Motivated by the recently reported high-temperature superconductivity in the bilayer ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ (LNO) under pressure, here we comprehensively study this system using ab initio techniques. The Ni $3d$ orbitals have a large bandwidth at ambient pressure, increasing by $\sim 22\%$ at 29.5 GPa. Without electronic interactions, the Ni $d_{3z^2-r^2}$ orbitals form a bonding-antibonding molecular orbital state via the O $p_z$ inducing a “dimer” lattice in the LNO bilayers. The Fermi surface consists of two-electron sheets with mixed $e_g$ orbitals and a hole pocket defined by the $d_{3z^2-r^2}$ orbital, suggesting a Ni two-orbital minimum model. Different from the infinite-layer nickelate, we obtained a large interorbital hopping between $d_{3z^2-r^2}$ and $d_{x^2-y^2}$ states in LNO, caused by the ligand “bridge” of in-plane O $p_x$ or $p_y$ orbitals connecting those two orbitals, inducing $d\text{−}p$ $\sigma$-bonding characteristics. The competition between the intraorbital and interorbital hoppings leads to an interesting dominant spin stripe $(\pi ,0)$ order because of bond ferromagnetic tendencies via the recently discussed “half-empty” mechanism.

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• Electronic structure
• Magnetic coupling
• Orbital order
• Phase transitions
• Strongly correlated systems
• Superconductors
• Density functional theory
• First-principles calculations