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

Abstract

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