Intertwined charge and spin correlations are ubiquitous in a wide range of transition metal oxides and are often perceived as intimately related to unconventional superconductivity. Theoretically envisioned as driven by strong electronic correlations, the intertwined order is usually found to be strongly coupled to the lattice as signaled by pronounced phonon softening. Recently, both charge/spin density waves (CDW/SDW) and superconductivity have been discovered in several Ruddlesden-Popper (RP) nickelates, in particular trilayer nickelates RE4Ni3O10 (RE=Pr, La). The nature of the intertwined order and the role of lattice-charge coupling are at the heart of the debate about these materials. Using inelastic X-ray scattering, we mapped the phonon dispersions in RE4Ni3O10 and found no evidence of phonon softening near the CDW wavevector over a wide temperature range. Calculations of the electronic susceptibility revealed a peak at the observed SDW ordering vector but not at the CDW wavevector. The absence of phonon softening is in sharp contrast to that in canonical oxide materials, notably cuprates. Our experimental and theoretical findings highlight the crucial role of the spin degree of freedom and establish a foundation for understanding the interplay between superconductivity and density-wave transitions in RP nickelate superconductors and beyond.
@article{arxiv.2507.13513,
title = {Lattice-charge coupling in a trilayer nickelate with intertwined density wave order},
author = {Xun Jia and Yao Shen and Harrison LaBollita and Xinglong Chen and Junjie Zhang and Yu Li and Hengdi Zhao and Mercouri G. Kanatzidis and Matthew Krogstad and Hong Zheng and Ayman Said and Ahmet Alatas and Stephan Rosenkranz and Daniel Phelan and Mark P. M. Dean and M. R. Norman and J. F. Mitchell and Antia S. Botana and Yue Cao},
journal= {arXiv preprint arXiv:2507.13513},
year = {2026}
}