$3d_{z^2}$ orbital delocalization and magnetic collapse in superconducting (La,Pr)$_3$Ni$_2$O$_{7-\delta}$ films

By independently tuning strain and oxygen content in (La,Pr)$_3$Ni$_2$O$_{7-\delta}$ films, researchers identified a two-step mechanism for superconductivity driven by the delocalization of Ni $3d_{z^2}$ and O $2p_z$ orbitals, which suppresses long-range magnetic order while preserving robust short-range magnons.

The Gist

Imagine you have a very stubborn, non-conductive material (an insulator) that you want to turn into a superconductor—a material that conducts electricity with zero resistance. In the world of physics, this is like trying to turn a heavy, rusted brick into a super-highway for electrons.

This paper is about a specific type of "brick" called a Ruddlesden-Popper Nickelate (specifically a film made of Lanthanum, Praseodymium, and Nickel). Recently, scientists discovered that if you squeeze these materials hard enough (using high pressure), they suddenly become superconductors. But squeezing them in a lab is like trying to hold a watermelon with your bare hands while it's on a rocket; it's incredibly difficult to study how the magic happens.

So, the researchers in this paper decided to use a different trick. Instead of squeezing the whole block, they grew these materials as ultra-thin films on special tiles (substrates). By choosing the right tiles, they could "stretch" or "squeeze" the atoms in the film from the outside, mimicking the pressure without the rocket.

Here is the story of what they found, broken down into simple concepts:

1. The Two Magic Knobs

The researchers realized they could turn the material into a superconductor by adjusting two specific "knobs":

• Knob A: The Squeeze (Strain): They grew the films on tiles that forced the atoms closer together (compressive strain).
• Knob B: The Air (Oxygen): They controlled how much oxygen was in the film. Too little oxygen (vacancies) or too much (extra oxygen) acts like a pothole or a roadblock for electricity. They found the "Goldilocks" zone where the oxygen was just right.

2. The "Traffic Jam" vs. The "Highway" (Delocalization)

In the starting material (the insulator), the electrons are stuck. Imagine a crowd of people in a tiny, crowded room where everyone is holding hands and refusing to let go. They are localized.

• The "Upper Hubbard" Peak: In the data, this looked like a sharp, distinct peak. It's like seeing a single, frozen statue of a person.
• The Transformation: As they turned the "Squeeze" and "Air" knobs, the researchers saw the electrons start to let go of each other. The sharp statue melted into a blur.
• The Analogy: The electrons moved from being stuck in a "traffic jam" to flowing freely on a "highway." This is called delocalization. Specifically, they found that the electrons in the Nickel atoms (the $3d_{z^2}$ orbital) and the Oxygen atoms (the $2p_z$ orbital) started dancing together as a team. They formed a "molecular highway" connecting the layers of the material.

3. The Magnetic Tug-of-War

Before the material became a superconductor, it had a strong magnetic order called a Spin-Density Wave (SDW).

• The Analogy: Imagine a stadium full of people doing "The Wave." In the insulating state, the wave is perfect, long, and synchronized. Everyone knows exactly when to stand up. This is Long-Range Order.
• The Change: As the material got closer to becoming a superconductor, this perfect wave started to break down. The "synchronization" got messy. The wave became shorter and weaker.
• The Result: The long, perfect magnetic wave disappeared completely in the superconducting state. The researchers found that the magnetic order and the superconductivity are rivals; they fight for the same electrons. When the magnetic wave dies, the superconductivity is born.

4. The "Damped" Spin

Even though the long, perfect magnetic wave died, something interesting remained.

• The Analogy: Think of a guitar string. When you pluck it, it rings out clearly (the long wave). But if you dampen it with your hand, it still vibrates, but the sound is shorter and fuzzier.
• The Finding: The researchers saw that the magnetic vibrations (magnons) didn't disappear entirely; they just became "damped" or fuzzy. They lost their long-range coordination but kept their energy. This suggests that while the order is gone, the fluctuations (the jittery movement) remain strong. These "jittery" fluctuations might actually be the glue that holds the superconducting electrons together.

The Big Picture Conclusion

The paper tells us that to make this nickelate superconductor work, you need a specific recipe:

1. Squeeze the atoms (strain) and fix the oxygen (stoichiometry).
2. This forces the electrons to stop being stuck and start flowing freely, specifically through a special channel connecting the Nickel and Oxygen atoms.
3. This flow kills the long, rigid magnetic order (the "perfect wave").
4. In the chaos of that broken magnetic order, the electrons find a new way to pair up and flow without resistance.

Why does this matter?
It gives scientists a "roadmap." Instead of guessing how to make better superconductors, they now know they need to focus on delocalizing specific electron orbits and breaking long-range magnetic order while keeping short-range magnetic "jitter." It's like telling a chef: "To make the perfect cake, you don't just add more sugar; you have to make sure the flour is aerated and the butter is melted, or the cake won't rise."

This discovery moves us closer to understanding how to create room-temperature superconductors, which could revolutionize everything from power grids to maglev trains.

Technical Summary

1. Problem Statement

The recent discovery of high-temperature superconductivity in Ruddlesden–Popper (RP) bilayer nickelates (specifically La$_3$Ni$_2$O$_{7-\delta}$) under high hydrostatic pressure has opened a new frontier in unconventional superconductivity. However, the microscopic pathway from the parent insulating phase to the superconducting phase remains elusive. Key challenges include:

• Extreme Conditions: High-pressure experiments make it difficult to isolate specific structural and electronic variables.
• Orbital Complexity: Unlike cuprates, RP nickelates involve both Ni $d_{x^2-y^2}$ and $d_{z^2}$ orbitals, with ongoing debate regarding their relative roles in pairing.
• Magnetic Competition: The evolution of magnetic order (specifically Spin-Density-Wave, or SDW) and its competition with superconductivity is not fully understood.
• Material Control: Oxygen stoichiometry and strain are critical but difficult to decouple experimentally. Oxygen vacancies are known to be detrimental, while interstitial oxygen can suppress superconductivity.

The study aims to map the microscopic evolution of electronic and magnetic properties from a non-superconducting parent phase to a superconducting state by independently tuning compressive strain and oxygen content in thin films at ambient pressure.

2. Methodology

The authors synthesized two distinct series of high-quality (La,Pr)$_3$Ni$_2$O$_{7-\delta}$ thin films to independently control variables:

• Strain-Tuning Series:
  • Grown on LaAlO$_3$ (LAO, $\sim$-1% strain) and SrLaAlO$_4$ (SLAO, $\sim$-2% strain) substrates.
  • Both samples were insulating (non-superconducting) with comparable oxygen content.
  • This series isolates the effect of biaxial compressive strain on the NiO$_6$ octahedra.
• Oxygen-Stoichiometry-Tuning Series:
  • Grown on SLAO substrates using Gigantic-Oxidative Atomic-Layer-by-Layer Epitaxy (GAE).
  • Controlled via ozone-oxygen atmosphere and laser pulse ratios.
  • Produced two samples: one insulating (oxygen-deficient) and one superconducting ($T_c \approx 50$ K, near-optimal doping).
  • This series isolates the effect of hole doping and oxygen content.

Experimental Techniques:

• X-ray Absorption Spectroscopy (XAS): Performed at the O K-edge and Ni L$_3$-edge to probe unoccupied states and orbital character (in-plane vs. out-of-plane).
• Resonant Inelastic X-ray Scattering (RIXS): Used to map electronic excitations (dd transitions) and magnetic excitations (magnons) with high energy and momentum resolution.
• Measurements were conducted at 20 K using grazing incidence geometry to enhance sensitivity to out-of-plane orbitals ($d_{z^2}$ and O $2p_z$).

3. Key Contributions

• Decoupling Tuning Knobs: Successfully separated the effects of compressive strain and oxygen doping, demonstrating that both drive the system toward superconductivity via a common microscopic mechanism.
• Orbital-Selective Delocalization: Identified that the transition to superconductivity is driven specifically by the delocalization of the interlayer Ni $3d_{z^2}$ - O $2p_z$ - Ni $3d_{z^2}$ molecular orbital channel, while the in-plane $d_{x^2-y^2}$ orbital remains largely itinerant throughout.
• Magnetic Phase Diagram: Established a direct competition between long-range SDW order and superconductivity, showing that SDW is fully suppressed in the superconducting state, while short-range magnetic fluctuations (paramagnons) persist.
• Challenge to Theory: Provided experimental evidence contradicting Density Functional Theory (DFT) predictions that the $d_{z^2}$ band shifts significantly away from the Fermi level under strain; instead, the data suggests robust crystal-field splitting with delocalization.

4. Key Results

A. Electronic Structure Evolution

• O K-edge XAS: In the out-of-plane ($\pi$-polarized) spectra, spectral weight transfers from a "Upper Hubbard Band"-like peak (Peak B) to a hole-like peak (Peak A) associated with O $2p_z$ states. This transfer occurs in both strain-tuned and oxygen-tuned series, indicating that both methods drive the system from a Mott-like insulator to a delocalized state.
• Ni L-edge XAS & RIXS:
  • The Ni $3d_{z^2}$ orbital character (probed via $\pi$-polarization) shows progressive broadening and weakening of satellite features and dd orbital excitations (specifically $dd_2$ at $\sim$1.6 eV and $dd_3$ at $\sim$0.4 eV).
  • The broadening signifies increased itinerancy (delocalization) of the $d_{z^2}$ electrons.
  • Crucially, the excitation energies remain rigid, implying the local crystal field splitting is unaffected, but the electrons become less localized.
  • The in-plane $d_{x^2-y^2}$ orbitals show minimal change, suggesting they were already itinerant in the parent phase.

B. Magnetic Excitations

• Long-Range SDW Order:
  • The bulk parent compound exhibits long-range SDW order with a correlation length ($\xi$) of $\sim$30 nm.
  • In strained and oxygen-tuned films, the SDW intensity and correlation length decrease progressively ($\xi \approx 10-13$ nm).
  • In the superconducting sample (SC LPNO/SLAO3), the long-range SDW order is completely suppressed (no discernible signal), confirming a direct competition between magnetism and superconductivity.
• Short-Range Magnons:
  • Despite the loss of long-range order, short-range magnetic excitations (paramagnons) persist.
  • These magnons become significantly damped (lifetime reduced) but retain their bandwidth and energy scale.
  • This finding challenges theoretical predictions that compressive strain significantly enhances interlayer exchange coupling ($J_\perp$); the data suggests $J_\perp$ does not increase by the predicted 50%, but rather the system enters a regime of strong quantum fluctuations.

5. Significance and Conclusion

The paper establishes a coherent "orbital-selective" route to superconductivity in RP nickelates:

1. Prerequisites for Superconductivity: The transition requires the delocalization of the interlayer $3d_{z^2}$-$2p_z$-$3d_{z^2}$ molecular orbital channel and the melting of long-range SDW order.
2. Robust Fluctuations: Superconductivity emerges in the presence of robust, short-range magnetic fluctuations (damped magnons), similar to the paramagnon scenario in cuprates.
3. Design Roadmap: These findings provide strong constraints for theoretical models (ruling out simple band-shift models) and offer a roadmap for designing nickelate superconductors: maximize interlayer orbital hybridization and oxygen stoichiometry to suppress long-range magnetic order while preserving short-range spin fluctuations.

This work resolves the microscopic pathway from the parent phase to the superconducting state, highlighting the critical role of apical oxygen and interlayer coupling in high-temperature superconductivity.