Magnon excitation and spin-phonon coupling in A2Ir2O7 (A=Gd, Dy, and Er)

We present a comparative study of the temperature-dependent Raman scattering of pyrochlore iridates ${A}₂{\mathrm{Ir}}₂{\mathrm{O}}₇$, where $A=\mathrm{Gd}$, Dy, and Er, spanning the temperature range from 295 to 5 K. Our investigation covers the metal-insulator phase transition, coinciding with the paramagnetic-to-all-in/all-out (AIAO) spin ordering at the magnetic transition temperature ${T}_N$. The crystal symmetry remains unchanged across this magnetic transition. Below ${T}_N$, two additional modes (${N}₁$ and ${N}₂$) emerge, associated with single magnon excitations within the AIAO-ordered state. Analysis of magnon energies enables us to estimate the isotropic exchange $(J)$ and Dzyaloshinskii-Moriya interaction parameter $(D)$. The resulting $D/J$ ratios are $\ensuremath{\sim}0.15$ for ${\mathrm{Gd}}₂{\mathrm{Ir}}₂{\mathrm{O}}₇$ and ${\mathrm{Dy}}₂{\mathrm{Ir}}₂{\mathrm{O}}₇$. In all the three systems, the Ir-O-Ir bond bending vibrations, ${A}_1g$ and ${E}_g$, exhibit anomalous frequency softening in the magnetically ordered AIAO state, primarily originating from the spin-phonon interaction induced by the phonon modulation of the Dzyaloshinskii-Moriya spin-exchange interaction. The two stretching modes ${T}_2g²$ and ${T}_2g⁴$ experience significant hardening in the magnetic insulating phase. Additionally, substantial anomalous linewidth broadening of the ${E}_g$ mode is observed in all samples, indicating strong phonon renormalization below ${T}_N$. Our experimental findings establish experimental evidence of magnon excitations and strong spin-phonon coupling in the AIAO-ordered state for these iridates.