Probing emergent QED in quantum spin ice via Raman scattering of phonons: Shallow inelastic scattering and pair production

We present an unconventional mechanism for Raman scattering of phonons, which is based on the linear magnetoelastic coupling present in non-Kramers magnetic ions. This provides a direct coupling of Raman-active phonons to the magnet's quasiparticles. We propose to use this mechanism to probe the emergent magnetic monopoles, electric charges, and photons of the emergent quantum electrodynamics (eQED) of the U(1) quantum spin liquid known as quantum spin ice. Detecting this eQED in candidate rare-earth pyrochlore materials, or indeed signatures of topological magnetic phases more generally, is a challenging task. We show that the Raman scattering cross section of the phonons directly yields relevant information, with the broadening of the phonon linewidth, which we compute, exhibiting a characteristic frequency dependence reflecting the two-particle density of states of the emergent excitations. Remarkably, we find that the Raman linewidth is sensitive to the details of the symmetry fractionalization and hence can reveal information about the projective implementation of symmetry in the quantum spin liquid, thereby providing a diagnostic for a $\ensuremath{\pi}$-flux phase. The Raman scattering of the phonons thus provides a useful experimental tool to probe the fractionalization in quantum spin liquids that turns out to closely mirror pair production in quantum electrodynamics and the deep inelastic scattering of quantum chromodynamics. Indeed, the difference to the latter is conceptual more than technical: the partons (quarks) emerge from the hadrons at high energies due to asymptotic freedom, while those in eQED arise from fractionalization of the spins at low energies.