Lattice dynamics of the heavy fermion compound URu$_2$Si$_2$

TL;DR

This study provides a comprehensive analysis of the lattice dynamics in URu$_2$Si$_2$, revealing phonon behavior linked to Kondo physics, electron-phonon coupling, and symmetry-breaking, with detailed experimental and theoretical insights.

Contribution

It presents new experimental and theoretical data on phonon modes, their temperature dependence, and their relation to Kondo physics and hidden order in URu$_2$Si$_2$.

Findings

B$_{1g}$ phonon mode softens below 100 K.

Strong electron-phonon coupling evidenced by Fano line shapes.

No significant phonon changes across the hidden order transition.

Abstract

We report a comprehensive investigation of the lattice dynamics of URu$_2$Si$_2$ as a function of temperature using Raman scattering, optical conductivity and inelastic neutron scattering measurements as well as theoretical {\it ab initio} calculations. The main effects on the optical phonon modes are related to Kondo physics. The B$_{1g}$ ($\Gamma_3$ symmetry) phonon mode slightly softens below $\sim$100~K, in connection with the previously reported softening of the elastic constant, $C_{11}-C_{12}$, of the same symmetry, both observations suggesting a B$_{1g}$ symmetry-breaking instability in the Kondo regime. Through optical conductivity, we detect clear signatures of strong electron-phonon coupling, with temperature dependent spectral weight and Fano line shape of some phonon modes. Surprisingly, the line shapes of two phonon modes, E$_u$(1) and A$_{2u}$(2), show opposite temperature dependencies. The A$_{2u}$(2) mode loses its Fano shape below 150 K, whereas the E$_u$(1) mode acquires it below 100~K, in the Kondo cross-over regime. This may point out to momentum-dependent Kondo physics. By inelastic neutron scattering measurements, we have drawn the full dispersion of the phonon modes between 300~K and 2~K. No remarkable temperature dependence has been obtained including through the hidden order transition. {\it Ab initio} calculations with the spin-orbit coupling are in good agreement with the data except for a few low energy branches with propagation in the (a,b) plane.