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While the existence of a spin-liquid ground state of the spin-1/2 kagomeHeisenberg antiferromagnet (KHAF) is well established, the discussion of theeffect of an interlayer coupling (ILC) by controlled theoretical approaches isstill lacking. Here we study this problem by using the coupled-cluster methodto high orders of approximation. We consider a stacked KHAF with aperpendicular ILC $J_\perp$, where we study ferro- as well as antiferromagnetic$J_\perp$. We find that the spin-liquid ground state (GS) persists untilrelatively large strengths of the ILC. Only if the strength of the ILC exceedsabout 15\% of the intralayer coupling the spin-liquid phase gives way for $q=0$magnetic long-range order, where the transition between both phases iscontinuous and the critical strength of the ILC, $|J^c_\perp|$, is almostindependent of the sign of $J_\perp$. Thus, by contrast to the quantum GSselection of the strictly two-dimensional KHAF at large spin $s$, the ILC leadsfirst to a selection of the $q=0$ GS. Only at larger $|J_\perp|$ the ILC drivesa 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 withtwo continuous and two discontinuous transitions driven by the ILC.

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