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This paper proposes a microscopic Hamiltonian that faithfully reflects the crystal symmetry of the bilayer nickelate La₃Ni₂O₇ under ambient pressure, addressing its unconventional magnetic order. Large-scale density matrix renormalization group calculations reveal that under a large Hund coupling (J_H), a ((\pi/2, \pi/2)) spin stripe order emerges due to hidden quasi-one-dimensionality and persists over a range of electron concentrations. In the more symmetric high-pressure regime, when the interlayer antiferromagnetic coupling (J_\perp) is sufficiently strong, the model exhibits an enhanced tendency for interlayer pairing. This study unveils the microscopic origin of the diagonal spin stripe order and identifies both the Hund coupling (J_H) and the interlayer coupling (J_\perp) as key factors controlling the magnetic order and pairing tendency in La₃Ni₂O₇.

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The recent discovery of superconductivity in pressurized bilayer nickelate La3Ni2O7 has triggered tremendous research interest. However, the experimentally observed oxygen deficiency implies that obtaining perfect stoichiometric single crystals is still challenging. The influence of oxygen deficiency on physical properties remains unexplained. Here, we construct a chemical potential phase diagram to characterize the stability of La3Ni2O7. The narrow stable region explains the difficulty of synthesizing pure samples. First, oxygen defect studies reveal that the interlayer apical oxygen vacancy has the highest defect concentrations and is responsible for oxygen deficiency. Second, unfolding band structures show as the oxygen-deficient variant increases, Ni $$3d_{\;z^{2}}$$bands shift toward a lower energy position under the Fermi level at Γ point, which is adverse to the metallization of Ni $$3d_{\;z^{2}}$$bands. Third, high-pressure calculations indicate that oxygen vacancy would destroy the hybridization of interlayer Ni $$3d_{\;z^{2}}$$orbitals, and the larger the oxygen deficiency, the higher the pressure needed to metalize the Ni $$3d_{\;z^{2}}$$bands. Thus, the oxygen deficiency would suppress the emergence of superconductivity in La3Ni2O7−δ. Our results elucidate the mechanism of oxygen deficiency for superconductivity in La3Ni2O7−δ and provide instructive guidance to the experimental research.

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This study systematically explores the isotope effects on the charge density wave (CDW) and spin density wave (SDW) transitions in the bilayer Ruddlesden-Popper nickelate La₃Ni₂O₇ through oxygen isotope substitution (¹⁶O→¹⁸O) using resistivity and muon spin rotation (μSR) experiments. Resistivity measurements reveal a significant increase in the CDW transition temperature by approximately 6 K after ¹⁸O substitution, while μSR results indicate that the SDW transition temperature remains unaffected within experimental error. Raman spectroscopy confirms the effectiveness of the isotope substitution and the softening of lattice phonon modes. This contrasting isotope response suggests that lattice vibrations, i.e., electron-phonon coupling, play a crucial role in the formation of the CDW order, whereas the SDW order primarily originates from electronic interactions. The findings unveil distinct microscopic origins of the two density wave orders and hint at the potential relevance of electron-phonon coupling to the superconducting pairing mechanism in Ruddlesden-Popper nickelates, providing key constraints for theoretical models.

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