Lattice dynamics and spin-phonon coupling in the kagome spin ice HoAgGe

We employ polarization-resolved Raman spectroscopy and first-principles phonon calculations to study the lattice dynamics and spin-phonon coupling in the kagome spin ice compound HoAgGe. Upon cooling, HoAgGe shows transitions from a nonmagnetic state at 300 K to a partially magnetic ordered phase below ${T}_{2}=11.6\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, eventually reaching a fully magnetic ordered phase below ${T}_{1}=7\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. We detect 8 of 10 Raman-active phonon modes at room temperature, with frequencies consistent with first-principles phonon calculations. We find that the low-energy phonon modes harden upon cooling, soften slightly below ${T}_{2}$, and, finally, harden again below ${T}_{1}$, suggesting finite spin-phonon coupling in HoAgGe. Furthermore, one high-energy mode at $185\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ with ${E}^{\ensuremath{'}}$ symmetry exhibits a Fano line shape due to electron-phonon coupling. Our Raman results establish finite spin-phonon coupling and electron-phonon coupling in the magnetic phase of HoAgGe, providing a foundation for future studies of the novel field-induced phases at low temperatures in HoAgGe.