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Lattice-Charge Coupling in a Trilayer Nickelate with Intertwined Density Wave Order

Xun Jia1,2,*, Yao Shen3,†, Harrison LaBollita4,‡, Xinglong Chen1,§, Junjie Zhang1,∥, Yu Li1, Hengdi Zhao1, Mercouri G. Kanatzidis1,5, Matthew Krogstad6 et al.

Hong Zheng1, Ayman H. Said6, Ahmet Alatas6, Stephan Rosenkranz1, Daniel Phelan1, Mark P. M. Dean3,7, M. R. Norman1, J. F. Mitchell1, Antia S. Botana4,¶, and Yue Cao1,**

  • *Contact author: jiaxun@ihep.ac.cn
  • †Present address: Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
  • ‡Present address: Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA.
  • §Present address: School of Physics, Southeast University, Nanjing, 211189, China.
  • ∥Institute of Crystal Materials, State Key Laboratory of Crystal Materials, Shandong University, Jinan, Shandong 250100, China.
  • Contact author: antia.botana@asu.edu
  • **Contact author: yue.cao@anl.gov
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Phys. Rev. X 16, 011013 – Published 23 January, 2026

DOI: https://doi.org/10.1103/s5j9-cbg7

Abstract

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 and spin density waves (CDW and 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 low-energy phonon dispersions in RE4Ni3O10 and found no evidence of softening near the CDW wave vector over a wide temperature range, which contrasts with the pronounced anomalies frequently observed in cuprate superconductors. Calculations of the electronic susceptibility revealed a peak at the observed SDW ordering vector but not at the CDW wave vector. 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.

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Popular Summary

Understanding the relationship between intertwined charge and spin density wave (CDW and SDW) order and superconductivity remains a central, unresolved question in condensed matter physics. This is made more challenging by the involvement of the lattice, as revealed by the phonon softening observed in many materials like cuprates. Using high-resolution inelastic x-ray scattering, we reveal the surprising absence of low-energy phonon anomalies at the CDW wave vector in the intertwined CDW and SDW nickelate superconductors RE4Ni3O10 (RE=Pr, La). Density-functional theory and electron susceptibility calculations further revealed that the intertwined order is magnetically driven. Our results contrast with past observations in cuprates and highlight the crucial role of the spin degree of freedom in nickelate superconductors.

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Phys. Rev. X 16, 011013– Published 23 January, 2026
  • Received 10 July 2025
  • Revised 9 November 2025
  • Accepted 9 December 2025
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