Spectroscopic Evidence of Competing Diagonal Spin Interactions and Spin Disproportionation in the Bilayer Nickelate La$_3$Ni$_2$O$_7$

A comprehensive spectroscopic map of the electronic, magnetic, and lattice excitations is presented for the bilayer nickelate La$3$Ni$2$O$7$ using Raman scattering at ambient pressure. Upon entering the spin density wave state below 153 K, the $A{1g}$ channel exhibits an abrupt electronic spectral gap with a clear isosbestic point. In contrast, the $B{1g}$ and $B{2g}$ channels are dominated by pronounced two-magnon (2M) excitations, representing an unambiguous signature of incipient Mottness. These 2M signals in both channels constitute direct evidence for two distinct in-plane spin exchange interactions along the Ni-O bonding and its diagonal directions. Calculations based on the spin wave theory further reveal that the 2M mode in the $B_{2g}$ channel arises from the competition between two bond-diagonal antiferromagnetic interactions mediated by nickel $d_{x^2-y^2}$ orbitals. Furthermore, emergent low-energy 2M excitations below 10 meV are found to originate from distinct, weaker spin moments, strongly supporting spin disproportionation. Simultaneously, an anomalous softening of $B_{1g}$ phonons from 280 down to 4.5 K is uncovered, suggesting the presence of an incipient lattice instability leading to checkerboard-type breathing modulations. Collectively, these findings identify a ground state of the bilayer nickelate characterized by competing bond-diagonal interactions, spin disproportionation, and an incipient lattice instability, establishing key ingredients for understanding the mechanism of nickelate superconductivity.

💡 Research Summary

The authors present a comprehensive Raman‑scattering study of the bilayer nickelate La₃Ni₂O₇ at ambient pressure, aiming to elucidate the microscopic interactions that underlie its spin‑density‑wave (SDW) state and, by extension, its high‑temperature superconductivity under pressure. Using symmetry‑resolved Raman configurations (A₁g, B₁g, B₂g), they map the electronic, magnetic, and lattice excitations across a wide temperature range.

In the A₁g channel, cooling below the SDW transition temperature (T_SDW ≈ 153 K) produces a clear electronic gap opening, manifested as an abrupt loss of low‑energy spectral weight and an isosbestic point near 50 meV. This indicates that the SDW order reconstructs the electronic band structure, a behavior also observed in the related trilayer nickelate La₄Ni₃O₁₀.

The magnetic response is dominated by two‑magnon (2M) excitations that appear sharply in both B₁g (bond‑axis) and B₂g (diagonal) symmetry channels. Unlike cuprates, where 2M peaks are strong only in B₁g, La₃Ni₂O₇ shows a pronounced B₂g 2M peak at 47 meV, lower in energy than the B₁g peak at 81 meV. This dual‑channel observation directly signals sizable in‑plane exchange interactions not only along the Ni–O bonds (J₃) but also along the Ni–Ni diagonals (J₂ᵃ, J₂ᵇ).

To quantify these interactions, the authors construct a spin‑wave model that incorporates two distinct Ni magnetic moments, a large moment m₁ ≈ 0.66 μ_B and a much smaller moment m₂ ≈ 0.05 μ_B, as suggested by previous μSR and neutron powder diffraction work. Using the Fleury‑Loudon Raman scattering Hamiltonian and a random‑phase‑approximation (RPA) renormalization to account for magnon‑magnon interactions, they calculate the non‑interacting two‑magnon density of states and obtain the interacting Raman response. The best fit to the experimental spectra yields exchange constants J_c ≈ 52.8 meV (inter‑layer), J₃ ≈ 1.98 meV (bond‑axis), J₂ᵃ ≈ 0.99 meV and J₂ᵇ ≈ 0.5 meV (diagonal). Crucially, reproducing the B₂g lineshape requires both diagonal antiferromagnetic couplings; the data are best described when J₂ᵃ is roughly twice J₂ᵇ. This competition stabilizes the observed SDW wave vector Q_SDW = (π/2, π/2, 0) in the orthorhombic low‑pressure phase, where the lattice distortion lifts the degeneracy between the two diagonal directions. In the high‑pressure tetragonal phase, the orthorhombic distortion disappears, making J₂ᵃ ≈ J₂ᵇ, which introduces strong in‑plane frustration and enhanced spin fluctuations—conditions that are conducive to the emergence of superconductivity.

Below 10 meV, additional low‑energy 2M features appear in both B₁g and B₂g channels at temperatures below 30 K. Theoretical calculations show that these low‑energy peaks vanish if the small moment m₂ is set to zero (i.e., a pure spin‑charge stripe) or if m₂ = m₁ (a uniform double‑spin stripe). Their persistence therefore provides unambiguous spectroscopic evidence for spin disproportionation: the coexistence of two inequivalent Ni spin magnitudes within the same crystal. This finding aligns with mixed‑valence (d⁸ + d⁸L + d⁷) scenarios reported by resonant inelastic X‑ray scattering and X‑ray absorption studies, reinforcing the picture of charge‑transfer driven spin differentiation.

On the lattice side, the authors track several optical phonons. While most harden with cooling as expected from anharmonic effects, a subset of B₁g modes (notably the low‑energy phonons around 280 cm⁻¹ and 300 cm⁻¹) exhibit anomalous softening that begins well above T_SDW and continues through the magnetic transition. The most dramatic softening occurs for the 280 cm⁻¹ mode, which smoothly decreases in energy across the SDW transition. Such behavior signals strong spin‑phonon coupling and hints at an incipient lattice instability, possibly a checkerboard‑type breathing modulation that could couple to the electronic degrees of freedom.

Overall, the study delivers three pivotal insights: (1) the presence of significant diagonal antiferromagnetic exchange interactions alongside the conventional bond‑axis superexchange, (2) direct spectroscopic confirmation of spin disproportionation with two distinct Ni moments, and (3) evidence for a latent lattice instability manifested in anomalous phonon softening. Together, these ingredients delineate a complex, intertwined spin‑charge‑lattice landscape that likely underpins the pressure‑induced superconductivity in La₃Ni₂O₇, offering a concrete experimental foundation for future theoretical models of nickelate high‑T_c superconductivity.