Terahertz Lattice Imprint of a Hidden Multipolar Ordering Transition in Gd$_2$Ru$_2$O$_7$
Magnetic order carried by higher-rank multipoles produces no net moment and couples only weakly to conventional dipolar probes. Recently, the lattice has been proposed as an alternative detection channel for the associated ordering transitions. Here we report magneto-terahertz time-domain spectroscopy of the pyrochlore ruthenate Gd$_2$Ru$_2$O$_7$, in which a single spectrum resolves an exchange-split Gd$^{3+}$ transition and an infrared-active optical phonon. The temperature and field dependence of the magnetic mode give two independent determinations of the internal exchange field at the rare-earth site, which yield a magnitude of 5-6 T and a free-ion $g$-factor. The optical phonon, sensitive to spin-disorder scattering rather than to the static exchange field, exhibits a sharp anomaly in frequency and lifetime at 10 K that shifts to 30 K under 7 T, which we identify as an ordering transition of the Gd sublattice hidden from bulk thermodynamic probes. These results identify spin-phonon coupling as a route to rare-earth ordering transitions in multipolar magnets, one that is applicable to polycrystalline samples.