Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet

Abstract

The kagome Heisenberg antiferromagnet is a leading candidate in the search for a spin system with a quantum spin liquid ground state. The nature of its ground state remains a matter of great debate. We conducted 17 O single crystal NMR measurements of the spin S = 1 / 2 kagome lattice in herbertsmithite ZnCu 3 (OH) 6 Cl 2 , which is known to exhibit a spinon continuum in the spin excitation spectrum. We demonstrate that the intrinsic local spin susceptibility χ kagome deduced from the 17 O NMR frequency shift asymptotes to zero below temperature T~0.03J , where 200 J K is the Cu-Cu super-exchange interaction. Combined with the magnetic field dependence of χ kagome we observed at low temperatures, these results imply that the kagome Heisenberg antiferromagnet has a spin liquid ground state with a finite gap. 2The realization and characterization of a kagome Heisenberg antiferromagnet (KHA) with a corner-shared triangle structure (Fig.1A) is crucial for the search for a quantum spin liquid ground state (1,2). Spin-liquids consist of entangled pairs of spin-singlets, and do not undergo a magnetic phase transition. The successful synthesis of the structurally ideal kagome lattice of Cu 2+ ions (spin S = 1 / 2 ) in herbertsmithite ZnCu 3 (OH) 6 Cl 2 (Fig.1B-E) (3) was welcomed as a major milestone (4). ZnCu 3 (OH) 6 Cl 2 remains paramagnetic at least down to ~50 mK (5,6).Moreover, inelastic neutron scattering measurements (7) on single crystals (8) demonstrated that the spin excitation spectrum does not exhibit conventional magnons, but rather a spinon continuum. Despite the recent progress, fundamental issues regarding the nature of the ground state of the KHA remain to be understood. For example, the central question on the existence of a gap in the spin excitation spectrum has not been settled. This information is critical to distinguish between the leading theories for the ground state of the S = 1 / 2 KHA: a gapped spin liquid, gapless spin liquid, or valence bond solid (1,2,9-14)In ZnCu 3 (OH) 6 Cl 2, weakly interacting Cu 2+ defects occupy the non-magnetic Zn 2+ sites between the kagome-layers with ~15% probability (15). Their contributions dominate bulkaveraged thermodynamic properties at low temperatures (3,5,8,16,17), making it difficult to measure the intrinsic low energy properties of this material. Similarly, the Cu 2+ impurity moments can contribute to the inelastic neutron scattering, obscuring the response of the intrinsic kagome spins at low energies (< 2meV) (7 A major advantage of using a single crystal for NMR is that we can achieve high resolution by applying an external magnetic field B ext along specific crystallographic directions.In Fig (c) . In addition, the central peak frequency f for the I z = −1 / 2 to +1 / 2 transition is shifted from the bare resonance frequency f o = (γ n / 2π )B ext by the effects of the hyperfine magnetic fields from nearby Cu 2+ sites, and the shift of the peak (marked as Main in Fig. 2A) is proportional to χ kagome . Such a NMR frequency shift may be expressed i...

Structure factors of the kagome-lattice Heisenberg antiferromagnets at finite temperatures

“…The lack of structural distortions and magnetic isolation of copper based Kagome planes by intervening non-magnetic zinc planes, makes these materials well suited to the exploration of the rich quantum spin-liquid physics in these systems. Recent neutron-scattering [9] and NMR [10] measurements on large single-crystal materials find no evidence for magnetic order down to temperatures many orders of magnitude below the exchange energy scale. While the as obtained neutron-scattering spectra clearly shows gapless excitations, a recent analysis of the spectra taking into account the anti-site copper impurities in the zinc planes, assigns the low energy scattering entirely to these impurities [11].…”

Variational Monte Carlo study of chiral spin liquid in quantum antiferromagnet on the triangular lattice

“…At the experimental side, the most promising materials to realize a spin liquid on a kagomé lattice are the spin-1/2 antiferromagnets herbertsmithite and kapellasite [12][13][14][15][16][17]. Theoretically, densitymatrix renormalization group (DMRG) studies consistently find a gapped spin liquid in the spin-1/2 kagomé Heisenberg model with the nearest-neighbor (NN) interactions [18][19][20].…”

Gapped spin liquid with Z2 topological order for the kagome Heisenberg model

“…ZnCu 3 (OH) 6 Cl 2 (herbertsmithite) [33][34][35][36][37][38][39][40][41][42][43][44] and Cu 3 Zn(OH) 6 FBr [45] are promising compounds for experimental realizations of KAFHM with additional interactions. Many different ground states have been proposed for KAFHM .…”