Quantifying the Interactions Distance in a Model Ferroquadrupolar System

Nematicity is a phenomenon seen in many strongly correlated systems, often associated with superconductivity and magnetism. However, understanding the relationship between nematicity and the other underlying physics is often a challenge due to the complicated phase diagrams of many of these systems. We take a model system, the series Tm_xY_1-xVO4, for which x = 1.0 has a ferroquadrupolar (nematic) transition at 2.15 K and study the underlying ferroquadrupolar interactions using frequency-dependent sound velocity and ultrasonic attenuation measurements. We examine the evolution of the strength of the quadrupole-quadrupole coupling parameter for x = 0.01, 0.03, 0.1, and 1.0 members of this series. We fit our data to a well-established mean field model and find that the quadrupolar interaction parameter saturates to its maximum x = 1.0 value for substitutions even as low as x = 0.1. From this saturation value we deduce the effective quadrupolar interaction distance which is of order a few unit cells. This short interaction length suggests that optical phonons play an important role in coupling quadrupoles in this material.