Magnon excitation and spin-phonon coupling in 𝐴₂⁢Ir₂⁢O₇ (𝐴=Gd, Dy, and Er)

We present a comparative study of the temperature-dependent Raman scattering of pyrochlore iridates 𝐴_2⁢Ir_2⁢O₇, where 𝐴=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 (𝑁₁ and 𝑁₂) 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 ∼0.15 for Gd₂⁢Ir_2⁢O₇ and Dy₂⁢Ir_2⁢O₇. In all the three systems, the Ir-O-Ir bond bending vibrations, 𝐴_1⁢𝑔 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_2⁢𝑔 ²and 𝑇_2⁢𝑔⁴ 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.