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$^{139}$ La nuclear quadrupole resonance studies of pressurized La $_4$ Ni $_3$ O $_{10}$

Using $^{139}$ La nuclear quadrupole resonance, this study reveals that intertwined short- and long-range spin and charge density wave orders in La $_4$ Ni $_3$ O $_{10}$ are suppressed by hydrostatic pressure, confirming their role as competing orders to unconventional superconductivity.

Original authors: Meng Zhang, Zhuo Wang, Yantao Cao, Yang Yuan, Kangjian Luo, Shanxiang Gao, Hanjie Guo, Yongkang Luo

Published 2026-09-09

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CC BY 4.0

Original authors: Meng Zhang, Zhuo Wang, Yantao Cao, Yang Yuan, Kangjian Luo, Shanxiang Gao, Hanjie Guo, Yongkang Luo

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the quest to understand how materials conduct electricity without any loss, scientists have long focused on a special class of substances known as superconductors. These are materials that, when cooled to very low temperatures, allow electric current to flow with zero resistance, a property that could revolutionize everything from power grids to medical imaging. For decades, the most famous superconductors were made of copper and oxygen, but recently, a new family of materials containing nickel has captured the attention of researchers. These nickel-based compounds, arranged in specific layered structures, have shown the ability to become superconducting when squeezed under immense pressure, reaching temperatures far higher than previously thought possible for this type of material. However, before these materials can superconduct, they often undergo a different kind of transformation where the electrons arrange themselves into repeating patterns of charge or spin, effectively freezing the flow of electricity. Understanding how these patterns form, how they interact with each other, and how they disappear under pressure is crucial for figuring out how to make these materials superconduct at even higher temperatures.

A team of researchers has now peered into the heart of one such nickel compound, a material called La4Ni3O10, to see exactly how these electron patterns behave. By using a technique that listens to the tiny magnetic whispers of the atoms inside the crystal, they discovered that the material does not simply switch from a normal state to a superconducting one. Instead, it passes through a complex phase where two different types of electron orderings, one involving magnetic spins and the other involving electric charge, become tightly woven together. This finding challenges previous ideas that these two orderings might be separate or independent, suggesting instead that they are deeply linked in this specific material.

The researchers studied a high-quality crystal of La4Ni3O10, which is built from layers of nickel and oxygen sandwiched between layers of lanthanum. They used a method called nuclear quadrupole resonance, which acts like a highly sensitive microphone listening to the atomic nuclei. In this case, they focused on the lanthanum atoms, which sit in two different positions within the crystal structure. By tuning into the specific frequencies at which these atoms vibrate, the team could detect subtle changes in the local magnetic and electric environment, revealing how the electrons were organizing themselves as the material was cooled.

At normal pressure, as the researchers cooled the material, they first noticed the emergence of a short-range ordering of electrons at a temperature of about 150 Kelvin. This is a state where the electron patterns are present but only exist over small distances, like ripples on a pond that haven't yet spread across the whole surface. As the temperature dropped further to around 139 Kelvin, these ripples grew into a long-range order that spanned the entire crystal. The data showed that the magnetic spin ordering and the electric charge ordering appeared at the same time and were intertwined, meaning they could not be separated or understood independently. This is a significant departure from what was seen in a similar, two-layer nickel compound, where these two types of orderings seemed to act independently of one another.

To understand how robust these patterns were, the team placed the crystal under a steady, high pressure of 2.3 gigapascals, which is roughly the pressure found deep within the Earth's crust. Under this squeeze, the behavior of the material changed in a revealing way. The temperature at which the long-range, crystal-wide ordering appeared dropped sharply, falling by about 10 Kelvin for every gigapascal of pressure applied. In contrast, the temperature for the short-range, local ordering decreased much more slowly, only dropping by about 1 Kelvin per gigapascal. This difference in how quickly the two states responded to pressure suggests that the long-range order is much more fragile and easier to suppress than the short-range fluctuations.

The study also revealed that as the pressure increased, the material's ability to superconduct was likely hindered by this competition between the electron patterns and the superconducting state. In the two-layer nickel compound, pressure seemed to help the magnetic ordering, which did not compete with superconductivity. But in this three-layer material, the intertwined nature of the spin and charge orders meant that they fought more directly against the superconducting state. The researchers concluded that the suppression of these intertwined orders by pressure is a key factor in the material's behavior, offering a clearer picture of the microscopic tug-of-war that determines whether a material becomes a superconductor or remains an insulator.

By mapping out exactly how these electron patterns form and evolve, the researchers have provided a detailed snapshot of the internal life of this nickel compound. They confirmed that short-range electron orders appear well before the long-range ones, and that these two types of orders are inextricably linked. This work does not just describe a single material; it helps refine the broader understanding of how complex electron behaviors compete in layered nickelates. The findings suggest that to unlock the full potential of these materials for high-temperature superconductivity, scientists must learn how to manage or suppress these intertwined electron patterns, which currently stand in the way of the superconducting state. The precise measurements of how pressure affects these different orders provide a new set of clues for theorists and experimentalists alike as they continue to explore the frontier of quantum materials.

Technical Summary: 139La Nuclear Quadrupole Resonance Studies of Pressurized La4Ni3O10

Problem Statement
The discovery of pressure-induced superconductivity (SC) with a critical temperature ( $T_c$ ) exceeding 80 K in bilayer Ruddlesden-Popper (RP) nickelate La $_3$ Ni $_2$ O $_7$ has spurred investigations into competing orders within layered nickelates. While density-wave (DW) orders are known to exist in both bilayer (La $_3$ Ni $_2$ O $_7$ ) and trilayer (La $_4$ Ni $_3$ O $_{10}$ ) RP nickelates at ambient pressure, their nature and evolution under pressure remain distinct. In La $_3$ Ni $_2$ O $_7$ , spin-density-wave (SDW) and a secondary DW order appear decoupled and evolve differently under pressure. Conversely, in La $_4$ Ni $_3$ O $_{10}$ , previous studies suggested simultaneous SDW and charge-density-wave (CDW) transitions, but it remained unclear whether these orders are intertwined and how they respond to hydrostatic pressure. Local microscopic probes capable of distinguishing spin and charge degrees of freedom are required to resolve these issues.

Methodology
The authors employed $^{139}$ La nuclear quadrupole resonance (NQR) on high-quality single-crystalline La $_4$ Ni $_3$ O $_{10}$ to investigate local electronic and magnetic environments. Measurements were conducted at ambient pressure and under hydrostatic pressure ( $\sim$ 2.3 GPa) over a temperature range of 80–300 K.

Probe Selection: The study focused on the La(2) site (located in the La-O fluorite-type layers outside the NiO $_6$ bilayers) due to its stronger signal intensity compared to the La(1) site.
Spectral Analysis: NQR spectra were analyzed by decomposing line shapes into a disordered-state Lorentzian component (L) and an ordered-state Gaussian component (G) to distinguish between short-range and long-range order.
Relaxation Dynamics: The spin-lattice relaxation time ( $T_1$ ) was extracted by fitting the recovery curves of the $\pm 5/2 \leftrightarrow \pm 7/2$ transition to a stretched exponential formula, allowing for the calculation of $1/T_1T$ and the stretching exponent $b$ .
Linewidth Decomposition: Full width at half maximum (FWHM) analysis was used to separate magnetic ( $w_m$ ) and quadrupolar ( $w_q$ ) contributions to linewidth broadening, testing for coupling terms between spin and charge orders.

Key Results

Intertwined Short- and Long-Range Orders: At ambient pressure, the NQR spectra reveal the onset of short-range DW orders at $T^* \approx 150$ K, well above the long-range DW transition temperature ( $T_{DW} \approx 139$ K). The coexistence of Lorentzian and Gaussian spectral components below 150 K indicates that short-range ordering precedes long-range ordering.
Coupling of SDW and CDW: Analysis of the linewidths reveals that the magnetic broadening ( $w_m$ ) decreases rather than increases as the system transitions from short-range to long-range order. This anomaly, combined with the simultaneous modification of the electric field gradient (EFG), implies a negative coupling term between charge and spin fluctuations. This provides evidence that SDW and CDW orders are intertwined in La $_4$ Ni $_3$ O $_{10}$ , contrasting with the decoupled behavior observed in La $_3$ Ni $_2$ O $_7$ .
Pressure Evolution: Under 2.3 GPa hydrostatic pressure:
- The long-range transition temperature ( $T_{DW}$ ) is suppressed significantly, dropping from 139 K to 116 K (a rate of $\sim$ 10 K/GPa).
- The short-range transition temperature ( $T^*$ ) is suppressed much more slowly, from 150 K to 148 K (a rate of $\sim$ 1 K/GPa).
- The stretching exponent $b$ , which quantifies the homogeneity of spin-lattice relaxation, deviates from unity below $T^*$ . Under pressure, the reduction of $b$ is slower, consistent with the persistence of short-range order.
- The $1/T_1T$ values in the high-temperature regime are consistently lower under pressure, indicating a reduction in the density of states at the Fermi level.

Significance and Claims
The paper establishes that in La $_4$ Ni $_3$ O $_{10}$ , both SDW and CDW orders are intertwined and act as competing orders to the superconducting state. This stands in stark contrast to La $_3$ Ni $_2$ O $_7$ , where SDW appears decoupled and potentially enhanced by pressure. The authors claim that the strong competition between these intertwined density waves and superconductivity in the trilayer system may be a factor contributing to its lower $T_c$ compared to the bilayer counterpart. The study provides new microscopic insights into the interplay between density-wave instabilities and unconventional superconductivity in RP-phase nickelates, highlighting the distinct evolution of short-range versus long-range orders under pressure. The work does not claim to resolve the sequential layer effect (inner vs. outer Ni-O layers) due to the exclusive probing of La(2) sites, noting that future NMR studies on La(1) sites would be necessary for a complete picture.

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