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

The bilayer nickelate La$_3$Ni$_2$O$_7$ has emerged as a new high temperature superconductor. We propose and study a microscopic Hamiltonian that addresses the interplay of lattice structure and magnetism in this system. Using state-of-the-art density matrix renormalization group calculations, we show that $(\pi/2,\pi/2)$ spin stripe order emerges in our model and exhibits a hidden quasi-one dimensionality. The spin stripe order occurs over a range of electron concentrations, but requires a sizable Hund's coupling $J_H$. Our model exhibits superconducting tendency only when the interlayer antiferromagnetic coupling $J_\bot$ becomes sufficiently large, which naturally occurs under pressure. Our study unveils the microscopic origin of both the unusual spin stripes and superconductivity in La$_3$Ni$_2$O$_7$, and highlights the indispensable role of Hund's coupling $J_H$ in this system.