Phonon softening and atomic modulations in EuAl${}_4$

Abstract

EuAl${}_4$ is a rare earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal X-ray diffraction, inelastic X-ray scattering, and lattice dynamics calculations to clarify the origin of the CDW in EuAl${}_4$. We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at $T_{\mathrm{CDW}}=142$ K, freezes out in an atomic displacement mode described by the superspace group $Immm(00\gamma )s00$. In the context of previous work, our observation is a clear confirmation that the CDW in EuAl${}_4$ is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl${}_4$ and ThCr${}_2$Si${}_2$-type rare-earth intermetallics known to combine CDW instabilities and complex magnetism.