The discovery of high-temperature superconductivity in bilayer nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ necessitates a minimal theoretical model that unifies the superconducting phase with the spin-density-wave (SDW) phase without external pressure or strain. We propose a model where half-filled $d_{z^2}$ local moments interact with itinerant $d_{x^2-y^2}$ electrons via strong Hund's coupling $J_H$, which reduces to a bilayer type-II $t\text{−}J$ model in the large $J_H$ limit. Using infinite density-matrix renormalization-group calculations on a $L_y=4,L_z=2$ cylinder, where $L_y$ is the system size along the $y$ direction and $L_z=2$ corresponds to the two layers of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$, we demonstrate that the competition between double-exchange ferromagnetism and in-plane superexchange generates period-4 stripelike SDW order—a feature absent in the one-orbital $t\text{−}J$ model with only the $d_{x^2-y^2}$ orbital. Furthermore, increasing the interlayer exchange coupling suppresses magnetic order and stabilizes interlayer $s$-wave superconductivity. These results identify the type-II $t\text{−}J$ model as a minimal framework for capturing the interplay of magnetism and superconductivity in bilayer nickelates.

Close

PrevNext

View figure in article

• Density matrix renormalization group
• Spin density waves
• Superconductivity
• Nickelates
• Strongly correlated systems
• t-J model