Collective spin excitations in trilayer nickelate La$_4$Ni$_3$O$_{10}$

Abstract: Ruddlesden-Popper (RP) nickelates have recently emerged as a new family of high-temperature superconductors. In bilayer RP nickelates, magnetic excitations with large exchange couplings have been observed, supporting a spin-mediated pairing mechanism. Whether comparable spin correlations persist in trilayer nickelates, however, remains unknown. Here, we present a Ni $L$-edge resonant inelastic X-ray scattering (RIXS) study of La$<em>4$Ni$_3$O$</em>{10}$ single crystals. While the orbital excitations remain similar to those of La$<em>3$Ni$_2$O$</em>{7}$, the collective spin excitations in La$<em>4$Ni$_3$O$</em>{10}$ exhibit a comparable bandwidth of about $60$ meV but substantially suppressed spectral weight, implying a weaker electronic correlation in the trilayer compounds. Our results underscore the three-dimensional and multi-orbital electronic character in La$<em>4$Ni$_3$O$</em>{10}$, highlighting important differences from the bilayer nickelates. These findings provide crucial insights into the evolution of magnetism across the RP nickelate family and its connection to superconductivity.

• The paper demonstrates that localized spin-flip and dispersive magnon modes coexist in La₄Ni₃O₁₀ using high-resolution RIXS and theoretical modeling.
• It quantifies exchange interactions (SJ₁=12 meV, SJ₂=8 meV, SJ⊥=20 meV), underscoring the transition to 3D magnetic dynamics over bilayer systems.
• The study reveals suppressed magnetic spectral weight in trilayer nickelates, emphasizing its relevance for spin-mediated superconductivity.

Collective Spin Excitations in Trilayer Nickelate La$_4$Ni$_3$O$_{10}$

Introduction

The paper "Collective spin excitations in trilayer nickelate La$_4$Ni$_3$O$_{10}$" (2604.04643) presents a comprehensive Ni $L$-edge RIXS investigation into the magnetic excitation spectrum of bulk La$_4$Ni$_3$O$_{10}$, a member of the Ruddlesden-Popper (RP) nickelate family. The study critically addresses the persistence and character of spin correlations in trilayer nickelates and their contrast with bilayer analogs, scrutinizing their implications for unconventional superconductivity. Through combined high-resolution spectroscopy and theoretical modeling, the authors dissect the interplay between dimensionality, electronic correlations, multiorbital effects, and low-energy magnetic dynamics.

Electronic Structure and Low-Energy Excitations

The characterization starts with oxygen $_3$0-edge and Ni $_3$1-edge XAS, establishing strong hybridization between O 2$_3$2 and Ni 3$_3$3 orbitals and the presence of substantial ligand hole character in La$_3$4Ni$_3$5O$_3$6, consistent with the extended multiband character of RP nickelates.

Figure 1: Crystal structure, comparative XAS of La$_3$7Ni$_3$8O$_3$9 (10), La$_{10}$0Ni$_{10}$1O$_{10}$2 (7), NiO, and LaNiO$_{10}$3, and RIXS energy dependence at the Ni $_{10}$4-edge, highlighting the resonance conditions and incident energy selection.

The fine structure around the Ni $_{10}$5-edge enables selective enhancement of both $_{10}$6 and low-energy spin excitations in the RIXS response. The main resonance corresponds to $_{10}$7 transitions, with a significant satellite at higher energy reflecting less efficient core-hole screening. The robust pre-edge features and comparison among reference systems confirm the importance of ligand holes and substantial three-dimensional and multiorbital character.

Magnetic Excitation Spectrum: Dispersion and Localization

Detailed momentum-resolved RIXS at low energies reveals several distinct excitation features. The excitations at ~100 meV and ~200 meV are sharp, resolution-limited, and momentum-independent, with polarization analysis indicating their predominant magnetic origin. In contrast, a weaker mode at ~60 meV shows clear dispersion, especially along high-symmetry directions in reciprocal space.

Figure 2: Representative RIXS spectra deconvolved into elastic, magnetic, and high-energy contributions; momentum-mapped RIXS intensity with the assignment of in-plane tracks and low-temperature data acquisition.

The dispersionless excitations are understood as localized single-ion spin-flip processes, whereas the 60 meV excitation is assigned to collective magnon modes associated with the incommensurate SDW order observed in previous neutron studies.

Polarimetric RIXS and Theoretical Modeling

Polarimetric selection rules confirm the magnetic nature of the low-energy excitations. Exact diagonalization (ED) simulations of a high-spin $_{10}$8 configuration under an effective exchange field of $_{10}$9 meV successfully reproduce both the energies and selection rules of the localized excitations, supporting the single-ion interpretation.

Figure 3: Polarimetric RIXS of La$_4$0Ni$_4$1O$_4$2, showing decomposed $_4$3- and $_4$4-channels, and ED-based calculation of spin excitation spectra capturing experimental features with lifetime broadening.

The collective mode's dispersion is quantitatively captured using linear spin wave theory (LSWT) for a Heisenberg Hamiltonian including two distinct in-plane and one interlayer exchange interactions. The exchange constants $_4$5 meV, $_4$6 meV, and $_4$7 meV describe a quasi-3D magnetically ordered state with the interlayer coupling being the dominant exchange. This three-dimensionality contrasts the more two-dimensional bilayer compounds.

Figure 4: Momentum dependence and dispersion of low-energy RIXS intensity, spectral weight comparison between La$_4$8Ni$_4$9O$_3$0 and La$_3$1Ni$_3$2O$_3$3, and depiction of the adopted magnetic structure for LSWT.

Comparative Analysis and Implications

The bandwidth (~60 meV) of collective excitations in La$_3$4Ni$_3$5O$_3$6 is comparable to that of La$_3$7Ni$_3$8O$_3$9; however, the spectral weight is nearly an order of magnitude lower, consistent with reduced correlation strength and an itinerant SDW ground state induced by Fermi surface nesting. The lower $_{10}$0 in trilayer nickelates correlates with this diminished interlayer exchange and suppressed magnetic spectral weight, reinforcing the spin-mediated pairing hypothesis for unconventional superconductivity in RP nickelates.

The coexistence of localized and dispersive spin excitations underscores complex interplay between orbital selective correlation effects and nesting-driven itinerancy. ARPES studies referenced by the authors corroborate the electronic signatures of SDW formation and substantial three-dimensionality, emphasizing that increasing $_{10}$1 in RP structures shifts the balance from two-dimensional Mott physics toward strongly hybridized three-dimensional metallicity with itinerant magnetism.

Future Outlook

The data and analysis advocate for treating trilayer and higher-nickelate compounds as intrinsically three-dimensional systems with essential multi-orbital and itinerant features. Future investigations should integrate RIXS, ARPES, and neutron scattering with advanced models incorporating both quasi-local and itinerant magnetism, and explore doping and pressure tuning. The results suggest that variations in dimensionality and correlation strength, more so than strict analogy to cuprates, will be decisive in defining the pairing mechanism and the ultimate $_{10}$2 in RP nickelate superconductors.

Conclusion

This study demonstrates that La$_{10}$3Ni$_{10}$4O$_{10}$5 realizes a unique regime in the RP nickelates, where three-dimensionality and multiorbital physics manifest in both the collective and local spin excitation spectrum. The experimentally established suppression of magnetic spectral weight and enhanced three-dimensional exchange highlight essential differences with the bilayer analogs and emphasize the need for a broader theoretical framework for nickelate superconductivity. These findings provide critical constraints for future modeling of high-temperature superconductivity beyond the cuprate paradigm.