Multiorbital Anisotropy and Magnetic Excitations in Trilayer Nickelate Pr₄Ni₃O₁₀

Summary

Here, combining X-ray absorption spectroscopy and resonant inelastic X-ray scattering, we investigate the multi-orbital electronic structure and magnetic excitations of the trilayer nickelate Pr₄Ni₃O₁₀. Because the Pr resonances do not cover the Ni L₃ edge, the Ni L₃ edge can be probed directly; polarization-dependent measurements at the Ni L edge and O K edge resolve in-plane and out-of-plane Ni-O hybridization channels. Momentum-resolved RIXS reveals dispersive magnetic excitations that soften at the incommensurate spin-density-wave wavevector. Effective spin-wave analysis yields substantial intra-trilayer exchange coupling, comparable in magnitude to the dominant in-plane interaction and insensitive to rare-earth substitution. These results indicate that the multilayer structure, rather than rare-earth substitution alone, is the key factor tuning the magnetic interactions in this class of materials.

Materials

• Pr₄Ni₃O₁₀
• La₄Ni₃O₁₀ (reference)

Methods

• X-ray absorption spectroscopy (XAS)
• resonant inelastic x-ray scattering (RIXS)
• polarization-dependent XAS
• momentum-resolved Ni L₃-edge RIXS
• linear spin-wave theory (LSWT)
• entangled-dimer spin-wave calculations
• stripe-dimer calculations
• high-oxygen-pressure optical floating-zone crystal growth
• x-ray Laue diffraction
• total-electron-yield (TEY) and total-fluorescence-yield (TFY) detection

Keywords

• multiorbital electronic structure
• magnetic excitations
• ni o hybridization
• incommensurate spin density wave
• intra trilayer exchange coupling
• multilayer architecture
• rare earth substitution
• charge transfer excitations
• orbital anisotropy
• interlayer coupling

Highlights

• Pr₄Ni₃O₁₀ provides direct access to the Ni L₃ edge because Pr resonances do not overlap it, avoiding the La-Ni overlap that complicates Ni-edge interpretation in La-based Ruddlesden-Popper nickelates.
• Polarization-dependent measurements at the Ni L- and O K-edges reveal a common anisotropy and approximately 0.2 eV shifts between predominantly in-plane and out-of-plane hybridized Ni-O states.
• The fitted effective interlayer coupling is comparable to or slightly larger than the nearest-neighbor in-plane coupling despite spanning the full trilayer across the middle NiO₂ layer.
• The observed magnetic-excitation periodicity is consistent with antiparallel outer-layer moments and an inner layer near a magnetic node; a sizable inner-layer moment would double the periodicity along the nominal direction and is inconsistent with the data.
• Entangled-dimer and stripe-dimer calculations independently support a substantial effective interlayer coupling, confirming the robustness of the inferred interaction hierarchy.
• Compared with La₄Ni₃O₁₀, Pr₄Ni₃O₁₀ shows broader orbital excitations and lacks the broad 3-6 eV La-hybridized charge-transfer feature, reflecting structural and electronic changes induced by Pr substitution.

Conclusions

• Polarization-dependent XAS and RIXS resolve distinct planar and out-of-plane Ni-O hybridization channels and the multiorbital electronic structure of Pr₄Ni₃O₁₀.
• Momentum-resolved RIXS reveals dispersive magnetic excitations that soften toward the incommensurate spin-density-wave wave vector, consistent with an outer-layer-dominated spin configuration and a magnetically suppressed inner layer.
• An effective spin-wave analysis yields a sizable intra-trilayer exchange coupling comparable to the leading in-plane interactions and robust against rare-earth substitution.
• The dominant magnetic interaction scales of trilayer Ruddlesden-Popper nickelates remain robust against rare-earth substitution, identifying the multilayer architecture rather than rare-earth substitution alone as a key control parameter of the magnetic interactions.

Main claims

• Pr₄Ni₃O₁₀ provides direct access to the Ni L₃ edge because the Pr resonance does not overlap the Ni L₃ edge.
  • Evidence: The abstract states that the absence of an overlapping rare-earth resonance provides direct access to the Ni L₃ edge.,The full text notes that in La₄Ni₃O₁₀ a strong La edge contribution overlaps the low-energy side of the Ni L₃-edge resonance and must be modeled and subtracted, whereas Pr₄Ni₃O₁₀ provides direct access to the Ni resonance without overlapping rare-earth states.
• Polarization-dependent XAS and RIXS resolve distinct planar and out-of-plane Ni-O hybridization channels.
  • Evidence: The abstract states that polarization-dependent measurements at the Ni L- and O K-edges resolve distinct planar and out-of-plane Ni-O hybridization channels.,The full text reports common polarization-dependent resonance shifts at the Ni and O edges by approximately 0.2 eV, enhanced pi-polarized response, and redistribution of O K-edge charge-transfer spectral weight.
• Momentum-resolved RIXS reveals dispersive magnetic excitations that soften toward the incommensurate spin-density-wave wave vector.
  • Evidence: The abstract states that momentum-resolved RIXS reveals dispersive magnetic excitations that soften toward the incommensurate spin-density-wave wave vector.,The full text reports fitted excitation energies spanning approximately 20-85 meV and softening along the direction toward the incommensurate SDW wave vector near r.l.u., with spectral weight accumulating near zero energy loss.
• Effective spin-wave analysis yields a sizable intra-trilayer exchange coupling comparable to the leading in-plane interactions and robust against rare-earth substitution.
  • Evidence: The abstract states that an effective spin-wave analysis yields a sizable intra-trilayer exchange coupling comparable to the leading in-plane interactions and robust against rare-earth substitution.,The full text reports that the effective coupling between the two outer NiO₂ layers is comparable to, and slightly larger than, the nearest-neighbor in-plane coupling, and that entangled-dimer calculations yield a comparable interlayer coupling.,The full text also states that recent RIXS studies of La₄Ni₃O₁₀ find similar interaction scales, indicating similar interlayer interaction between Pr- and La-based trilayer compounds.
• The multilayer architecture, rather than rare-earth substitution alone, is a key control knob of the magnetic interactions in these materials.
  • Evidence: The abstract states that the results identify the multilayer architecture, rather than rare-earth substitution alone, as a key control knob of the magnetic interactions.,The full text contrasts the weak La-Pr dependence with the pronounced variation of interaction scales across different layer numbers, and compares trilayer Pr₄Ni₃O₁₀ with bilayer La₃Ni₂O₇.
• Because Pr₄Ni₃O₁₀ is metallic, the fitted exchange parameters represent effective interaction scales that may incorporate charge degrees of freedom and itinerant band effects.
  • Evidence: The full text states that the metallic nature of these materials suggests that charge degrees of freedom may also play a role in the magnetism in trilayer nickelates.,The full text states that the fitted exchange parameters therefore represent effective interaction scales incorporating the combined effect of local moments together with electronic correlations and itinerant band effects.,The full text notes that multiband Hartree-Fock and random-phase approximation calculations reproduce an outer-layer-dominated SDW structure within an itinerant framework without assuming preexisting localized moments.

Workflow

• sample_preparation — High-quality oriented Pr₄Ni₃O₁₀ single crystals were prepared for spectroscopic measurements.
  • Materials: Pr₄Ni₃O₁₀ single crystals
  • Methods: high-oxygen-pressure optical floating-zone growth; x-ray Laue diffraction for crystal quality and orientation
  • Observations: High-quality single crystals of Pr₄Ni₃O₁₀ were synthesized.; Crystal quality and orientation were verified by x-ray Laue diffraction before XAS and RIXS measurements.
• measurement — XAS and RIXS measurements resolve multiorbital electronic anisotropy and magnetic excitations in Pr₄Ni₃O₁₀.
  • Materials: Pr₄Ni₃O₁₀ single crystals; Ni L-edge; O K-edge
  • Methods: x-ray absorption spectroscopy (XAS); resonant inelastic x-ray scattering (RIXS); polarization-dependent XAS and RIXS; momentum-resolved Ni L₃-edge RIXS; total-electron-yield (TEY) and total-fluorescence-yield (TFY) detection
  • Observations: The absence of an overlapping rare-earth resonance provides direct access to the Ni L₃ edge.; Polarization-dependent measurements at the Ni L- and O K-edges resolve distinct planar and out-of-plane Ni-O hybridization channels.; Momentum-resolved RIXS reveals dispersive magnetic excitations that soften toward the incommensurate spin-density-wave wave vector.
• analysis — Effective spin-wave analysis yields a sizable intra-trilayer exchange coupling comparable to the leading in-plane interactions.
  • Materials: XAS spectra; RIXS spectra; Ni L₃-edge RIXS spectra
  • Methods: spectral fitting with elastic line, mid-infrared background, and damped harmonic oscillator components; linear spin-wave theory using the Sunny package; simultaneous fit to in-plane and fixed-q scans; structural twin averaging; entangled-dimer calculations
  • Observations: Fitted magnetic excitation energies span approximately 20-85 meV.; The effective coupling between the two outer NiO₂ layers is comparable to, and slightly larger than, the nearest-neighbor in-plane coupling.; Alternative entangled-dimer calculations yield an interlayer coupling comparable to the leading in-plane interactions.
• interpretation — The multilayer architecture, rather than rare-earth substitution alone, is a key control knob of the magnetic interactions in these materials.
  • Materials: multiorbital electronic structure; magnetic excitation spectrum; exchange interaction scales
  • Methods: comparison with La₄Ni₃O₁₀; comparison with bilayer La₃Ni₂O₇; comparison with square-planar R4Ni3O8
  • Observations: Dominant magnetic interaction scales of trilayer Ruddlesden-Popper nickelates remain robust against rare-earth substitution.; The contrast with the pronounced variation across different layer numbers identifies multilayer architecture as a primary control parameter.; The interaction scales provide an ambient-pressure reference for how the hierarchy may evolve under pressure toward superconductivity.