XXZ and Ising Spins on the Triangular Kagome Lattice

TL;DR

This paper studies a novel XXZ-Ising spin model on a triangular kagome lattice, deriving its phase diagram and residual entropies, revealing quantum effects reduce entropy and induce new phases under magnetic fields.

Contribution

It provides an exact mapping and analysis of the XXZ-Ising model on the TKL, including phase diagrams and entropy calculations, extending understanding of quantum spin liquids.

Findings

Quantum fluctuations reduce residual entropy from 4.2767 to 2.5258 per unit cell.

Applied magnetic field induces a non-intersecting loop gas phase with entropy 1.4053.

A critical spin liquid phase maps to close-packed dimers on the honeycomb lattice.

Abstract

The recently fabricated two-dimensional magnetic materials Cu9X2(cpa)6.xH2O (cpa=2-carboxypentonic acid; 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 ln72=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 non-intersecting 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 which maps to close-packed dimers on the honeycomb lattice, which survives even when the a-spins are in the Heisenberg limit.