Spin Stripes and Superconductivity in Bilayer Nickelates

The bilayer nickelate La_{3}Ni_{2}O_{7} has recently emerged as a high-temperature superconductor with unusual spin stripe order in its ambient pressure phase. We propose a microscopic Hamiltonian that faithfully reflects the crystalline symmetry of this system, with the primary aim of addressing its unconventional magnetism at ambient pressure. Using state-of-the-art density matrix renormalization group calculations, we show that (π/2,π/2) spin stripe order arises in our model at sizable Hund's coupling J_{H} from a hidden quasi one-dimensionality and persists over a range of electron concentrations. In the more symmetric high-pressure regime, our model exhibits enhanced interlayer pairing tendencies when the interlayer antiferromagnetic coupling J_{⊥} becomes sufficiently large. Our results provide a microscopic origin of the diagonal spin stripes and identify Hund's coupling J_{H} and interlayer coupling J_{⊥} as key ingredients governing magnetic order and pairing tendencies in La_{3}Ni_{2}O_{7}.