Spin and orbital excitations in undoped infinite layers: a comparison between superconducting PrNiO2 and insulating CaCuO2

This study utilizes RIXS measurements to demonstrate that while superconducting PrNiO2 and insulating CaCuO2 share most spin and orbital properties despite their different charge-transfer energies, they exhibit distinct behaviors in the dispersion of Ni-dxy orbital excitations due to orbital superexchange coupling.

The Gist

Imagine two neighboring houses built on the same blueprint. One house is made of Copper (the "Cuprate," specifically CaCuO₂), and the other is made of Nickel (the "Nickelate," specifically PrNiO₂). Both houses are famous in the physics world because, under the right conditions, they can conduct electricity with zero resistance—a phenomenon called superconductivity.

For a long time, scientists thought these two houses were almost identical twins. They share the same floor plan (a flat, square grid of atoms) and the same basic wiring (electrons moving in specific patterns). But this new paper asks: Are they really the same, or are there subtle differences that explain why the Copper house is a better conductor than the Nickel house?

To find out, the researchers used a high-tech "flashlight" called RIXS (Resonant Inelastic X-ray Scattering). Think of this as a super-powerful camera that can take pictures of how the electrons inside the atoms are dancing, spinning, and jumping.

Here is what they discovered, explained through simple analogies:

1. The "Spin" Dance (Magnetism)

Inside these materials, the electrons act like tiny spinning tops. When they spin in opposite directions, they create a magnetic order, like a line of soldiers marching in perfect formation.

• The Copper House (CaCuO₂): The soldiers here are very energetic. They hold hands tightly with their neighbors, creating a strong, fast-moving wave of magnetism.
• The Nickel House (PrNiO₂): The soldiers here are a bit more laid back. They still march in formation, but they hold hands more loosely. The "grip" between them is weaker, meaning the magnetic waves move slower and with less energy.

The Big Surprise: Even though the Nickel house has some extra "guests" (electrons) that shouldn't be there (called self-doping), which usually messes up the marching formation, the soldiers in the Nickel house stay in line surprisingly well. In the Copper house, adding extra guests usually breaks the formation immediately. This suggests the Nickel house has a more robust way of staying organized even when it's "doped."

2. The "Orbital" Jumps (Electron Energy Levels)

Electrons don't just spin; they also live in specific "rooms" (orbitals) around the atom. Sometimes, they get a boost of energy and jump to a different room.

• The Copper House: When an electron jumps to a specific room (the dxy room), it can travel diagonally across the house, skipping over its immediate neighbors to talk to the ones two steps away. It's like a dancer skipping a beat to reach the person across the room.
• The Nickel House: Here, the electron in that same room behaves differently. It prefers to talk to its immediate neighbor right next to it. Furthermore, the energy required to make this jump is much lower in the Nickel house than in the Copper house.

The "Why": The researchers found that the "glue" holding the electrons together (the charge-transfer energy) is stronger in the Nickel house. This makes the electrons feel more "stuck" to their home atoms (more localized) and less free to roam around the whole house compared to the Copper electrons.

3. The "Rare Earth" Factor

The Nickel house has a special guest in the basement: a Rare Earth element (Praseodymium). The Copper house doesn't have this.

• This guest seems to act like a self-doping mechanism, putting extra electrons into the system without anyone physically adding them.
• The paper suggests this guest might be interacting with the Nickel electrons in a unique way, creating a "cloud" of charge that helps the material become superconducting, even though the magnetic waves are weaker.

The Bottom Line

The paper concludes that while the Nickel and Copper houses are cousins with very similar blueprints, they aren't identical twins.

• Similarities: Both have 3D magnetic order (the soldiers march in 3D, not just 2D) and both support superconductivity.
• Differences: The Nickel house has weaker magnetic waves and stronger electron localization (electrons are more stuck to their atoms).

Why does this matter for superconductivity?
The researchers suggest that the reason the Nickel house has a lower "superconducting temperature" (it needs to be colder to work) is exactly because of these differences. The magnetic waves are weaker, and the electrons are more stuck in place. In the Copper house, the stronger, more energetic magnetic waves seem to be the secret sauce that allows it to superconduct at higher temperatures.

In short, the Nickel house is a great mimic of the Copper house, but it's missing a few key ingredients (stronger magnetic energy and more mobile electrons) that make the Copper house the champion of high-temperature superconductivity.

Technical Summary

Technical Summary: Spin and Orbital Excitations in Undoped Infinite-Layer Nickelates vs. Cuprates

Problem and Motivation
Infinite-layer (IL) nickelates have emerged as a promising family of cuprate-analogous superconductors, sharing a square-lattice structure and $3d^9$ electronic configurations (Ni$^{1+}$ vs. Cu$^{2+}$). However, significant differences persist regarding their electronic ground states and the mechanism of superconductivity. While IL cuprates like CaCuO$_2$ are well-characterized insulators with long-range antiferromagnetic (AFM) order, IL nickelates (e.g., PrNiO$_2$) are nominally undoped yet exhibit superconductivity in thin films, often accompanied by spin-glass behavior and self-doping effects. A critical open question is whether the spin and orbital excitation spectra of IL nickelates mirror those of cuprates sufficiently to support a unified mechanism for unconventional superconductivity, or if fundamental differences in charge-transfer energy ($\Delta$) and hopping integrals dictate distinct physics. Specifically, the nature of magnetic exchange interactions and the propagation mechanisms of orbital excitations (orbitons) in the absence of apical oxygens require direct comparative investigation.

Methodology
The authors employed momentum- and polarization-resolved Resonant Inelastic X-ray Scattering (RIXS) at the Ni $L_3$ edge (852.4 eV) and Cu $L_3$ edge (930.6 eV) to probe the dynamical spin and orbital responses of nominally undoped, superconducting PrNiO$_2$ (PNO) and insulating CaCuO$_2$ (CCO).

• Samples: High-quality PNO thin films were grown via Pulsed Laser Deposition (PLD) on SrTiO$_3$ and reduced topotactically to the IL phase. CCO data were re-analyzed from previously published datasets.
• Measurements: Spectra were collected along high-symmetry cuts of the Brillouin zone ($M-\Gamma-X$). The study utilized linear polarization analysis ($\sigma$ and $\pi$ incident light) to disentangle spin-conserving and spin-flip channels and to identify orbital symmetries.
• Analysis: Magnetic dispersions were fitted using the Linear Spin Wave (LSW) model to extract exchange coupling constants ($J$). Orbital excitations were analyzed via single-ion cross-section calculations and fitted with Voigt profiles. Theoretical modeling of orbiton propagation utilized a Kugel-Khomskii spin-orbital Hamiltonian mapped onto a polaronic model, incorporating Hund's exchange ($J_H$) and Hubbard $U$ parameters derived from charge-transfer models.

Key Results

1. Magnetic Excitations and Exchange Couplings:

   • Both PNO and CCO exhibit sharp spin excitation peaks dispersing up to $\sim$200 meV (PNO) and $\sim$400 meV (CCO), consistent with single-magnon behavior.
   • In-plane Exchange ($J_1$): The nearest-neighbor in-plane exchange integral in PNO ($J_1 \approx 46$ meV) is approximately half that of CCO ($J_1 \approx 82$ meV).
   • Out-of-plane Exchange ($J_\perp$): Despite the structural differences (absence of apical oxygens in both), the out-of-plane exchange is comparable ($J_\perp \approx 6$ meV for PNO, $7$ meV for CCO). This indicates that both materials support a three-dimensional AFM order, with a similar ratio of out-of-plane to in-plane coupling.
   • Damping: The magnetic peak in PNO shows a damping coefficient of $\sim$100 meV, significantly larger than the resolution-limited CCO but much smaller than that of doped cuprates. This suggests that self-doping in IL nickelates has a milder disruptive effect on spin order compared to chemical hole doping in cuprates.

2. Orbital Excitations (dd-transitions):

   • The $d_{xy}$, $d_{xz/yz}$, and $d_{3z^2-r^2}$ orbital excitations are observed in both materials. The $d_{xy}$ peak in PNO is at a significantly lower energy (1.29 eV) compared to CCO (1.65 eV), attributed to larger charge-transfer energy $\Delta$ and smaller hopping integrals in nickelates.
   • Dispersion Anomaly: The $d_{xy}$ orbital excitation displays an opposite dispersion shape in the two materials. In CCO, the energy is minimal at $\Gamma$ and maximal at the zone boundary. In PNO, the energy is maximal at $\Gamma$ and decreases toward the boundary.
   • Polarization: The $d_{xy}$ peak in PNO exhibits mixed polarization character at positive momentum transfers, unlike the purely crossed polarization expected for CCO. This is attributed to hybridization between Ni $3d$ and Pr $5d$ (or interstitial $s$) states.

3. Mechanism of Orbiton Propagation:

   • The opposite dispersion shapes are explained by distinct dominant orbital superexchange pathways.
   • CCO: The dispersion is driven by dominant next-nearest-neighbor (NNN) orbital superexchange ($J^{orb}_{NNN}$), which allows orbitons to propagate along diagonals, avoiding the "magnetic string effect" (frustration caused by coupling to magnons) that suppresses nearest-neighbor (NN) motion in AFM backgrounds.
   • PNO: The dispersion is driven by dominant nearest-neighbor (NN) orbital superexchange ($J^{orb}_{NN}$). In PNO, the NN orbital hopping is enabled because a finite Hund's exchange ($J_H$) in the intermediate state allows for a concomitant orbital and spin flip, preserving the AFM order and bypassing the string effect. Theoretical calculations confirm that $J^{orb}_{NN}$ dominates in PNO, whereas $J^{orb}_{NNN}$ dominates in CCO due to stronger covalency in the latter.

Significance and Claims
The paper demonstrates that while infinite-layer nickelates and cuprates share the fundamental architecture of spin and orbital excitations, quantitative differences in interaction parameters lead to distinct physical behaviors.

• Similarities: Both systems exhibit 3D magnetic correlations despite the lack of apical oxygens, and both support dispersive orbital excitations.
• Differences: The larger charge-transfer energy ($\Delta$) and smaller hopping integrals in nickelates result in weaker spin-fluctuation energies and stronger localization of doping charges on the metal site. The mechanism for orbiton propagation differs fundamentally: CCO relies on NNN exchange to bypass magnetic frustration, while PNO utilizes NN exchange facilitated by Hund's coupling.
• Implications for Superconductivity: The authors conclude that IL nickelates mimic the essential physics of cuprates but with reduced interaction energies. The lower critical temperature ($T_c$) in nickelates is attributed to the overall smaller energy scale of spin fluctuations. Furthermore, the Mott-Hubbard character of nickelates implies stronger charge localization, potentially suppressing charge density waves and electron-phonon interactions that are ubiquitous in hole-doped cuprates. The presence of rare-earth ions in nickelates provides a unique self-doping mechanism absent in IL cuprates, enabling superconductivity without the need for chemical doping that disrupts magnetic order.

The study establishes that IL nickelates are unconventional superconductors closely related to cuprates but lacking specific ingredients (such as high-energy spin fluctuations and specific charge-ordering tendencies) that enhance $T_c$ in the copper-oxide family.