[Paper Review] Intertwined Charge and Spin Density Waves in Trilayer Nickelate La$_4$Ni$_3$O$_{10}$ Revealed by $^{139}$La NQR

Jie Dou, Feiyu Li+8 more|arXiv (Cornell University)|Jan 25, 2026

Solid-state spectroscopy and crystallography0 citations

TL;DR

The paper uses 139La NQR on La4Ni3O10 to reveal intertwined incommensurate charge and spin density waves below T_DW ≈ 133 K, with a first-order-like transition and strong SDW-related spin fluctuations.

ABSTRACT

The discovery of superconducting transitions in pressurized La$_3$Ni$_2$O$_{7}$ and La$_4$Ni$_3$O$_{10}$ has highlighted the pivotal role of density wave (DW) orders in nickelate superconductors. To gain a comprehensive understanding of the superconducting state, it is essential to elucidate the nature of the DW order. In this study, we utilized $^{139}$La nuclear quadrupole resonance (NQR) to investigate the charge density wave (CDW) and spin density wave (SDW) orders in both single-crystal and polycrystalline La$_4$Ni$_3$O$_{10}$. Near $T_{ m{DW}} \approx 133$ K, an abrupt change in both the linewidth and frequency of the La(2) site in the single-crystal sample provides compelling evidence for a first-order-like phase transition. The pronounced broadening of the NQR lines indicates the incommensurate nature of the DW order. Furthermore, the spin-lattice relaxation rate divided by temperature 1/$T_1$$T$ exhibits a strong enhancement at $T_{ m{DW}}$, indicating the strong spin fluctuations above the first-order DW transition. These observations suggest an intricate interplay between incommensurate CDW and SDW orders. Our findings offer critical insights into the microscopic mechanisms of the DW state in La$_4$Ni$_3$O$_{10}$ and establish an essential framework for exploring the interplay between DW and superconducting phases in nickelate superconductors.

Motivation & Objective

• Clarify the nature of density wave orders in La4Ni3O10 at ambient pressure.
• Distinguish charge versus spin contributions and their interplay in the density wave state.
• Characterize the transition order and the role of sample quality on observed DW behavior.
• Provide microscopic insight into the DW state relevant to nickelate superconductivity.

Proposed method

• Perform 139La NQR on both polycrystalline and single-crystal La4Ni3O10 at ambient pressure.
• Monitor linewidths, resonance frequencies, and their temperature dependence across T_DW.
• Measure spin-lattice relaxation rate 1/T1 and its T dependence to assess spin fluctuations.
• Model NQR line shifts and broadenings with contributions from CDW and SDW via internal fields.
• Compare La(2) site signals (outer NiO2 planes) to infer SDW/CDW characteristics and moment orientations.

Figure 1: (a) Crystal structure of La 4 Ni 3 O 10 . Light green atoms denote La(2) atoms, while dark green atoms denote La(1) atoms. (b-c) The 139 La NQR spectra of La 4 Ni 3 O 10 single-crystal (b) and polycrystalline (c) samples in the normal state and the DW state, respectively. The yellow and bl

Experimental results

Research questions

• RQ1 What is the nature (commensurate vs incommensurate) of density wave order in La4Ni3O10 at ambient pressure?
• RQ2 Do charge density wave (CDW) and spin density wave (SDW) orders coexist and how do they interplay at T_DW ~133 K?
• RQ3 Is the DW transition first-order-like or second-order, and how does sample quality affect it?
• RQ4 What is the orientation and magnitude of internal magnetic fields at La sites, and what does this imply about Ni moments?

Key findings

• Below T_DW ≈ 133 K, La(2) NQR lines broaden and shift abruptly in single crystals, indicating a first-order-like DW transition.
• The broadening and non-splitting of lines suggest an incommensurate DW order, likely two-dimensional in nature.
• 1/T1T shows a strong enhancement at T_DW, signaling significant spin fluctuations above the transition.
• Simulation indicates an internal field at La(2) of about 210 mT with CDW broadening ~0.3 MHz reproducing observed spectra, implying intertwined CDW and SDW orders.
• The SDW-related fluctuations appear to originate from outer NiO2 planes, with Ni moments potentially oriented along or perpendicular to the c-axis as discussed; the data support c-axis alignment of outer Ni moments.

Figure 2: The temperature-dependent 139 La(2) NQR spectra of La 4 Ni 3 O 10 single-crystal (a) and polycrystal (b) samples. The yellow and blue peaks represent the ±5/2 $\leftrightarrow$ ±7/2 transition lines of La 4 Ni 3 O 10 before and after the DW transition, respectively. The solid lines represe