dc-magnetization data measured down to 40 mK speak against conventional freezing and reinstate YbMgGaO4 as a triangular spin-liquid candidate. Magnetic susceptibility measured parallel and perpendicular to the c-axis reaches constant values below 0.1 and 0.2 K, respectively, thus indicating the presence of gapless low-energy spin excitations. We elucidate their nature in the triple-axis inelastic neutron scattering experiment that pinpoints the low-energy (E ≤ J0 ∼ 0.2 meV) part of the excitation continuum present at low temperatures (T < J0/kB), but completely disappearing upon warming the system above T J0/kB. In contrast to the high-energy part at E > J0 that is rooted in the breaking of nearest-neighbor valence bonds and persists to temperatures well above J0/kB, the low-energy one originates from the rearrangement of the valence bonds and thus from the propagation of unpaired spins. We further extend this picture to herbertsmithite, the spin-liquid candidate on the kagome lattice, and argue that such a hierarchy of magnetic excitations may be a universal feature of quantum spin liquids.Introduction.-Quantum spin liquids (QSLs) have a special place in condensed-matter physics as states with unconventional excitations solely driven by spin degrees of freedom in the absence of charge and orbital fluctuations. The QSL physics may be behind many intriguing phenomena studied over the last decades, including the high-temperature superconductivity [1,2]. Exotic properties of the QSLs are also central to new technologies, such as topological quantum computing [3]. The prototype of a QSL was proposed by Anderson back in 1973 as a resonating-valence-bond (RVB) state, a superposition of many different partitions of the triangular spin network into valence bonds (VBs, spin-0 singlets), 1

Nearly a century of research has established the Born–Oppenheimer approximation as a cornerstone of condensed-matter systems, stating that the motion of the atomic nuclei and electrons may be treated separately. Interactions beyond the Born–Oppenheimer approximation are at the heart of magneto-elastic functionalities and instabilities. We report comprehensive neutron spectroscopy and ab initio phonon calculations of the coupling between phonons, CEF-split localized 4f electron states, and conduction electrons in the paramagnetic regime ofCeAuAl3, an archetypal Kondo lattice compound. We identify two distinct magneto-elastic hybrid excitations that form even though all coupling constants are small. First, we find a CEF–phonon bound state reminiscent of the vibronic bound state (VBS) observed in other materials. However, in contrast to an abundance of optical phonons, so far believed to be essential for a VBS, the VBS inCeAuAl3arises from a comparatively low density of states of acoustic phonons. Second, we find a pronounced anticrossing of the CEF excitations with acoustic phonons at zero magnetic field not observed before. Remarkably, both magneto-elastic excitations are well developed despite considerable damping of the CEFs that arises dominantly by the conduction electrons. Taking together the weak coupling with the simultaneous existence of a distinct VBS and anticrossing in the same material in the presence of damping suggests strongly that similarly well-developed magneto-elastic hybrid excitations must be abundant in a wide range of materials. In turn, our study of the excitation spectra ofCeAuAl3identifies a tractable point of reference in the search for magneto-elastic functionalities and instabilities.

We report first principles calculations of the structural parameters and phonon dispersion of the tetragonal non-centrosymmetric heavy fermion compound CeAuAl3. Taking into account weak magnetoelastic interactions of the rare-earth (RE) ions with the spectrum of phonons, we obtain an analytical expression for the hybridization of quadrupole excitations and phonons from the poles of the one-phonon Green-function. In the paramagnetic phase, we predict the formation of mixed modes that may be observed by inelastic neutron scattering. Our results show that magnetoelastic interactions, albeit being moderate, play an important role in CeAuAl3. This suggests that magnetoelastic interactions may be equally important in a wide range of related compounds.