We employ correlated density-functional theory methods (DFT $+$ Hubbard $U$) to investigate the spin-density wave state of the bilayer Ruddlesden-Popper (RP) nickelate ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ which becomes superconducting under pressure. We predict that the ground state of this bilayer RP material has traits of both the double spin-stripe and the single spin-charge stripe phases proposed in the literature as it corresponds to in-plane $\mathrm{up}/{\mathrm{up}}^{\prime }/\mathrm{down}/{\mathrm{down}}^{\prime }$ diagonal stripes with up/down being high spin (formally ${\mathrm{Ni}}^{2+}$: $d^8$), and ${\mathrm{up}}^{\prime }/{\mathrm{down}}^{\prime }$ being low spin (formally ${\mathrm{Ni}}^{3+}$: $d^7$). The main feature of this solution (that is insulating even at $U=0$) is the dominant role of the $d_{x^2-y^2}$ bands around the Fermi level, which would become doped with the introduction of electrons via oxygen vacancies. In spite of the similarity with cuprates in terms of the dominant role of $d_{x^2-y^2}$ bands, some differences are apparent in the magnetic ground state of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$: the antiferromagnetic out-of-plane coupling within the bilayer (linked to the $d_{z^2}$ orbitals forming a spin-singlet-like configuration) is found to be the dominant one while in-plane interactions are reduced due to the stripe order of the ground state. With pressure, this striped magnetic ground state remains similar in nature but the increase in bandwidth quickly transitions ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ into a metallic state with all the activity close to the Fermi level involving, to a large extent, $d_{x^2-y^2}$ orbitals. This is reminiscent of the cuprates and may provide key insights into how superconductivity arises in this material under pressure.

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• Spin density waves
• Nickelates
• DFT+U