Numerical study of the thermodynamics of clinoatacamite

Abstract

We study thermodynamic properties of the clinoatacamite compound, Cu2(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 kagomé lattice weakly coupled to spins that sit on a triangular lattice. We utilize 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 suggest a weak ferromagnetic coupling between the kagomé and triangular layers in clinoatacamite. We also study these thermodynamic quantities in a geometrical transition between a planar pyrochlore lattice and the kagomé lattice.

A short introduction to numerical linked-cluster expansions

“…and the specific heat per site (c), [Eq. (14)]. Two things are apparent in those plots: (i) with increasing order, the NLCE results converge to the exact ones at lower temperatures.…”

“…How to deal with Hamiltonians and observables that break some of the symmetries of the underlying lattice was discussed in Refs. [13,14]. Finally, how to generalize NLCEs to calculate ground-state as well as low-temperature properties of lattice Hamiltonians with dimerized ground states was the subject of Ref.…”

“…distinct Topo . 1 1 1 1 2 2 1 1 3 6 2 1 4 19 5 3 5 63 12 4 6 216 35 10 7 760 108 19 8 2725 369 51 9 9910 1285 112 10 36446 4655 300 11 135268 17073 746 12 505861 63600 2042 13 1903890 238591 5450 14 7204874 901971 15197 15 27394666 3426576 42192 16 104592937 13079255 119561 17 interest [4,5,6,10,11,12,13,14,15]. In Wynn's algorithm, one defines…”

Barlowite: A Spin-1/2Antiferromagnet with a Geometrically Perfect Kagome Motif

“…Magnetically, barlowite is better modeled by a stack of weakly coupled kagome layers-instead of a threedimensional network of tetrahedrons-regarding J ′ /J, where J ′ is the exchange between a kagome Cu and the average position for an interkagome Cu. Down to T ∼ 0.2J/k B , the magnetic susceptibility has been calculated, using numerical linked-cluster expansion (NLCE), on a 16-site cluster by considering a kagome lattice coupled to interkagome spins 17 . As shown in Fig.…”

Lanczos-boosted numerical linked-cluster expansion for quantum lattice models

“…Figure 2 shows the first five topologically-distinct clusters in the square expansion. In previous studies, triangular building blocks were used to study magnetic models on the Kagome lattice [6,22], and rectangular clusters were considered in the study of entanglement at a twodimensional critical point [12].…”