We investigate the magnetism of a previously unexplored distorted spin-1/2 kagome model consisting of three symmetry-inequivalent nearest-neighbor antiferromagnetic Heisenberg couplings and uncover a rich ground state phase diagram even at the classical level. Using analytical arguments and numerical techniques we identify a collinear $vec{Q} = 0$ magnetic phase, two unusual non-collinear coplanar $vec{Q} = (1/3,1/3)$ phases and a classical spin liquid phase with a degenerate manifold of non-coplanar ground states, resembling the jammed spin liquid phase found in the context of a bond-disordered kagome antiferromagnet. We further show with density functional theory calculations that the recently synthesized Y-kapellasite $text{Y}_{text{3}}text{Cu}_{text{9}}text{(OH)}_{text{19}}text{Cl}_{text{8}}$ is a realization of this model and predict its ground state to lie in the region of $vec{Q} = (1/3,1/3)$ order, which remains stable even after inclusion of quantum fluctuation effects within variational Monte Carlo and pseudofermion functional renormalization group. Interestingly, the excitation spectrum of Y-kapellasite lies between that of an underlying triangular lattice of hexagons and a kagome lattice of trimers. The presented model opens a new direction in the study of kagome antiferromagnets.
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