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 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 coupledcluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC J ⊥ , where we study ferro-as well as antiferromagnetic J ⊥ . 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 ⊥ |, is almost independent of the sign of J ⊥ . 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 ⊥ | the ILC drives a first-order transition to the √ 3 × √ 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. Introduction.-The search for exotic quantum spin liquid (QSL) states and fractionalized quasiparticles in frustrated magnets attracts currently much attention both from the theoretical and experimental side. One of the most promising, fascinating, and, at same time, challenging problems is the investigation of the ground state (GS) of the quantum antiferromagnet on the kagome lattice. Over the last 25 years a plethora of theoretical approaches has been applied to understand the GS properties of the spin-1/2 kagome antiferromagnet (KAFM), see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Clearly, the GS of the s = 1/2 Heisenberg KAFM does not exhibit GS magnetic longrange order (LRO). However, there is a long-standing debate on the nature of the quantum GS. Recent largescale numerical studies [6,8,11] provide arguments for a gapped Z 2 topological QSL for spin s = 1/2. However, the gap state is not fully proven, and also a gapless spin liquid is suggested, see, e.g., Refs. [9,12,16].

Negative-vector-chirality 120∘ spin structure in the defect- and distortion-free quantum kagome antiferromagnet YCu3(OH)6ClZorko1, Pregelj2, Gomilšek3 et al. 2019Phys. Rev. B376400View full textAdd to dashboardCite

“…Therefore, we do not expect exchange interactions beyond the second neighbors to play any significant role in this compound. Lastly, we note that magnetic ordering in kagome materials can also be induced by the interlayer exchange coupling [13]. However, the required value of the interlayer exchange is very high, J ⊥ /J 1 0.15, which is unlikely to be satisfied in YCu 3 (OH) 6 Cl 3 , where the neighboring kagome layers are separated by chlorine ions and the interlayer distance is as large as 5.6Å.…”

Weyl magnons in noncoplanar stacked kagome antiferromagnets

“…If the DMI is also set to zero (i.e. D z = 0), the magnon bands of stacked 120 • non-collinear spin structure show zero energy modes for a constant out-of-plane momentum k z along H-A line [36,37]. Therefore, the absence of magnetic long-range order in the 2D frustrated kagomé antiferromagnets also persists in the 3D limit.…”

Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin S

“…1. The selection of one of these states is a subtle issue and depends on spin quantum number, anisotropy etc., see, e.g., [8,25,38,46,[62][63][64][65]. While for the widely studied GS properties a plethora of many-body methods are available, the tool box for the calculation of finite-temperature properties of highly frustrated quantum magnets is sparse.…”