The low-pressure phase diagram of ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ provides an important reference for understanding its pressure-induced high-temperature superconductivity. While the spin-density-wave transition at $T_{\text{SDW}}\approx 150\mathrm{K}$ is increasingly well established, the origin of the second density-wave transition at $T_{\text{DW}}\approx 130\mathrm{K}$ has remained unresolved. Here, we perform unrestricted Hartree-Fock calculations to investigate the potential origin of the second transition. Within the orthorhombic phase, the degeneracy between possible ordering wave vectors at ${\mathit{Q}}_Y=(0,\pi )$ and at ${\mathit{Q}}_X=(\pi ,0)$ is lifted and the electronic system develops a double-stripe spin-density wave with ordering vector ${\mathit{Q}}_Y=(0,\pi )$. We identify that the pure double-stripe spin state is unstable in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$ towards a commensurate charge-density wave instability, which favors a spin-modulated double-stripe order with intertwined charge and spin instabilities and establish the hierarchy of ordered states in ${\mathrm{La}}_3{\mathrm{Ni}}_2{\mathrm{O}}_7$. We further discuss our results in the context of available experimental literature and propose further experimental tests to elucidate the origin of the SDW/DW states in this system.

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• Charge density waves
• Magnetic order
• Magnetic texture
• Spin density waves
• Nickelates
• Hartree-Fock methods
• Mean field theory