Exploring low-temperature dynamics in triple perovskite ruthenates using nonlinear dielectric susceptibility measurements

We report the nonlinear dielectric properties of three triple-perovskite ruthenates: Ba$_3$CoRu$_2$O$_9$, Ba$_3$BiRu$_2$O$_9$, and Sr$_3$CaRu$_2$O$_9$. These compounds exhibit notable correlations among their spin, charge, lattice, and polar degrees of freedom. Ba$_3$CoRu$_2$O$_9$ displays a pronounced frequency-dependent relaxation in $\chi_{2,3}$ just above the magnetoelastic transition, occurring around 100K, followed by an abrupt loss of polarization within the ordered phase. In Ba$_3$BiRu$_2$O$_9$, we encounter the possibility of multiple coexisting relaxation behaviors, indicating a complex phase strongly influenced by the spin-gap opening at 175K. Lastly, Sr$_3$CaRu$_2$O$_9$ displays anomalies with strong dispersion effects close to its magnetic transitions, pointing to a robust coupling between magnetic and dipolar orders in the system. These measurements highlight the significance of higher-order (hyper-)susceptibilities in providing profound insight into the dynamics of a system, offering information otherwise inaccessible through the linear polarization response alone.