The bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ 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 $(\pi /2,\pi /2)$ 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 $J_{\perp }$ becomes sufficiently large. Our results provide a microscopic origin of the diagonal spin stripes and identify Hund’s coupling $J_H$ and interlayer coupling $J_{\perp }$ as key ingredients governing magnetic order and pairing tendencies in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$.

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• Magnetic order
• Superconductivity
• Nickelates
• Density matrix renormalization group