Observation of correlated plasmons in low-valence nickelates

Using resonant inelastic x-ray scattering, researchers detected correlated plasmons in the low-valence nickelate Pr4Ni3O8, revealing that these collective excitations are more heavily damped, slower, and temperature-softening compared to cuprates, thereby highlighting distinct charge-screening mechanisms and limiting direct analogies between the two material families.

The Gist

Imagine a bustling city where the citizens are electrons. In some materials, these citizens move freely, creating a smooth flow of electricity. In others, they are so crowded and chaotic that they bump into each other constantly, creating "traffic jams" that lead to strange behaviors, like superconductivity (electricity flowing with zero resistance).

For decades, scientists have studied a specific type of city called cuprates (copper-based materials) to understand how these electron crowds behave. Recently, they discovered a new type of city called nickelates (nickel-based materials) that looks very similar on the map but behaves differently. The big question was: How do the electrons in these new nickel cities move and interact?

This paper acts like a high-tech traffic camera, using a technique called RIXS (Resonant Inelastic X-ray Scattering) to take a snapshot of the electron traffic. Specifically, the researchers looked for "plasmons."

What is a Plasmon?

Think of a plasmon as a wave in a crowd. If you push a group of people in a stadium, a wave ripples through them. In a metal, when electrons are pushed together, they create a collective ripple or "sloshing" motion. This wave is the plasmon. By watching how fast this wave moves and how quickly it dies out, scientists can learn how tightly the electrons are holding hands (interacting) and how easily they can hop from one spot to another.

The Main Discovery: Two Different Cities

The researchers compared two specific cities:

1. La₂₋ₓSrₓCuO₄ (LSCO): A well-known copper city (cuprate) that is heavily "doped" (filled with extra charge carriers).
2. Pr₄Ni₃O₈ (Pr438): A newly discovered nickel city (nickelate) with a similar level of doping.

Here is what they found when they watched the electron waves (plasmons) in both cities:

1. The Nickel Waves are Sluggish
In the copper city, the electron waves zoomed along at a certain speed. In the nickel city, the waves moved much slower.

• The Analogy: Imagine a race between a sprinter (copper) and a runner carrying a heavy backpack (nickel). The nickel electrons are "heavier" or more sluggish because they have a harder time hopping from one atom to the next. The paper suggests this is because the "road" between the nickel atoms is more difficult to travel, even though the atoms themselves look similar.

2. The Nickel Waves Die Out Faster
In the copper city, the waves traveled a decent distance before fading away. In the nickel city, the waves damped out (faded) very quickly.

• The Analogy: In the copper city, the crowd is a bit chaotic, but the wave can still travel. In the nickel city, the crowd is so well-organized and "screened" (shielded) that the wave gets absorbed almost immediately. It's like trying to shout a message in a room full of soundproof foam versus a room with hard walls; the message (the wave) gets lost much faster in the nickel room.

3. The Temperature Twist
This is where the two cities behave completely differently when the weather changes (temperature goes up).

• The Copper City: When it gets hotter, the waves get a bit messier (more damped), but they keep the same speed and energy. It's like a party getting louder and more chaotic, but the music tempo stays the same.
• The Nickel City: When it gets hotter, the waves slow down and lose energy (they "soften").
• The Analogy: Imagine a rubber band. In the copper city, heating it up just makes it vibrate more wildly. In the nickel city, heating it up actually makes the rubber band go limp and lose its tension. The researchers suspect this might be because the nickel electrons are starting to form "stripes" or patterns that change how they move as things get warmer.

Why Does This Matter?

Scientists have been trying to figure out why some materials become superconductors (perfect conductors) and others don't. They thought nickelates and cuprates were almost twins, so they should behave the same way.

This paper says, "No, they are cousins, not twins."

The study reveals that in nickelates:

• Electrons don't hop as easily (slower waves).
• They are more shielded from each other (faster fading waves).
• They react to heat in a completely different way (softening waves).

These differences explain why nickelates might struggle to reach the same high temperatures for superconductivity as copper materials. It's like trying to build a better engine: if you swap the copper parts for nickel parts, you can't just assume the engine will run the same way. You have to account for the fact that the nickel parts are heavier, more shielded, and react differently to heat.

Summary

The paper successfully took the first clear "traffic photos" of electron waves in a new nickel material. It showed that while this material looks like the famous copper superconductors, its internal traffic rules are different: the waves are slower, they die out faster, and they get "tired" when it gets hot. This gives scientists a new, more accurate map for understanding how these materials work and why they might not be as good at superconducting as their copper cousins.

Technical Summary

Technical Summary: Observation of Correlated Plasmons in Low-Valence Nickelates

Problem and Motivation
The discovery of superconductivity in nickelates has established a new platform for investigating the correlated electron liquids responsible for unconventional superconductivity. While the band structures of low-valence nickelates (specifically the $R_{n+1}Ni_nO_{2n+2}$ family) share notable similarities with cuprates, their dynamical properties in the normal state remain poorly understood. A critical gap exists in the quantification of screened Coulomb interactions, which are essential for determining whether attractive extended-Hubbard interactions (potentially phonon-mediated) can overcome long-range repulsion to promote superconductivity. These interactions manifest as plasmon excitations—collective charge-density oscillations. Although plasmons have been extensively studied in cuprates using techniques like resonant inelastic x-ray scattering (RIXS), they have not yet been observed in nickelate materials. Filling this gap is imperative for a direct comparison of charge-screening landscapes and for identifying universal features of unconventional superconductivity.

Methodology
The authors employed O K-edge resonant inelastic x-ray scattering (RIXS) to investigate the metallic, low-valence nickelate $Pr_4Ni_3O_8$ (Pr438). This material was selected as a reference low-valence nickelate with a Ni $3d^{9-1/3}$ valence state (effectively overdoped, $\delta = 1/3$) that remains metallic down to 2 K without phase transitions. The study utilized single crystals prepared via floating-zone growth followed by topotactic reduction.

The experimental approach involved:

1. Momentum Mapping: Measuring in-plane plasmon dispersions along the $(H, 0)$ direction and out-of-plane dispersions along the $L$ direction at 40 K.
2. Comparative Analysis: Directly comparing Pr438 with the overdoped single-layer cuprate $La_{2-x}Sr_xCuO_4$ (LSCO, $\delta = 0.35$), which possesses a similar effective hole-doping level.
3. Theoretical Modeling: Employing Random Phase Approximation (RPA) calculations of the charge dynamical susceptibility. The authors utilized a trilayer model for Pr438 and a single-layer model for LSCO, incorporating anisotropic long-range Coulomb interactions and electronic hopping parameters ($t, t', t_z$). Parameters were constrained exclusively by fitting the experimental RIXS plasmon dispersions.
4. Temperature Dependence: Investigating the response of plasmon excitations to thermal fluctuations by varying temperature from 40 K to 200 K.

Key Results
The study successfully detected dispersive plasmons in $Pr_4Ni_3O_8$, marking the first observation of these collective modes in low-valence nickelates. The key findings include:

• Plasmon Velocity and Hopping: The plasmons in Pr438 exhibit a significantly lower velocity ($1.2 \pm 0.1$ eV·Å) compared to LSCO ($2.4 \pm 0.2$ eV·Å). RPA analysis attributes this reduction to weaker effective electronic hopping in the nickelate, despite the nominally smaller nuclear charge of Ni compared to Cu.
• Damping and Screening: Nickelate plasmons are more heavily damped than those in cuprates, disappearing at smaller in-plane momenta. The damping is attributed to enhanced screening of long-range Coulomb interactions. The extracted long-range Coulomb interaction ($V_c$) in Pr438 is approximately five times smaller than in LSCO.
• Out-of-Plane Dispersion: Unlike LSCO, which shows clear out-of-plane periodic dispersion, Pr438 exhibits no resolvable out-of-plane plasmon dispersion. This is interpreted as a consequence of the three coupled planes in the trilayer structure, potentially leading to out-of-phase oscillations that are undetectable by RIXS, rather than a fundamental difference in interaction physics.
• Temperature Dependence: A distinct contrast was observed in thermal response. In LSCO, plasmon energy remains nearly fixed while damping increases with temperature. In contrast, plasmons in Pr438 "soften" (decrease in energy) with increasing temperature while maintaining similar peak widths. This softening suggests increased electronic compressibility and susceptibility to charge order, potentially linked to incipient stripe fluctuations.

Significance and Claims
The paper claims that these results reveal a distinct charge-screening landscape in low-valence nickelates compared to cuprates. The authors assert that the combination of reduced electronic hopping and smaller, more strongly screened long-range Coulomb interactions constitutes a defining feature differentiating the two material classes.

The study places quantitative constraints on analogies between nickelates and cuprates, challenging the assumption that they share identical dynamical properties. The authors suggest that these specific differences—particularly the reduced energy scale of charge dynamics—could contribute to the suppression of the superconducting energy scale, offering a potential explanation for the lower critical temperatures ($T_c$) observed in low-valence nickelates compared to cuprates. Furthermore, the anomalous temperature dependence of nickelate plasmons provides new experimental benchmarks that may stimulate theoretical efforts beyond the conventional Hubbard framework, including approaches incorporating long-range Coulomb interactions, to better understand the mechanisms of unconventional superconductivity in these materials.