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Unified Terahertz Framework for Magnetic and Lattice Responses Reveals an Elusive Ordering Transition in Gd$_2$Ru$_2$O$_7$
Magnetic order in materials combining localized rare earth moments with itinerant transition metal sublattices generates internal fields whose lattice imprint is rarely accessed directly. In Gd pyrochlore ruthenate, we find that a single terahertz spectrum resolves an exchange split Gd$^{3+}$ mode and an optical phonon. Their coupled evolution quantifies the internal field, oriented as predicted for cluster multip...