Probing La-based nickelates with Ni 1$s$ core-level photoelectron spectroscopy

This study demonstrates that Ni $1s$ core-level photoelectron spectroscopy overcomes the spectral overlap issues inherent in Ni $2p$ measurements of La-based nickelates, offering a clearer view of intrinsic electronic excitations and enabling detailed comparisons across the Ruddlesden-Popper series.

The Gist

Imagine you are trying to listen to a specific musician playing a violin in a very loud orchestra. You want to hear exactly how that violin sounds, but the problem is that right next to the violin, a trumpet is playing a note at almost the exact same pitch. To make things worse, the trumpet also has a "ringing" echo that overlaps with the violin's higher notes. Trying to figure out the violin's true sound by just listening to the whole mix is nearly impossible; you might think the violin is playing a different song than it actually is.

This is exactly the problem scientists faced when studying a new family of superconducting materials called nickelates (specifically those based on Lanthanum).

The Problem: The "Trumpet" Overwhelms the "Violin"

For decades, scientists have used a technique called Photoelectron Spectroscopy (PES) to "listen" to the electrons inside materials. Think of this like shining a flashlight (X-rays) into a dark room to see what's there.

• The Standard Method (Ni 2p): Usually, scientists look at the "Ni 2p" electrons. In a perfect world, this is like looking at a clear, sharp violin note.
• The Reality: In Lanthanum-based nickelates, there is a "trumpet" called Lanthanum (La). The Lanthanum electrons (La 3d) vibrate at almost the exact same energy as the Nickel electrons (Ni 2p).
• The Result: When scientists tried to look at the Nickel, the Lanthanum signal was so loud and overlapping that it was impossible to tell what the Nickel was actually doing. It was like trying to hear a whisper in a hurricane. This led to confusion and different scientists arguing about what the electronic structure of these materials actually looked like.

The Solution: Tuning into a "Deep Bass" Channel

The researchers in this paper decided to stop trying to fix the noisy "violin" channel. Instead, they decided to tune into a completely different channel: the Ni 1s core level.

Think of the Ni 1s electron as a deep bass drum located very deep inside the atom.

• Why it's better: This "bass drum" is so deep and distinct that the Lanthanum "trumpet" doesn't play anywhere near that frequency. There is no overlap.
• The Benefit: By using high-energy X-rays (Hard X-rays) to reach this deep level, the scientists got a "clean view." They could finally hear the Nickel's true sound without the Lanthanum noise interfering.

What They Discovered

Once they cleared away the noise, they compared three different materials:

1. La₃Ni₂O₇ (A two-layer nickelate)
2. Nd₃Ni₂O₇ (A similar two-layer nickelate, but with Neodymium instead of Lanthanum)
3. LaNiO₃ (A single-layer nickelate)

Using their new "clean microphone" (Ni 1s), they found:

• The Two-Layer vs. One-Layer: The two-layer materials (like La₃Ni₂O₇) sounded distinctly different from the one-layer material (LaNiO₃). The one-layer material had a very "lopsided" sound, while the two-layers were more balanced.
• The Lanthanum vs. Neodymium: Even between the two similar two-layer materials, they found subtle differences. The Lanthanum version had a slightly "fuzzier" or broader sound compared to the Neodymium version.

Why the Sound Changed

To understand why the sounds were different, the scientists used a computer simulation (DFT+DMFT) to model the materials. They realized the difference wasn't just about the atoms themselves, but about how tightly the atoms were holding hands with their neighbors (a concept called hybridization).

• The Analogy: Imagine the atoms are dancers holding hands. In the Lanthanum material, the "dance floor" (the crystal structure) was stretched slightly differently than in the Neodymium material. This stretching made the dancers hold hands a bit more loosely.
• The Result: This slight change in how tightly they held hands changed the way the electrons moved, which showed up clearly in their new "clean" Ni 1s spectra.

The Bottom Line

This paper is a success story of finding a better way to listen. The authors showed that the old method (Ni 2p) was too noisy to give a clear answer for Lanthanum-based nickelates. By switching to the deeper, cleaner Ni 1s method, they were able to:

1. Prove that the old method was unreliable for these specific materials.
2. Reveal subtle, real differences in the electronic structure of these materials that were previously hidden.
3. Show that these differences are caused by how the atoms are stretched and how they interact with their neighbors.

In short, they found a new, clearer window into the microscopic world of these superconducting materials, allowing for a much more accurate understanding of how they work.

Technical Summary

Technical Summary: Probing La-based Nickelates with Ni 1s Core-Level Photoelectron Spectroscopy

Problem Statement
The electronic structure of La-based Ruddlesden–Popper nickelates ($La_{n+1}Ni_nO_{3n+1}$), particularly the bilayer compound $La_3Ni_2O_7$, is of significant interest due to recent discoveries of superconductivity. However, characterizing these materials using standard Ni 2p core-level photoelectron spectroscopy (PES) presents a fundamental challenge: the Ni 2p and La 3d core levels exhibit substantial energy overlap. Specifically, the La 3d$_{3/2}$ level fully overlaps with the Ni 2p$_{3/2}$, and the La 3d$_{5/2}$ level introduces complex satellite features that interfere with the Ni 2p$_{1/2}$ region. These La-derived features, including intrinsic and extrinsic energy loss satellites, vary between materials due to differences in crystal structure and bonding environments, rendering standard subtraction-based analysis (using La-only reference compounds) ineffective. Consequently, reliable extraction of the intrinsic Ni 2p line shape and the determination of electronic parameters for La-based nickelates remain difficult.

Methodology
To address these limitations, the authors employed Hard X-ray Photoelectron Spectroscopy (HAXPES) to probe the deep Ni 1s core level in $La_3Ni_2O_7$, $Nd_3Ni_2O_7$, and the reference compound $LaNiO_3$. The use of hard x-rays (6.5 keV and 10 keV) provided sufficient bulk sensitivity to mitigate surface-dominated signals, which is critical for these challenging thin-film and crystal samples.

The experimental approach involved:

1. Comparative Spectroscopy: Direct comparison of Ni 1s spectra against Ni 2p spectra (specifically in the La-free $Nd_3Ni_2O_7$) to establish baseline line shapes and identify intrinsic features.
2. Reference Analysis: Examination of La 3d and La 3p spectra in La-containing and La-free compounds to map the extent of spectral overlap and satellite structures in the Ni 2p energy region.
3. Theoretical Modeling: Simulation of core-level spectra using Density Functional Theory combined with Dynamical Mean-Field Theory (DFT+DMFT). The authors utilized hybridization densities ($V(\epsilon)$) and charge-transfer energies ($\Delta_{dp}$) to systematically investigate how variations in these parameters affect the spectral weight distribution between the main peak and charge-transfer satellites.

Key Results

• Limitations of Ni 2p Analysis: The study confirmed that the Ni 2p$_{1/2}$ signal in La-based nickelates is obscured by high-energy satellites from the La 3d core level. These satellites, arising from both intrinsic and extrinsic excitations, prevent a clean isolation of the Ni 2p$_{1/2}$ features, making quantitative comparison between La- and Nd-based systems unreliable using 2p data alone.
• Viability of Ni 1s Spectroscopy: The Ni 1s core level offers a "clean" view of intrinsic electronic excitations. Unlike the 2p level, the 1s level lacks spin-orbit coupling, avoiding the overlap of $2p_{1/2}$ and $2p_{3/2}$ features. Furthermore, the multiplet interaction between the 1s core hole and 3d electrons is negligibly weak.
• Spectral Comparison: In $Nd_3Ni_2O_7$, the Ni 1s spectrum exhibits a main asymmetric peak and a satellite ~7 eV higher in energy, mirroring the features found in the Ni 2p spectra. While the Ni 1s peak is slightly broader than the Ni 2p$_{3/2}$ (due to core-hole lifetime effects), it is significantly sharper than the Ni 2p$_{1/2}$ and free from La interference.
• Material-Specific Differences: The Ni 1s spectra revealed distinct electronic structure differences between the bilayer compounds ($La_3Ni_2O_7$, $Nd_3Ni_2O_7$) and the perovskite $LaNiO_3$. Notably, $La_3Ni_2O_7$ displayed a broader main peak with reduced intensity and enhanced satellite spectral weight compared to $Nd_3Ni_2O_7$. These subtle distinctions were not evident in the overlapping Ni 2p spectra.
• Theoretical Interpretation: DFT+DMFT calculations indicated that the observed spectral broadening and satellite enhancement in $La_3Ni_2O_7$ (relative to $Nd_3Ni_2O_7$) are primarily driven by changes in hybridization strength rather than just charge-transfer energy. This is consistent with the different strain environments (tensile strain in $La_3Ni_2O_7$ on NdGaO$_3$ vs. compressive strain in $Nd_3Ni_2O_7$ on LaAlO$_3$) imposed by the substrates.

Significance and Claims
The paper claims that Ni 1s core-level photoelectron spectroscopy is a suitable and necessary alternative to the traditional Ni 2p method for investigating La-based nickelates. By avoiding the spectral congestion caused by La 3d overlap, the Ni 1s technique allows for the resolution of detailed differences in electronic structure within the strongly correlated Ruddlesden–Popper series.

The authors assert that this approach enables the isolation of specific effects—such as changes in charge-transfer energy and hybridization strength—on the electronic structure. While the complexity of the spectra makes fully quantitative comparisons between different compounds challenging when multiple parameters change simultaneously, the study demonstrates that systematic variations (e.g., changing the rare-earth element, layer number $n$, or substrate strain) can be used to disentangle these factors. This establishes a roadmap for detailed characterization of nickelate electronic structures, particularly for materials where surface sensitivity or spectral overlap has previously hindered analysis.