Spectroscopic Evidence of Competing Diagonal Spin Interactions and Spin Disproportionation in the Bilayer Nickelate La₃Ni₂O₇

Summary

This study used an ambient-pressure Raman scattering system to measure the electronic, magnetic, and lattice excitations of the bilayer nickelate La₃Ni₂O₇. Upon entering the spin-density-wave state below 153 K, the A₁g channel exhibits an abrupt electronic spectral gap and an isosbestic point at about 50 meV, whereas the B₁g and B₂g channels are dominated by pronounced two-magnon excitations, indicating two in-plane spin exchange interactions along the Ni–O bond and its diagonal direction. Calculations based on spin-wave theory further indicate that the B₂g two-magnon mode originates from competition between two bond-diagonal antiferromagnetic interactions mediated by the Ni d_x²−y² orbitals; the low-energy two-magnon excitations below 10 meV arise from weaker spin moments, supporting spin disproportionation. The study also finds anomalous softening of the B₁g phonon from 280 K to 4.5 K, suggesting an incipient lattice instability that leads to checkerboard-like breathing modulation. These results link competing bond-diagonal interactions, spin disproportionation, and lattice instability, providing key elements for understanding the superconducting mechanism of nickelates.

Materials

• La₃Ni₂O₇

Methods

• Raman scattering
• spin wave theory calculations
• random phase approximation (RPA) renormalization
• Holstein-Primakoff transformation
• Bogoliubov transformation
• powder x-ray diffraction (XRD)
• STEM
• x-ray Laue diffraction
• focused ion beam (FIB)

Keywords

• spin density wave
• two magnon excitations
• spin disproportionation
• incipient lattice instability
• checkerboard type breathing modulation
• spin phonon coupling
• spin frustration
• fleury loudon exchange scattering
• bond diagonal antiferromagnetic interactions
• mottness

Highlights

• First spectroscopic evidence for two distinct intralayer exchange interactions: along the Ni-O bond direction and along the diagonal.
• The simultaneous observation of prominent two-magnon peaks in both B1g and B2g channels marks a key feature distinguishing La₃Ni₂O₇ from cuprate superconductors.
• The presence of bond-diagonal spin exchange interactions marks a key distinction between the magnetism of La₃Ni₂O₇ and that of the cuprates.
• The pronounced two-magnon signals indicate that La₃Ni₂O₇ is positioned closer to the localized, Mott-insulating limit compared to other layered nickelates such as La₄Ni₃O₁₀.
• The B1g phonon softening exceeds 1.5 meV, over 25% of its room-temperature frequency and an order of magnitude larger than shifts in other phonons, indicating a lattice softening driven by a separate degree of freedom.
• The dynamic Ni-O bond disproportionation provides a natural microscopic mechanism for the site-selective magnetic state by favoring inequivalent long and short Ni-O bond environments.
• The two-magnon features are robust against applied magnetic fields up to 7 T and reproduced at a different excitation wavelength, confirming intrinsic Raman scattering signals.

Conclusions

• The A1g channel exhibits an abrupt electronic spectral gap with an isosbestic point near 50 meV upon entering the spin density wave state below 153 K.
• The B1g and B2g channels are dominated by pronounced two-magnon excitations, providing evidence for two distinct in-plane spin exchange interactions along the Ni-O bonding and its diagonal directions.
• The B2g two-magnon mode arises from competition between two bond-diagonal antiferromagnetic interactions mediated by nickel d_x²-y² orbitals.
• Emergent low-energy two-magnon excitations below 10 meV originate from distinct, weaker spin moments, supporting spin disproportionation with the weaker moment approximately an order of magnitude smaller than the stronger one.
• An anomalous softening of B1g phonons from 280 down to 4.5 K suggests an incipient lattice instability leading to checkerboard-type breathing modulations that remain dynamic without freezing.
• The ground state of the bilayer nickelate is characterized by competing bond-diagonal interactions, spin disproportionation, and an incipient lattice instability, establishing key ingredients for understanding nickelate superconductivity.

Main claims

• Below the spin density wave transition at 153 K, the A1g Raman channel shows an abrupt electronic spectral gap with an isosbestic point near 50 meV.
  • Evidence: low-energy spectral weight below 50 meV sharply suppressed below T_SDW,low-energy dynamic susceptibility difference decreases sharply below T_SDW,reproduced in additional crystals (Samples 3 and 4)
• Prominent two-magnon excitations in both B1g and B2g channels provide evidence for two distinct in-plane spin exchange interactions along the Ni-O bond and diagonal directions.
  • Evidence: sharp B2g peak at 47 meV with about 37% of B1g intensity,spin-wave plus Fleury-Loudon calculations reproduce peak energies, lineshapes, and relative intensities,exclusion of phonon, single-magnon, and interband origins
• The B2g two-magnon mode arises from competition between two bond-diagonal antiferromagnetic interactions mediated by Ni d_x²-y² orbitals.
  • Evidence: model requires two diagonal AF interactions J2 and J2' to reproduce lineshape,spectrum not reproduced if J2' is absent or ferromagnetic,magnetic structure unstable if J2' exceeds J2, constraining J2' about twice J2
• Emergent low-energy two-magnon excitations below 10 meV originate from weaker spin moments, supporting spin disproportionation.
  • Evidence: low-energy features reproduced by low-energy magnon branches below 5 meV,features vanish in calculations assuming uniform spin moments,consistent with muSR and NPD reports of coexisting spin moments
• Anomalous softening of B1g phonons from 280 K to 4.5 K indicates an incipient lattice instability toward checkerboard-type breathing modulations.
  • Evidence: B1g phonon energy decreases by more than 1.5 meV, over 25% of room-temperature frequency,softening is continuous across T_SDW and insensitive to magnetic ordering,soft mode remains at finite frequency, consistent with dynamic rather than static disproportionation
• The magnetism of La₃Ni₂O₇ differs from cuprates because of significant bond-diagonal exchange interactions and proximity to the Mott-insulating limit.
  • Evidence: strong two-magnon signal in B2g channel absent in cuprates,prominent two-magnon modes despite metallicity, unlike more metallic trilayer nickelate,resistivity comparable to or higher than typical metallic cuprates

Workflow

• sample_preparation — High-quality single-domain La₃Ni₂O₇ crystals suitable for symmetry-resolved Raman spectroscopy were obtained.
  • Materials: La₃Ni₂O₇ single crystals grown by optical floating-zone furnace under 15 bar oxygen; fresh mechanically cleaved crystal surfaces
  • Methods: optical floating-zone crystal growth; mechanical cleavage; powder XRD for crystallinity; STEM (Cs-corrected JEM-ARM200F, 200 kV) for microstructure; X-ray Laue diffraction for orthorhombic orientation
  • Observations: crystals refined to structure with minor intergrowths of other Ruddsten-Popper phases; single orthorhombic domain confirmed on millimeter scale by Laue; consistent polarization dependence across samples
• measurement — Symmetry-resolved Raman spectra reveal electronic gap, multichannel two-magnon excitations, and anomalous phonon softening in La₃Ni₂O₇.
  • Materials: La₃Ni₂O₇ crystals (Samples 1-4)
  • Methods: polarized micro-Raman scattering (532 nm, XperRam200); macro-Raman with triple spectrometer (514.5 nm) under magnetic field; phonon peak fitting and subtraction (Lorentzian profiles)
  • Observations: A1g channel shows abrupt electronic gap with isosbestic point near 50 meV below T_SDW = 153 K; B1g and B2g channels show prominent two-magnon peaks at 81 and 47 meV; low-energy two-magnon humps below 15 meV emerge below 30 K; B1g phonon softens from 280 K to 4.5 K by more than 1.5 meV
• analysis — The observed B1g and B2g peaks are two-magnon excitations arising from distinct in-plane exchange interactions along Ni-O bonds and diagonal directions.
  • Materials: phonon-subtracted Raman response data
  • Methods: spin-wave theory with 8-sublattice bilayer antiferromagnetic Heisenberg Hamiltonian; Holstein-Primakoff and Bogoliubov transformation; Fleury-Loudon exchange scattering formalism; RPA-type renormalization of two-magnon response; systematic exclusion of alternative origins (phonon, single-magnon, interband)
  • Observations: calculated spectra reproduce peak energies, lineshapes, and relative B1g/B2g intensities at 4.5 K; low-energy two-magnon peaks vanish for uniform-moment stripe models; competition of two diagonal AF interactions required to reproduce lineshape; B2g mode requires J2' approximately twice J2
• interpretation — The ground state of La₃Ni₂O₇ combines competing bond-diagonal interactions, spin disproportionation, and incipient lattice instability, key ingredients for nickelate superconductivity.
  • Materials: combined Raman, spin-wave, and literature muSR/NPD/RIXS/XAS data
  • Methods: comparison with cuprates and other layered nickelates; correlation of magnetic and lattice anomalies
  • Observations: two competing diagonal AF interactions and on-axis interaction coexist; low-energy two-magnon modes indicate weaker spin moments (spin disproportionation); soft B1g phonon indicates incipient lattice instability toward checkerboard breathing modulation