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Using the unrestricted Hartree-Fock method based on a multiorbital Hubbard-Hund model, we investigate the density-wave phase diagram of the low-pressure bilayer nickelate La₃Ni₂O₇. Our calculations reveal that in the orthorhombic phase, the electron system first develops a double-stripe spin-density-wave order with wave vector Q_Y = (0, π) at about 150 K; subsequently, at about 130 K, the pure double-stripe spin state becomes unstable against a commensurate charge density wave, resulting in a spin-modulated double-stripe ordered state where the magnetic moments and charge densities on the in-plane Ni1 and Ni2 sites are modulated, forming low-spin sites. This charge order parameter is an order of magnitude smaller than the magnetic order parameter and induces additional band gaps and folded Fermi surfaces in the electronic structure. The study establishes the hierarchical relationship between spin-density-wave and charge-density-wave orders in La₃Ni₂O₇, provides important clues for understanding the connection between the ambient-pressure ordered phases and the high-pressure superconducting phase, and proposes suggestions for further experimental verification.

In the ambient-pressure normal state of the trilayer Ruddlesden-Popper nickelate La₄Ni₃O₁₀, researchers observed a phonon thermal Hall effect enhanced by density-wave order. The material undergoes a density-wave transition at about 140 K, below which the thermal Hall response sharply increases; the thermal Hall angle rises from 1.5‰ at 160 K to 6‰ near 100 K, peaks at ~7‰ at 70 K, and two distinct plateaus appear in the thermal Hall resistivity. The longitudinal thermal conductivity shows almost no magnetic field dependence and has a negligible electronic contribution, confirming that phonons dominate both longitudinal and transverse thermal transport. The characteristic energy extracted from thermal Hall data is about 4.1 meV, which closely matches the magnon–phonon dispersion crossing energy of 3.2 meV, indicating that magnon–phonon hybridization induced by spin-density-wave order is the core mechanism enhancing the thermal Hall effect. This work reveals the significant modulation of phonon transport by spin–lattice coupling in nickelates and points out that such dynamic coupling may participate in suppressing antiferromagnetic order and promoting superconductivity under high pressure via softening of optical phonons, providing a new perspective for understanding the intertwining of charge, spin, and lattice degrees of freedom in unconventional superconductors.

Using a two-orbital bilayer model, this study systematically calculates the electronic Raman response in different Raman channels via both multiorbital and band-sum methods to distinguish the controversial pairing symmetry in the bilayer nickelate superconductor La₃Ni₂O₇. By comparing the Raman susceptibilities obtained from the multiorbital approach and the band-sum approximation, it is found that the Raman response can effectively differentiate various pairing symmetries and identify the Fermi-pocket-dependent gap sizes in fully gapped and nodal superconducting states. Specifically, nodal dₓ²⁻ᵧ²/dₓᵧ-wave pairing exhibits robust power-law behavior at low energies, distinctly different from fully gapped pairing; for s±-wave pairing, detailed gap anisotropy on the β pocket can be determined. The study also emphasizes the crucial role of multiorbital effects in shaping the Raman spectra, and points out that electronic Raman scattering, as a symmetry-resolving probe, provides a powerful means to determine the superconducting gap structure of unconventional superconductors, offering significant experimental implications for understanding the superconducting mechanism of bilayer nickelates.

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