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

Abstract

Motivated by a recent experiment on ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$, where spin-1/2 ${\text{Cu}}^{2+}$ 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 $\ensuremath{\alpha}J$ on certain lattice links appropriate for ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ with $\ensuremath{\alpha}=1$ 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 ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$. As a result, we find that a more likely quantum ground state in ${\text{Rb}}_{2}{\text{Cu}}_{3}{\text{SnF}}_{12}$ 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.