The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling

TL;DR

This study investigates how interlayer coupling influences the magnetic phases of the spin-1/2 kagome Heisenberg antiferromagnet, revealing a transition from a spin-liquid to magnetically ordered states as coupling strength increases.

Contribution

It provides a detailed theoretical analysis of the effects of interlayer coupling on the ground state phases of the kagome Heisenberg antiferromagnet using the coupled-cluster method.

Findings

Spin-liquid phase persists up to 15% interlayer coupling.

Transition to magnetic order occurs via continuous and first-order transitions.

Interlayer coupling induces a sequence of magnetic phases.

Abstract

While the existence of a spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we study this problem by using the coupled-cluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC $J_\perp$, where we study ferro- as well as antiferromagnetic $J_\perp$. We find that the spin-liquid ground state (GS) persists until relatively large strengths of the ILC. Only if the strength of the ILC exceeds about 15\% of the intralayer coupling the spin-liquid phase gives way for $q=0$ magnetic long-range order, where the transition between both phases is continuous and the critical strength of the ILC, $|J^c_\perp|$, is almost independent of the sign of $J_\perp$. Thus, by contrast to the quantum GS selection of the strictly two-dimensional KHAF at large spin $s$, the ILC leads first to a selection of the $q=0$ GS. Only at larger $|J_\perp|$ the ILC drives a first-order transition to the $\sqrt{3}\times\sqrt{3}$ long-range ordered GS. As a result, the stacked spin-1/2 KHAF exhibits a rich GS phase diagram with two continuous and two discontinuous transitions driven by the ILC.