Numerical study of the thermodynamics of clinoatacamite

TL;DR

This study uses numerical methods to analyze the thermodynamic behavior of clinoatacamite, comparing models to experimental data, and explores the effects of lattice geometry transitions on its properties.

Contribution

It introduces a numerical approach combining exact diagonalization and linked-cluster expansion to study complex quantum lattice models relevant to clinoatacamite.

Findings

Good agreement with experimental susceptibility data for certain models

Weak ferromagnetic coupling between kagome and triangular layers

Insights into thermodynamics during lattice geometry transition

Abstract

We study the thermodynamic properties of the clinoatacamite compound, Cu_2(OH)_3Cl, by considering several approximate models. They include the Heisenberg model on (i) the uniform pyrochlore lattice, (ii) a very anisotropic pyrochlore lattice, and (iii) a kagome lattice weakly coupled to spins that sit on a triangular lattice. We utilize the exact diagonalization of small clusters with periodic boundary conditions and implement a numerical linked-cluster expansion approach for quantum lattice models with reduced symmetries, which allows us to solve model (iii) in the thermodynamic limit. We find a very good agreement between the experimental uniform susceptibility and the numerical results for models (ii) and (iii), which suggests a weak ferromagnetic coupling between the kagome and triangular layers in clinoatacamite. We also study thermodynamic properties in a geometrical transition between a planar pyrochlore lattice and the kagome lattice.