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

Abstract

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.