Exchange Interactions and Phonon Topology in EuAuAs, GdAuGe, and GdAgGe

The RTX (where R represents rare earth, T represents 3d/4d/5d transition metal, and X represents p-block element) series comprises an extensive collection of equiatomic (1:1:1) intermetallic compounds that exhibit diverse crystal and magnetic structures with their vast array of physical properties, which includes field-induced phase transitions, commensurate, incommensurate, superconductivity, non-trivial topology, etc. In the present work, the exchange interactions and phonon topology of EuAuAs, GdAuGe, and GdAgGe have been discussed. By correlating the spin configurations to the underlying Heisenberg spin model, we have successfully estimated the exchange interactions. Furthermore, by using the mean-field approximation, the Neel temperatures of rare-earth compounds have been reported, which is consistent with the experimental value. The phonon dispersion of EuAuAs and GdAuGe exhibits non-trivial topological phononic states with nodal surfaces and Dirac points on the \(k_z\) = \(\pi \) plane. The calculated phonon spectrum of GdAgGe reveals the presence of a nodal line along the \(k_z\) = \(\pi \) plane. The exploration of phonon topology opens up a new pathway toward comprehending and harnessing the exotic physical characteristics exhibited by these rare-earth compounds and other analogous quantum materials.