We derive a $t\text{−}J$ model applicable to strongly correlated two-orbital systems including bilayer nickelate superconductors. Using the Schrieffer-Wolff transformation, we exclude the doubly occupied states, which raise the onsite Coulomb energy, and derive the resulting spin interactions from the two-orbital Hubbard model. We also introduce effective interactions attributed to the interorbital Coulomb interaction. To adapt the effective model to bilayer nickelates that exhibit high-temperature superconductivity, we quantitatively evaluate the strengths of the spin interactions based on the hopping parameters in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. Considering the evaluated effective interactions, we propose a simplified $t\text{−}J$ model for bilayer nickelate superconductors.

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• Strongly correlated systems
• Unconventional superconductors
• Hubbard model
• t-J model