From perovskite to infinite-layer nickelates: hole concentration from x-ray absorption

Using soft x-ray absorption spectroscopy, this study reveals that infinite-layer nickelate thin films do not achieve the assumed pure $d^9$ configuration even when maximally reduced, as quantitative analysis shows a persistent nickel $3d$hole count of 1.35 alongside oxygen$2p$ holes, indicating a complex interplay of self-doping and oxygen non-stoichiometry.

The Gist

Here is an explanation of the paper using simple language and creative analogies.

The Big Picture: The "Nickel Superconductor" Mystery

Imagine you are trying to bake the perfect cake (a superconductor) that conducts electricity with zero resistance. For decades, scientists have been obsessed with a specific type of cake made of Copper (cuprates). Recently, they discovered a new, very similar recipe using Nickel (nickelates) that might work even better.

The goal is to turn a blocky, 3D brick wall of atoms (a Perovskite) into a flat, 2D pancake stack (an Infinite-Layer structure). To do this, they have to "bake out" the oxygen atoms that hold the bricks together.

The Problem: Scientists have been struggling to figure out exactly what the "recipe" looks like once the cake is baked. They know when it becomes superconductive, but they don't know the exact chemical balance (how many electrons are missing) inside the nickel atoms. It's like trying to guess the exact amount of sugar in a cake just by looking at it, without being able to taste it.

The Experiment: X-Ray "Flash Photography"

The researchers in this paper used a powerful tool called Soft X-ray Absorption Spectroscopy (XAS).

• The Analogy: Imagine taking a high-speed flash photo of a crowded room. The light hits the people (atoms), and some people absorb the light while others reflect it. By analyzing exactly how the light is absorbed, you can tell exactly who is in the room and what they are wearing.
• The Application: They shone X-rays on thin films of Nickel-Oxygen. By looking at how the Nickel atoms absorbed the light, they could count exactly how many "holes" (missing electrons) were in the nickel atoms.

The Journey: From Brick Wall to Pancake Stack

The team took samples of Nickel-Oxygen and slowly removed the oxygen in stages, like peeling layers off an onion. They stopped at various stages to take their "X-ray photos."

1. The Start (Perovskite): The atoms are in a 3D cube shape. The nickel atoms have a specific number of electrons.
2. The Middle (Intermediate): As they remove oxygen, the structure changes. Some oxygen atoms leave, creating empty spots (vacancies).
3. The End (Infinite-Layer): The goal is to remove all the top and bottom oxygen, leaving only flat sheets of Nickel and Oxygen. This is the "superconducting" state.

The Big Surprise: The "Hole" Count

Scientists had a theory: To get superconductivity, you need a specific number of "holes" (missing electrons) in the nickel atoms. They thought the limit was around 1.2 holes.

What they actually found:
Even in the samples that were "fully reduced" (supposedly perfect), the nickel atoms still had 1.35 holes.

• The Twist: The samples that actually became superconductors had even more holes (around 1.55).

The Metaphor:
Imagine a parking lot where you need exactly 1.2 empty spots for a car to park perfectly. The scientists thought, "If we have more than 1.2 empty spots, the car won't fit."
But this paper says, "Actually, the car fits perfectly fine with 1.55 empty spots! We were measuring the parking lot wrong all along."

Why Was It So Hard to Measure? (The "Messy Kitchen" Problem)

The paper explains that making these films is messy.

• The Cation Mess: Sometimes the wrong atoms (like Calcium or Strontium) get mixed in by accident.
• The Oxygen Mess: It is very hard to remove exactly the right amount of oxygen. Sometimes you leave a few extra oxygen atoms behind, or you create a chaotic mix of ordered and disordered areas.

The Analogy:
Think of the film as a mosaic made of tiles.

• Some tiles are perfectly aligned (the "clean" superconducting zones).
• Some tiles are crooked or missing (the "disordered" zones).
• The X-ray beam is like a flashlight. If the flashlight is too big, it shines on both the clean tiles and the messy tiles at the same time, giving you an "average" picture that looks blurry.

The researchers found that the "messiness" (disorder) in the oxygen and atom arrangement was hiding the true nature of the superconducting state. The superconductivity happens in the clean, ordered pockets, but the "average" measurement made it look like the whole film was a bit different.

The "Self-Doping" Secret

The paper suggests that the nickel atoms are "self-doping."

• The Analogy: Imagine a group of friends (the atoms) sharing a pizza. Usually, you need to bring extra toppings (doping) to get the right flavor. But in these nickel films, the friends are rearranging the pizza slices among themselves so perfectly that they create the right flavor without needing extra toppings from the outside. The electrons are moving around in a way that creates the perfect conditions for superconductivity naturally.

The Conclusion: What Does This Mean?

1. We were wrong about the limit: Superconductivity in these nickel films happens at a higher "hole" concentration than we thought.
2. Oxygen is tricky: We can't just assume the oxygen count is perfect. There are likely hidden oxygen atoms messing up the count.
3. It's a complex dance: The superconductivity isn't just about one number; it's about a complex interplay between the arrangement of atoms, the missing oxygen, and how electrons move between them.

In a nutshell: The scientists used X-rays to take a closer look at the "recipe" for nickel superconductors. They realized the recipe isn't as simple as everyone thought. The "perfect" cake actually requires a bit more "missing sugar" (holes) than expected, and the kitchen (the film) is messier than we admitted. This new understanding helps us figure out how to bake better, more reliable superconducting cakes in the future.

Technical Summary

Here is a detailed technical summary of the paper "From perovskite to infinite-layer nickelates: hole concentration from x-ray absorption" by R. Pons et al.

1. Problem Statement

The emergence of infinite-layer nickelates ($RNiO_2$) as a new class of unconventional superconductors has sparked intense research, particularly regarding their electronic configuration and doping mechanisms. However, a critical bottleneck remains: the difficulty in precisely determining cation concentrations and oxygen stoichiometry in thin films.

• The Core Issue: Previous studies assumed that superconductivity in these materials occurs at a specific hole doping level (typically $h_{3d} \approx 1.2$ holes per Ni, analogous to cuprates) and that the nickel ion adopts a pure $d^9$ ($Ni^{1+}$) configuration in the superconducting phase.
• The Gap: The topotactic reduction process (converting perovskite $RNiO_3$ to $RNiO_2$) is often non-uniform, creating intermediate phases and disorder. It is unclear whether the superconducting state arises from a pure $d^9$ state, self-doping effects, or residual oxygen non-stoichiometry. Furthermore, the relationship between the lattice parameter ($c$) and the actual electronic filling ($n_{3d}$) has not been quantitatively established.

2. Methodology

The authors employed Soft X-ray Absorption Spectroscopy (XAS) to probe the local electronic structure of Praseodymium Nickelate ($PrNiO_x$) thin films at various stages of topotactic reduction.

• Sample Preparation:

  • Three sets of samples were studied:
    1. MBE-1: PrNiO$_3$ grown on NdGaO$_3$ (NGO), reduced without direct contact with the reducing agent ($CaH_2$) to capture intermediate states.
    2. MBE-2: Thinner films on SrTiO$_3$ (STO) with an STO capping layer, reduced via direct contact (Methods A and B).
    3. PLD: Pulsed Laser Deposition samples on STO with STO capping, including a superconducting sample (PLD-2).
  • Reduction was achieved via annealing with $CaH_2$, creating a series of samples with varying out-of-plane lattice parameters ($c$) ranging from the perovskite phase ($c \approx 3.80$ Å) to the infinite-layer phase ($c \approx 3.32$ Å).

• Experimental Techniques:

  • Ni-L Edge XAS: Measured using linearly polarized X-rays to determine the valence state, orbital polarization, and $3d$hole count. Both in-plane ($x$) and out-of-plane ($z$) polarizations were analyzed to calculate linear dichroism.
  • O-K Edge XAS: Used to investigate the hybridization strength between Ni-$3d$and O-$2p$ orbitals and to detect oxygen vacancies.
  • Quantitative Analysis: The Charge Sum Rule was applied to the polarization-averaged Ni-L spectra. The integrated intensity of the absorption spectrum is proportional to the number of $3d$holes ($h_{3d} = 10 - n_{3d}$).
  • Theoretical Modeling:
    • Single Cluster Ligand-Field Calculations: Modeled $d^7$, $d^8$ (high-spin and low-spin), and $d^9$ configurations.
    • Double Cluster Calculations: Modeled coupled Ni sites to account for charge transfer and interactions between different local environments (e.g., $d^8$ coupled with $d^9L$).

3. Key Results

A. Nickel Electronic Configuration and Hole Concentration

• No Pure $d^9$ State: Contrary to the assumption that the infinite-layer phase is a pure $Ni^{1+}$ ($d^9$) system, the XAS spectra of all samples, including the most reduced ones, showed deviations from a pure $d^9$ signature.
• Quantitative Hole Count: Using the charge sum rule calibrated against NiO and theoretical models, the authors found that even the "maximally reduced" films have an average nickel $3d$hole count of **$h_{3d} \approx 1.35$** (corresponding to$n_{3d} \approx 8.65$).
• Superconducting Samples: The superconducting sample (PLD-2) exhibited an even higher hole concentration ($h_{3d} \approx 1.55$, $n_{3d} \approx 8.45$) than the non-superconducting samples with similar lattice parameters. This challenges the previously assumed "optimal doping" limit of $\sim 1.2$ holes.
• Lattice Parameter vs. Electronic State: The out-of-plane lattice parameter $c$ is insufficient to characterize the electronic configuration. Samples with identical $c$ values ($\approx 3.33$ Å) exhibited significantly different hole concentrations and spectral features.

B. Oxygen Stoichiometry and Hybridization

• Oxygen K-edge Analysis: The O-K edge spectra revealed that even in the most reduced films, there is a finite degree of hybridization between O-$2p$and Ni-$3d$ states.
• Residual Oxygen: The presence of specific spectral features (e.g., at 530, 535, and 540 eV) and the high hole count suggest that the films are off-stoichiometric, likely containing residual oxygen (estimated around $PrNiO_{2.2}$ rather than ideal $PrNiO_2$).
• Doping Mechanism: The results suggest that hole doping is not solely driven by cation substitution (Sr/Ca) but is heavily influenced by oxygen non-stoichiometry and self-doping effects arising from $R-5d$ and $Ni-3d$ hybridization.

C. Orbital Polarization and Disorder

• Incomplete Polarization: While infinite-layer nickelates are expected to show complete orbital polarization (strong linear dichroism with $I_z \approx 0$), the experimental samples showed only partial polarization.
• Microstructural Disorder: The authors attribute this to a complex interplay of domains. Superconductivity requires a percolating path of ordered, self-doped regions. The XAS signal, being an average over a larger volume, detects a mixture of ordered ($d^9$-like) and disordered ($d^8$-like or oxygen-deficient) regions.
• Double Cluster Insight: Theoretical modeling suggests that coupling between $d^8$ (high-spin) and $d^9L$ sites destabilizes the low-spin $d^8$ state, leading to a mixed valence state that explains the observed spectral features better than a pure single-cluster model.

4. Significance and Implications

• Redefining the Phase Diagram: The study fundamentally challenges the existing phase diagrams of nickelate superconductors. It suggests that the superconducting dome extends to much higher hole doping levels ($h_{3d} \approx 1.55$) than previously thought, provided the oxygen stoichiometry is accounted for.
• Stoichiometry is Critical: The assumption of exact $O_2.0$ stoichiometry in previous literature is likely incorrect. The "parent" compounds (undoped $y=0$) may actually be oxygen-deficient, acting as the source of doping.
• Synthesis Control: The results highlight that the reduction method (direct vs. indirect contact with $CaH_2$) and the presence of capping layers significantly impact the crystallinity and electronic homogeneity. Direct contact reduction with a capping layer yields higher crystallinity and potentially more stable superconducting phases.
• Future Directions: The paper emphasizes that achieving reproducible superconductivity requires controlling disorder on length scales larger than the X-ray probe but smaller than transport measurements. Future work must focus on targeted heterostructure designs to minimize anion and cation disorder.

Conclusion

This work provides a rigorous quantitative analysis of the electronic structure of infinite-layer nickelates, demonstrating that they are not simple $d^9$ systems but rather complex mixtures of valence states driven by oxygen non-stoichiometry and self-doping. The finding that superconductivity persists at higher hole concentrations than previously assumed necessitates a revision of the theoretical understanding of the nickelate phase diagram and the mechanisms driving unconventional superconductivity in these materials.