The discovery of high-temperature superconductivity (SC) with $T_c\approx 80$ K in the pressurized ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ has aroused great interest. Currently, due to technical difficulties, most experiments on ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ can only be performed at ambient pressure. Particularly, various experiments have revealed the presence of a spin density wave (SDW) in the unidirectional diagonal double-stripe pattern with wave vector near $\pm (\pi /2,\pi /2)$ in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ at ambient pressure. In this work, we employ first-principles calculations followed by the random phase approximation (RPA)-based study to clarify the origin of this special SDW pattern and the potential SC in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ at ambient pressure. Starting from our density-functional-theory band structure, we construct an eight-band bilayer tight-binding model using the $\mathrm{Ni}\text{−}3d_{z^2}$ and $3d_{x^2-y^2}$ orbitals, which is equipped with the standard multiorbital Hubbard interaction. Our RPA calculation reveals an SDW order driven by Fermi surface nesting with wave vector $\mathit{Q}\approx (0,\pm 0.84\pi )$ in the folded Brillouin zone. From the view of the unfolded Brillouin zone, the wave vector turns to ${\mathit{Q}}_0\approx \pm (0.58\pi ,0.58\pi )$, which is near the one detected by various experiments. Further more, this SDW exhibits an interlayer antiferromagnetic order with a unidirectional diagonal double-stripe pattern, consistent with recent soft x-ray scattering experiments. This result suggests that the origin of the SDW order in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ at ambient pressure can be well understood in the itinerant picture as driven by Fermi surface nesting. In the aspect of SC, our RPA study yields an approximate $s^{\pm }$-wave spin-singlet pairing with $T_c$ much lower than that under high pressure. Furthermore, the $T_c$ can be strongly enhanced through hole doping, leading to possible high-temperature SC at ambient pressure.

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• Pairing mechanisms
• Superconducting order parameter
• Superconductivity
• Unconventional superconductors
• Methods in superconductivity
• Random phase approximation