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We design from first principles a new type of two-dimensional metal-organicframeworks (MOFs) using phenalenyl-based ligands to exhibit a half-filled flatband of the kagome lattice, which is one of the lattice family that showsLieb-Mielke-Tasaki's flat-band ferromagnetism. Among various MOFs, we find that$\textit{trans}$-Au-THTAP(trihydroxytriaminophenalenyl) has such an ideal bandstructure, where the Fermi energy is adjusted right at the flat band due tounpaired electrons of radical phenalenyl. The spin-orbit coupling opens a bandgap giving a non-zero Chern number to the nearly flat band, as confirmed by thepresence of the edge states in first-principles calculations and by fitting tothe tight-binding model. This is a novel and realistic example of a system inwhich a nearly flat band is both ferromagnetic $\textit{and}$ topologicallynon-trivial.

First-Principles Design of a Half-Filled Flat Band of the Kagome Lattice in Two-Dimensional Metal-Organic Frameworks