Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu$_3$(OH)$_6$Cl$_2$

TL;DR

This study provides experimental evidence that the mineral herbertsmithite exhibits a gapless ground state, supporting the theory of a Dirac spin liquid in the quantum kagome antiferromagnet.

Contribution

The paper presents low-temperature NMR experiments on herbertsmithite, conclusively showing the absence of a spin-gap, thus supporting the gapless Dirac spin liquid model.

Findings

Herbertsmithite has no spin-gap at low temperatures.

Results support the gapless Dirac spin liquid as the ground state.

Experimental data aligns with recent numerical predictions.

Abstract

Spin liquids are exotic phases of quantum matter challenging Landau's paradigm of symmetry-breaking phase transitions. Despite strong exchange interactions, spins do not order or freeze down to zero temperature. While well-established for 1D quantum antiferromagnets, in higher dimension where quantum fluctuations are less acute, realizing and understanding such states represent major issues, both theoretical and experimental. In this respect the simplest nearest-neighbor Heisenberg antiferromagnet Hamiltonian on the highly frustrated kagome lattice has proven to be a fascinating and inspiring model. The exact nature of its ground state remains elusive and the existence of a spin-gap is the first key-issue to be addressed to discriminate between the various classes of proposed spin liquids. Here, through low-temperature Nuclear Magnetic Resonance (NMR) contrast experiments on high quality single crystals, we single out the kagome susceptibility and the corresponding dynamics in the kagome archetype, the mineral herbertsmithite, ZnCu$_3$(OH)$_6$Cl$_2$. We firmly conclude that this material does not harbor any spin-gap, which restores a convergence with recent numerical results promoting a gapless Dirac spin liquid as the ground state of the Heisenberg kagome antiferromagnet.