Gapless spin excitations in nanographene-based antiferromagnetic spin-1/2 Heisenberg chains

TL;DR

This study demonstrates gapless spin excitations in nanographene-based antiferromagnetic spin-1/2 Heisenberg chains, revealing quantum spin liquid behavior through experimental measurements and visualization of spinon standing waves.

Contribution

It provides experimental evidence of gapless excitations in finite-length nanographene chains, extending understanding of quantum spin liquids in molecular systems.

Findings

Power-law decay of excitation energy with chain length

Observation of a V-shaped excitation continuum in long chains

Visualization of confined spinon standing waves

Abstract

Haldane's seminal work established two fundamentally different types of excitation spectra for antiferromagnetic Heisenberg quantum spin chains: gapped excitations in integer-spin chains and gapless excitations in half-integer-spin chains. In finite-length half-integer spin chains, quantization, however, induces a gap in the excitation spectrum, with the upper bound given by the Lieb-Schulz-Mattis (LSM) theorem. Here, we investigate the length-dependent excitations in spin-1/2 Heisenberg chains obtained by covalently linking olympicenes--Olympic rings shaped nanographenes carrying spin-1/2--into one-dimensional chains. The large exchange interaction (J~38 mV) between olympicenes and the negligible magnetic anisotropy in these nanographenes make them an ideal platform for studying quantum spin excitations, which we directly measure using inelastic electron tunneling spectroscopy. We observe a power-law decay of the lowest excitation energy with increasing chain length L, remaining below the LSM boundary. In a long chain with L = 50, a nearly V-shaped excitation continuum is observed, reinforcing the system's gapless nature in the thermodynamic limit. Finally, we visualize the standing wave of a single spinon confined in odd-numbered chains using low-bias current maps. Our results provide compelling evidence for the realization of a one-dimensional analog of a gapless spin liquid.