Van der Waals layered ferromagnetic compounds with high two-dimensional electronic conductivity hold a strong potential for quantum computing, future unconventional superconductors, catalysts, batteries, and fuel cells. We suggest a minimal theoretical model to understand the magnetic properties of the metal-organic framework ${\mathrm{CrCl}}_2{\left(\mathrm{pyz}\right)}_2$ (pyz = pyrazine). Using a Hubbard model we show that the ground state is dominated by a specific configuration of delocalized electrons on the pyz sites with a ferrimagnetic coupling to the localized spins on the Cr sites. This model suggests a magnetic moment of $2{\mu }_B$ which is remarkably close to the experimental value of $1.8{\mu }_B$ [K. S. Pedersen et al., Nat. Chem. 10, 1056 (2018)]. From Weiss mean-field theory we predict a weak ferromagnetic Cr-Cr coupling of $\approx 0.9$ meV. This is consolidated by second-order perturbation theory of the Ruderman-Kittel-Kasuya-Yosida interaction yielding a Cr-Cr coupling of $\approx 5$ meV. Understanding the interactions in these types of compounds can facilitate designs of metal-organic compounds with tailored magnetic properties.

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• Ferrimagnetism
• RKKY interaction
• Metal-organic framework
• van der Waals systems
• Exact diagonalization
• Hubbard model
• Mean field theory
• Tight-binding model