[Paper Review] Gapless spin excitations in nanographene-based antiferromagnetic spin-1/2 Heisenberg chains

Chenxiao Zhao, Lin Yang+9 more|arXiv (Cornell University)|Aug 19, 2024

Magnetism in coordination complexes6 citations

TL;DR

The paper reports the creation of covalently linked nanographene spin-1/2 chains on Au(111) that realize an isotropic antiferromagnetic Heisenberg chain. They observe gapless spin excitations whose lowest energy scales as 1/L and visualize a single spinon standing wave in odd-length chains, approaching the thermodynamic limit.

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.

Motivation & Objective

• Motivate and realize a one-dimensional gapless spin-1/2 Heisenberg chain using covalently linked nanographene units (olympicene) with isotropic exchange.
• Characterize chain-length dependent spin excitations using inelastic electron tunneling spectroscopy (IETS) and map spinon behavior along the chain.
• Demonstrate even-odd effects in ground states and identify a single spinon standing wave in odd-length chains.
• Compare experimental results with exact diagonalization and density matrix renormalization group calculations to test theoretical predictions (LSM bound, gap closure).
• Show robustness of gapless behavior under realistic exchange perturbations and finite-size effects.

Proposed method

• Fabricate olympicene-based spin chains on Au(111) via on-surface synthesis and covalent linking.
• Activate spin sites by tip-induced dehydrogenation and probe spin excitations with STM/STS and nc-AFM.
• Measure spin excitations with inelastic electron tunneling spectroscopy (IETS) and analyze d2I/dV2 spectra to extract excitation energies.
• Model the system with the Heisenberg Hamiltonian H = J sum_i S_i · S_{i+1} and compute spectra using exact diagonalization (ED) and density matrix renormalization group (DMRG).
• Use CAS (complete active space) plus Hubbard interactions to capture exchange mechanisms in the nanographene chain.
• Simulate dI/dV spectra by rotating through perturbative scattering theory up to third order to include Kondo and spin-flip processes.
• Assess perturbations in J along the chain to test robustness of gapless behavior (random δJ up to ±10%).

Experimental results

Research questions

• RQ1 Do nanographene-based spin-1/2 chains realize an isotropic antiferromagnetic Heisenberg model with gapless spin excitations?
• RQ2 How does the lowest spin excitation energy (ΔLEE) scale with chain length L, and does it respect the Lieb–Schultz–Mattis (LSM) bound?
• RQ3 Can odd-length chains host a localized single spinon, and can its standing-wave nature be imaged experimentally?
• RQ4 What is the evolution of the excitation spectrum toward the thermodynamic limit, and does it manifest a V-shaped continuum for long chains?
• RQ5 How robust are the observed features against realistic exchange fluctuations and substrate effects?

Key findings

• The nearest-neighbor exchange coupling is J ≈ 38 meV in the chains.
• Even-numbered chains exhibit a decreasing gap with increasing length, while odd-numbered chains show a zero-bias peak whose intensity diminishes with L, consistent with even and odd ground-state spins respectively.
• The lowest excitation energy ΔLEE decays with L following a power-law behavior and lies below the LSM bound for open boundary conditions, approaching linearity with 1/L in the large-L region.
• For long chains (L ≈ 50), the IETS spectra reveal a nearly V-shaped excitation continuum indicating a vanishing gap in the thermodynamic limit.
• Spinon states in odd chains can be described as localized spinon states, and the ground state of L = 2n+1 chains can be written as a superposition with coefficients C(m) peaking at odd sites, forming a standing-wave pattern.
• Low-bias current maps of L = 5 and L = 7 chains show pronounced Kondo-related modulation with maximal intensity at odd sites, consistent with a single spinon standing wave and ground-state spin-1/2 nature.
• The experimental ΔLEE evolution is consistent with theoretical ED and DMRG results, remaining below theoretical predictions due to substrate renormalization effects, yet preserving gapless behavior in the thermodynamic limit.
• The exchange perturbations (±5% to ±10%) do not significantly alter the decay rate of ΔLEE or the gapless character.