribution of defects. We relate (Formula presented) to the velocity of the small subset of pinned vortices via the lattice propagator (Formula presented). Measuring (Formula presented) versus (Formula presented) is equivalent to determining (Formula presented) versus (Formula presented). The range of (Formula presented) depends sensitively on the shear and tilt moduli. We describe the evaluation of (Formula presented) in two-dimensional (2D) and 3D lattices. The 2D analysis provides a close fit to the frequency dependence of Re(Formula presented) measured in an untwinned crystal of (Formula presented) at 89 K in a field of 0.5 and 1.0 T. We compare our results with earlier models.