Emergence of magnetic long-range order in kagome quantum antiferromagnets

Johannes Richter,Oliver Götze

doi:10.1088/1742-6596/828/1/012010

Abstract

The existence of a spin-liquid ground state of the s = 1/2 Heisenberg kagome antiferromagnet (KAFM) is well established. Meanwhile, also for the s = 1 Heisenberg KAFM evidence for the absence of magnetic long-range order (LRO) was found. Magnetic LRO in Heisenberg KAFMs can emerge by increasing the spin quantum number s to s > 1 and for s = 1 by an easy-plane anisotropy. In the present paper we discuss the route to magnetic order in s = 1/2 KAFMs by including an isotropic interlayer coupling (ILC) J⊥ as well as an easy-plane anisotropy in the kagome layers by using the coupled-cluster method to high orders of approximation. We consider ferro- as well as antiferromagnetic J⊥. To discuss the general question for the crossover from a purely two-dimensional (2D) to a quasi-2D and finally to a three-dimensional system we consider the simplest model of stacked (unshifted) kagome layers. Although the ILC of real kagome compounds is often more sophisticated, such a geometry of the ILC can be relevant for barlowite. We find that the spin-liquid ground state present for the strictly 2D s = 1/2 X X Z KAFM survives a finite ILC, where the spin-liquid region shrinks monotonously with increasing anisotropy. If the ILC becomes large enough (about 15% of intralayer coupling for the isotropic Heisenberg case and about 4% for the XY limit) magnetic LRO can be established, where the q = 0 symmetry is favorable if J⊥ is of moderate strength. If the strength of the ILC further increases, LRO can become favorable against q = 0 LRO.

Highlights

We investigate the effect of an isotropic interlayer coupling (ILC) on the ground state order in a stacked s = 1/2 XXZ kagome antiferromagnet (KAFM) with easy-plane anisotropy in the layers by using the coupled-cluster method (CCM) to high orders of approximation
The shape of the curves and the magnitude of the energies are very similar for both states, where from [30] it is known that for the 2D XY model, i.e., at J⊥ = 0 and ∆ = 0, the q = 0 state has slightly lower energy
We may conclude that (i) there is a good agreement of the critical ILCs obtained by both extrapolation schemes, (ii) the spin-liquid region survives a finite ILC even in the XY limit, and (iii) due to anisotropy this region becomes noticeably smaller

Summary

Introduction

One of the most fascinating problems in frustrated quantum magnetism is the investigation of the ground state (GS) of the s = 1/2 antiferromagnet on the kagome lattice, see, e.g., Refs. The existence of a spin-liquid ground state of the s = 1/2 Heisenberg kagome antiferromagnet (KAFM) is well established, the discussion of the nature of the spin-liquid state is still not settled. For the s = 1 Heisenberg KAFM evidence for the absence of magnetic long-range ord√er (L√RO) was found [12,21,22,23,24]. Recently it has been reported that magnetic 3× 3 LRO can be established by increasing the spin quantum number to s > 1 [12, 20, 25].

Objectives

Results

Conclusion