Effective spin-1 breathing kagome Hamiltonian induced by the exchange hierarchy in the maple leaf mineral bluebellite

The Heisenberg quantum antiferromagnet on the maple leaf lattice has been shown to feature highly exotic phases, and therefore material realizations are intensely sought after. We determine the magnetic Hamiltonian of the copper mineral bluebellite using density-functional theory based energy mapping. Due to significant distortion of the spin-1/2 maple leaf lattice, we find two of the five distinct nearest-neighbor couplings to be ferromagnetic. The solution of this Hamiltonian with density matrix renormalization group calculations points us to the surprising insight that this particular imperfect maple leaf lattice, due to the strongly ferromagnetic ${\mathrm{Cu}}^{2+}$ dimer, realizes an effective $S=1$ breathing kagome Hamiltonian. In fact, this is another highly interesting Hamiltonian that has rarely been realized in materials. Analysis of the effective model within a bond-operator formalism then allows us to identify a valence bond solid ground state and extract thermodynamic quantities using a low-energy bosonic mean-field theory. We resolve the puzzle of the apparent one-dimensional character of bluebellite as our calculated specific heat has a Bonner-Fisher-like shape, in good agreement with the experiment.