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

Abstract

As a highly frustrated model Hamiltonian with an exact dimer ground state, the Heisenberg antiferromagnet on the maple leaf lattice is of high theoretical interest, and a material realization is intensely sought after. We determine the magnetic Hamiltonian of the copper mineral bluebellite using density functional theory based energy mapping. As a consequence of the significant distortion of the spin $S=1/2$ maple leaf lattice, we find two of the five distinct nearest neighbor couplings to be ferromagnetic. 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 Cu${}^{2+}$ dimer, realizes an effective $S=1$ breathing kagome Hamiltonian. In fact, this is another highly interesting Hamiltonian which has rarely been realized in materials. Analysis of the effective model within a bond-operator formalism allows us to identify a valence bond solid ground state and to 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 experiment.

7 pages, 4 figures

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Cited by in corpus (8)

• Tensor network analysis of the maple-leaf antiferromagnet spangolite
• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• Chiral crossroads in $\mathrm{H}{\mathrm{o}}_3\mathrm{Sc}{\mathrm{O}}_6$: a tale of frustration in maple leaf lattice
• Symmetry breaking and competing valence bond states in the star lattice Heisenberg antiferromagnet
• Unconventional orders in the maple-leaf ferro-antiferromagnetic Heisenberg model
• Thermodynamics of the Heisenberg antiferromagnet on the maple-leaf lattice
• Spin excitation of the Heisenberg antiferromagnet with frustration: from the bounce-lattice antiferromagnet through the maple-leaf-lattice antiferromagnet to the exact-dimer system
• Crystallography-driven molecularization of a two-dimensional spin-$3/2$ magnet