  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.
