Anisotropic Electronic Correlations in the Spin Density Wave State of La$_3$Ni$_2$O$_7$

TL;DR

This study uses polarization-resolved electronic Raman scattering to resolve the electronic character of the SDW state in La$_3$Ni$_2$O$_7$, revealing two momentum-selective gaps with distinct symmetry and coupling strengths. The B$_{1g}$ channel near X/Y shows a smaller, more coherent gap (~23 meV), while the B$_{2g}$ channel along the diagonal exhibits a larger, more anisotropic gap (~37.5–40.4 meV), indicating an unconventional, anisotropic SDW driven by electronic correlations. The findings reconcile Raman results with optical and RIXS/NMR evidence of strong correlations, and suggest magnetism plays a central role in the path toward high-$T_c$ superconductivity under pressure in nickelates.

Abstract

The bilayer nickelate superconductor La$_3$Ni$_2$O$_7$ undergoes a density wave transition near 150 K that has attracted intensive scrutiny, yet its microscopic origin remains elusive. Here we report polarization-resolved electronic Raman scattering measurements on high-quality single crystals of La$_3$Ni$_2$O$_7$. Below 150\,K, we observe a pronounced, symmetry-dependent redistribution of spectral weight in B$_{1g}$ and B$_{2g}$ channels, consistent with the formation of spin-density-wave (SDW) gaps. Quantitative analysis reveals momentum-selective SDW gap amplitudes, with intermediate-to-strong coupling near X/Y points of the Brillouin zone and weaker coupling along the diagonal direction, indicating an unconventional SDW driven by anisotropic electronic correlations. Our results establish the electronic character of the SDW in La$_3$Ni$_2$O$_7$, and provide a microscopic foundation for understanding the emergence of high-temperature superconductivity under pressure in nickelates.

Figures (4)

• Figure 1: Comparison of the electronic structure and Raman spectroscopic characteristics in weak and strong coupling regimes in La$_3$Ni$_2$O$_7$ .a, Fermi surface in the weak coupling regime, calculated using an 8-band tight-binding model (see Supplementary Materials F for details). The solid lines represent the Brillouin zone (BZ) of the ideal unit cell (without considering tilted Ni-O octahedra), while the dashed lines indicate the BZ of the real unit cell (with tilted Ni-O octahedra). The blue and red curves denote hole ($\beta$) and electron ($\alpha$, $\beta'$, $\alpha'$) pockets arising from band 3 and band 4, respectively. The black arrows indicate the wavevectors Q$_1$ connecting $\alpha$ and $\beta$ pockets and Q$_2$ connecting $\beta$ and $\beta'$ pockets, respectively. b, Spectral weight $A(k,\omega)$ calculated within a mean-field approximation considering a density wave gap $\Delta$ induced by Fermi surface nesting with a specific wave vector. c, Fermi patches in the strong coupling regime, where strong interactions lead to a broadened distribution of electronic states near the Fermi level across the BZ. d, Spectral weight $A(k,\omega)$ in the strong coupling regime, where a broad continuum appears due to incoherent particle-hole mixing, allowing excitations both below and above the Fermi level, unlike the sharp features in a normal band picture. e, Typical Raman spectral features of an SDW system in the weak coupling regime, exhibiting well-defined coherence peaks. f, Raman spectral response of an SDW system in the strong coupling regime, characterized by a broad redistribution of spectral weight instead of sharp features. The spectra below $T_{\mathrm{{SDW}}}$ are calculated using simulated spectral functions at the mean-field level or including correlation effects, while those above $T_{\mathrm{{SDW}}}$ are simulated with the memory-function approach using reasonable parameters. Details of the simulations are provided in Supplementary Materials E and G.
• Figure 2: Polarization configurations and corresponding Raman spectra.a–d, Schematic definitions of the polarization configurations, where red and yellow spheres represent oxygen and nickel atoms, respectively. The $x$- and $y$-axes are aligned along the Ni–O–Ni bond directions. The $x'$ and $y'$ polarizations are rotated by 45$^\circ$ clockwise from the $x$ and $y$ axes, respectively. The symmetry channels shown in bule are defined within $D_{4h}$ point group. e–h, Raman spectra measured at 50 K and 300 K for the corresponding configurations. Raman-active phonon modes are labeled as indicated. Green triangles denote the presence of additional electronic Raman responses in the $xy$ and $x'y'$ channels.
• Figure 3: Normal and SDW state Raman spectra of La$_3$Ni$_2$O$_7$ at temperatures as indicated. The difference spectra between 50 K and 160 K are overlaid as light blue curves. Spectral weight redistribution is clearly observed in the ${B_{\rm{1g}}}$ and ${B_{\rm{2g}}}$ channels. The spectral weight loss is highlighted in blue, while the gain is indicated in red. Insets: Color maps of Raman vertices in the first BZ for the $A_{\rm{1g}}$ , ${B_{\rm{1g}}}$, and ${B_{\rm{2g}}}$ symmetries, respectively.
• Figure 4: Spectral weight and energy gap in La$_3$Ni$_2$O$_7$ .a,b, Fits of the electronic continuum at 50 K using phenomenological memory function (MF)–Tsuneto-Maki (TM) and MF–Lorentz models for the ${B_{\rm{1g}}}$ and ${B_{\rm{2g}}}$ spectra, respectively. A TM function convoluted with a Gaussian Burch:2007 is also used to fit the ${B_{\rm{2g}}}$ spectrum (yellow line). c,d, Electronic Raman responses (gray points) and their corresponding fits (red curves) at various temperatures. e,f, Integrated spectral weight of the total spectrum and SDW component for both the experimental data and fitted results from 100 to 1000 cm$^{-1}$ as a function of temperature in the ${B_{\rm{1g}}}$ and ${B_{\rm{2g}}}$ channels. The SDW transition temperature is marked by the light-blue vertical bands. g, Raman response in the ${B_{\rm{2g}}}$${B_{\rm{1g}}}$ symmetry at 160, 200, 260, and 300 K. h, Temperature dependence of the SDW energy gaps. The half-filled circles and squares are adapted from ultrafast spectroscopy Yuxiaohui:2024 and optical conductivity Liuzhe:2024, respectively. Blue and red (yellow) points represent the energy gaps measured in the ${B_{\rm{1g}}}$${B_{\rm{2g}}}$ and ${B_{\rm{2g}}}$${B_{\rm{1g}}}$ symmetries, respectively. The deviation from the mean-field prediction is illustrated by the blue curves.