Anomalous frequency dependence of magneto-electric effect in doped DTN

Highlights: • Magnetoelectric effect in Bose glass system has anomalous frequency dependence. • Droplet model for dynamics of frustrated spin glasses used to analyze dependence. • Scaling laws for quantum spin glasses are applicable. The anomalous frequency dependence observed for the magneto-electric effect in the Bose glass state of dichloro-tetrakis-thoiurea-nickel doped with bromine is analyzed in terms of the hierarchical droplet model of spin glasses. In this model low energy barriers must be overcome before accessing higher energy states leading to scaling laws for the spin correlation functions and an associated frequency dependence for transition rates.