Kagome quantum materials, with their frustrated lattice geometry and flat-band electronic structure, serve as a versatile platform for studying magnetism and electron correlation. The recently discovered kagome metal ${\mathrm{CsCr}}_3{\mathrm{Sb}}_5$ has garnered significant interest for its coexistence of multiple orders and the emergence of pressure-induced superconductivity. In this study, we theoretically investigate the correlation effects on the electronic structures and magnetism of ${\mathrm{CsCr}}_3{\mathrm{Sb}}_5$. Based on our proposed effective tight-binding model, we reveal orbital-selective correlation effects that induce a near-flat band just below the Fermi level, consistent with recent experimental observations. By combining the symmetry analysis and second-order perturbation theory, we construct an effective spin model and thoroughly explore its classical phase diagram, suggesting that a special $q=0$ state might correspond to the magnetic order in ${\mathrm{CsCr}}_3{\mathrm{Sb}}_5$. Our findings highlight the electron correlations in ${\mathrm{CsCr}}_3{\mathrm{Sb}}_5$ and provide novel insights into its magnetic properties. Furthermore, this spin model is applicable to kagome materials with similar structures, making the complete phase diagram relevant to other similar systems as well.

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• Electronic structure
• First-principles calculations
• Flat bands
• Magnetic order
• Phase diagrams
• Strongly correlated systems
• Electron-correlation calculations
• Monte Carlo methods