Valence bond solid phases on deformed kagome lattices: Application to Rb2Cu3SnF12

Motivated by a recent experiment on Rb2Cu3SnF12, where spin-1/2 Cu2+ moments reside on the layers of kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed kagome lattices. The deformation is characterized by a weaker exchange coupling alpha J on certain lattice links appropriate for Rb2Cu3SnF12 with alpha=1 corresponding to the ideal kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operator mean-field theory. It is shown that the valence bond solid phase with a 36-site unit cell of the ideal kagome lattice is quite sensitive to a small lattice distortion as the kind discovered in Rb2Cu3SnF12. As a result, we find that a more likely quantum ground state in Rb2Cu3SnF12 is the valence bond solid phase with a 12-site unit cell, where six dimers form a pinwheel structure, leading to strong modification of the elementary triplet and singlet excitation spectra in the deformed kagome lattices.