Role of spin-phonon and electron-phonon interactions in phonon renormalization of (Eu${}_{1-x}$Bi${}_x$)${}_2$Ir${}_2$O${}_7$ across the metal-insulator phase transition: Temperature-dependent Raman and X-ray studies

Abstract

We report temperature-dependent Raman scattering and X-ray diffraction studies of pyrochlore iridates, (Eu${}_{1-x}$Bi${}_x$)${}_2$Ir${}_2$O${}_7$, for x=0, 0.02, 0.035, 0.05 and 0.1. The temperature variation in Raman experiments spans from 4 K to 300 K, covering the metal-insulator phase transition accompanied by paramagnetic to all-in/all-out (AIAO) spin ordering (T${}_N$). These systems also show a Weyl semi-metal (WSM) phase at low temperatures (below ~50 K). We show that the Ir-O-Ir bond bending mode, A${}_{1g}$ (510 cm${}^{-1}$), shows anomalous softening in the magnetically ordered AIAO state, arising primarily from the spin-phonon interaction due to the phonon-modulation of the Dzyaloshinskii-Moriya (DM) spin-exchange interaction. The two stretching modes, T${}_{2g}^1$ (307 cm${}^{-1}$) and T${}_{2g}^2$ (382 cm${}^{-1}$) harden significantly in the magnetic insulating phase. The T${}_{2g}$ phonons also show anomalous temperature dependence of their mode frequencies, hitherto unreported, due to strong electron-phonon coupling. The signatures of the WSM state are observed in phonon renormalization below 50 K due to strong electron-phonon interaction. Our experimental results establish strong magneto-elastic coupling below T${}_N$ and significant electron-phonon interactions in the metallic phase above T${}_N$ as well as in the low-temperature WSM state.

31 pages, 11 figures (7 + 4)