  We investigate the magnetism of a previously unexplored distorted spin-1/2
kagome model consisting of three symmetry-inequivalent nearest-neighbor
antiferromagnetic Heisenberg couplings Jhexagon, J and J', and uncover a rich
ground state phase diagram even at the classical level. Using analytical
arguments and numerical techniques we identify a collinear Q = 0 magnetic
phase, two unusual non-collinear coplanar 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 Y3Cu9(OH)19Cl8
is a realization of this model and predict its ground state to lie in the
region of 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. The presented model opens a new direction in
the study of kagome antiferromagnets.
