We present the mean-field phase diagram of electrons in a kagome flat band with repulsive interactions. In addition to flat-band ferromagnetism, the Hartree-Fock analysis yields cascades of unconventional magnetic orders driven by on-site repulsion as filling changes. These include a series of antiferromagnetic (AFM) spin-charge stripe orders, as well as an evolution from ${120}^{\circ }$ AFM to intriguing noncoplanar spin orders with tetrahedral structures. We also map out the phase diagram under extended repulsion at half and empty fillings of the flat band. To examine the possibilities beyond the mean-field level, we conduct a projective symmetry group analysis and identify the feasible ${\mathbb{Z}}_2$ spin liquids and the magnetic orders derivable from them. The theoretical phase diagrams are compared with recent experiments on FeSn and FeGe, enabling a determination of the most likely magnetic instabilities in these and similar flat-band kagome materials.

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• Charge order
• Flat bands
• Magnetic order
• Phase diagrams
• Quantum spin liquid
• Kagome lattice
• Hubbard model
• Mean field theory
• Projective symmetries