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We present the mean-field phase diagram of electrons in a kagome flat bandwith repulsive interactions. In addition to flat-band ferromagnetism, theHartree-Fock analysis yields cascades of unconventional magnetic orders drivenby onsite repulsion as filling changes. These include a series ofantiferromagnetic (AFM) spin-charge stripe orders, as well as an evolution from$120^\circ$AFM to intriguing noncoplanar spin orders with tetrahedralstructures. We also map out the phase diagram under extended repulsion at halfand empty fillings of the flat band. To examine the possibilities beyondmean-field level, we conduct a projective symmetry group analysis and identifythe feasible $\mathbb Z_2$ spin liquids and the magnetic orders derivable fromthem. The theoretical phase diagrams are compared with recent experiments onFeSn and FeGe, enabling determination of the most likely magnetic instabilitiesin these and similar kagome flat-band materials.

Complex magnetic and spatial symmetry breaking from correlations in kagome flat bands