Origin of Spin Stripes in Bilayer Nickelate La${}_3$Ni${}_2$O${}_7$

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