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

TL;DR

This study probes the intertwined charge- and spin-density wave (CDW/SDW) orders in the trilayer nickelate $La_4Ni_3O_{10}$ at ambient pressure using $^{139}$La NQR. Zero-field NQR on both single-crystal and polycrystalline samples reveals an abrupt, first-order-like transition near $T_{ m{DW}} \approx 133$ K, accompanied by strong line broadening indicative of an incommensurate DW state and a pronounced increase in $1/T_1T$ signaling spin fluctuations. A two-component broadening model—attributing CDW-induced EFG changes and SDW-induced internal fields with $B_{ m int} \sim 210$ mT—best explains the data, suggesting an intertwined CDW/SDW scenario with incomplete Fermi surface gapping due to nesting. These results clarify the microscopic DW mechanisms in $La_4Ni_3O_{10}$ and provide a framework for understanding how density-wave states interact with superconductivity in nickelate systems.

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 $T_{\rm{DW}} \approx 133$ 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 $T_{\rm{DW}}$, 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.

Figures (5)

• 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 blue peaks correspond to the signals of La$_4$Ni$_3$O$_{10}$ before and after the transition, respectively. All lines are fitted using Lorentz functions, which serve as visual guides.
• 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 represent the Lorentz fit.
• Figure 3: The temperature-dependent NQR frequency (a) and full width at half maximum(FWHM) (b) of the line corresponding to the ±5/2 $\leftrightarrow$ ±7/2 transition in single-crystal(red dots) and polycrystal(blue dots) La$_4$Ni$_3$O$_{10}$. Both of them start to increase below $T_\textrm{DW} \approx$ 133 K marked by the dashed line. The error bar is the s.d. in fitting spectra by the Lorentz function.
• Figure 4: (a) Theoretical simulation of the NQR frequencies at the La(2) site with an internal magnetic field perpendicular to the $c$-axis. The red, green, and blue curves represent the field-dependent shifts of the ±5/2 $\leftrightarrow$ ±7/2, ±3/2 $\leftrightarrow$ ±5/2 and ±1/2 $\leftrightarrow$ ±3/2 transitions, respectively. If the SDW order is commensurate, distinct line splitting should be discerned for NQR lines corresponding to the ±5/2 $\leftrightarrow$ ±7/2 and ±3/2 $\leftrightarrow$ ±5/2 transitions. Nevertheless, in the DW state, only broad lines are observed owing to the incommensurate spin and charge modulation. The black dashed line depicts their average frequencies in the DW state. Solid circles represent the frequencies of three NQR lines derived from the experimental results presented in panel (b). The color bars represent the FWHM contributed by the internal magnetic field, which is proportional to the splitting of NQR lines due to SDW. (b) Spectrum of La$_4$Ni$_3$O$_{10}$ single crystal at 7.3 K. The solid lines denote Lorentz fits. The resolved three peaks correspond to the ±5/2 $\leftrightarrow$ ±7/2(red), ±3/2 $\leftrightarrow$ ±5/2(green) and ±1/2 $\leftrightarrow$ ±3/2(blue) transitions. The $v_q$ and $\eta$ are taken as 5.27 MHz and 0.1 for the calculation, respectively. (c) Schematic diagram of the internal magnetic field at the La(2) site within La$_4$Ni$_3$O$_{10}$. The grey and green arrows represent the Ni magnetic moments and the internal magnetic field $B_{int}$, respectively.
• Figure 5: (a) Red dots and blue symbols represent the 1/$T_1T$ measured at the La(2) site in La$_4$Ni$_3$O$_{10}$ single crystal and polycrystal, respectively. Grey squares and triangles represent the 1/$T_1$$T$ measured at the La(1) site reported by T. Fukamachi et al.Fukamachi2001b and M. Kakoi et al.Kakoi2024, respectively. (b) Orange and grey diamonds represent the 1/$T_1T$ measured at the La(2) and La(1) sites by J. Luo et al.Luo2025 and D. Zhao et al.wutao025, respectively. (c) Temperature dependence of the $\beta$ of La$_3$Ni$_2$O$_7$(orange diamonds)Luo2025, La$_4$Ni$_3$O$_{10}$ single crystal(red circles) and polycrystal(blue circles). The error bars of 1/$T_1T$ and $\beta$ are the s.d. in fitting the recovery curve. The dashed and dotted lines represent $T_\textrm{DW}$ in La$_4$Ni$_3$O$_{10}$ and La$_3$Ni$_2$O$_7$, respectively. Note that all the 1/$T_1T$ values for the La(1) site have been scaled by a factor of 10.