## Published in:

Physical Review B 78,2 ( 2008 )

## Abstract

The recently fabricated two-dimensional magnetic materials Cu9X2(cpa)(6)center dot xH(2)O (cpa=2-carboxypentonic acid and X=F,Cl,Br) have copper sites which form a triangular kagome lattice (TKL), formed by introducing small triangles ("a-trimers") inside of each kagome triangle ("b-trimer"). We show that in the limit where spins residing on b-trimers have Ising character, quantum fluctuations of XXZ spins residing on the a-trimers can be exactly accounted for in the absence of applied field. This is accomplished through a mapping to the kagome Ising model, for which exact analytic solutions exist. We derive the complete finite-temperature phase diagram for this XXZ-Ising model, including the residual zero-temperature entropies of the seven ground-state phases. Whereas the disordered (spin liquid) ground state of the pure Ising TKL model has macroscopic residual entropy ln 72=4.2767... per unit cell, the introduction of transverse (quantum) couplings between neighboring a-spins reduces this entropy to 2.5258... per unit cell. In the presence of applied magnetic field, we map the TKL XXZ-Ising model to the kagome Ising model with three-spin interactions and derive the ground-state phase diagram. A small (or even infinitesimal) field leads to a new phase that corresponds to a nonintersecting loop gas on the kagome lattice, with entropy 1.4053... per unit cell and a mean magnetization for the b-spins of 0.12(1) per site. In addition, we find that for moderate applied field, there is a critical spin liquid phase that maps to close-packed dimers on the honeycomb lattice, which survives even when the a-spins are in the Heisenberg limit.

## Keywords

Physics, Condensed Matter

## Date of this Version

January 2008