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

TL;DR

This paper identifies a new realization of an effective spin-1 breathing kagome Hamiltonian in the mineral bluebellite, derived from a distorted maple leaf lattice with ferromagnetic couplings, supported by DFT and many-body calculations.

Contribution

It demonstrates how a distorted maple leaf lattice with ferromagnetic couplings can realize an effective spin-1 breathing kagome Hamiltonian, a rare and interesting quantum magnetic model.

Findings

Bluebellite's magnetic Hamiltonian was determined via DFT.

The lattice distortion leads to an effective spin-1 breathing kagome model.

Calculated specific heat matches experimental data, indicating one-dimensional behavior.

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.