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arXiv:2610.34596

Non-magnetic impurities as a quantum microscope of finite size effects in spin chains

Quentin Faure, Shintaro Takayoshi, Virginie Simonet, B. Grenier, S. Raymond, E. Ressouche, X. Fabrèges, P. Léjay, Thierry Giamarchi, S. Petit

Published Oct 25, 2026• 0 citations
arXivHTMLPDF

Abstract

Finite-size effects are ubiquitous in quantum matter, yet typically invisible in the thermodynamic limit; when system size is restricted, boundaries and confinement reveal modified spectra, correlations, and emergent phenomena. With growing access to well-controlled few-spin systems, these effects are now directly observable and offer a route to probing universal physics and enabling quantum information applications. Here, we study finite-size physics in the quasi-one-dimensional Ising-like quantum antiferromagnet Ba(Co$_{1-x}$Mg$_x$)$_2$V$_2$O$_8$ with $x = 2\%$ and $x = 5\%$, where non-magnetic Mg$^{2+}$ ions fragment the Co$^{2+}$ spin chains into finite segments. Combining inelastic neutron scattering and numerical calculations, we identify distinct regimes with fundamentally different low-energy quantum excitations: spinons confined to chain boundaries, and a cluster mode in shorter chains corresponding to a collective reversal of the Néel-ordered segment without classical analogue. Our results demonstrate how chemical substitution acts as a quantum microscope providing direct access to boundary-shaped excitations in strongly correlated spin systems.

DOI
10.48550/arxiv.2610.34596

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Many phenomena in magnetism can be described using classical models, yet magnetism is a quantum mechanical effect. In addition to thermal fluctuations, quantum fluctuations arise due to the quantum uncertainty of the ground state. These fluctuations are enhanced by low dimensionality and low spin. Spin chains show interesting excitations associated with quasiparticles. Model materials for spin chains can be realized in compounds where the interchain interactions are weak enough. This thesis presents neutron scattering studies of two model materials for spin chains with different spin symmetry. The spin2 Heisenberg antiferromagnetic chain CuSO4*5D2O has a main exchange of J ∼ 3 K, which permits to study its excitation spectrum up to temperatures of ten times the exchange. The spin2 Heisenberg magnet has been studied widely both theoretically and experimentally. The excitation spectrum of the spin2 Heisenberg antiferromagnet consists of quasiparticles called spinons, and calculations for it exist for T = 0 and as a function of temperature. A quantitative comparison between experimental data and theoretical models across a range of temperatures is presented. The excitation spectrum of CuSO4*5D2O is excellently described by the excitation spectrum of a spin2 Heisenberg antiferromagnetic chain at finite temperatures. Energy-temperature scaling is observed at temperatures up to 2J . For these temperatures the Luttinger liquid description of the spin2 Heisenberg antiferromagnetic chain is valid. A spinon continuum is confirmed at all measured temperatures. Therefore, even at ten times the main exchange (T ≈ 10 J), CuSO4*5D2O shows the behavior of a quantum magnet, and not of a classical system at infinite temperatures, for which one would expect single spin flips. The Ising chain is one of the most studied models in magnetism, one model compound for it is RbCoCl3. Optical spectroscopy measurements suggest a lower gap than for similar compounds, which makes it better suited for high resolution neutron spectroscopy. Magnetic correlations along the chains arise in RbCoCl3 below 80 K. A gapped continuum is observed, which arises from isolated antiferromagnetic Ising chains. Below the first magnetic ordering temperature TN1 ≈ 28 K bound states are observed, which arise due to correlations which form between the chains. Strong diffuse scattering leads to the conclusion that disorder is still present. At the second magnetic ordering transition, at TN2 ≈ 14 K, the bound states split as the correlations between the chains change. Fits indicate that the correlations change continuously as a function of temperature. Above TN2 the excitation spectrum of RbCoCl3 can be described by a spin1 2 Ising chain with an XY-component which is treated as a perturbation. Below TN2 the main features are reproduced correctly, but deviations from the details indicate that additional terms in the Hamiltonian may be necessary. This thesis was carried out at the Institut Laue-Langevin, the Laboratory for Neutron Scattering and Imaging at the Paul Scherrer Institute and ETH Zurich.
Neutron inelastic-scattering experiments on an Ising-like quantum antiferromagnetic chain with nonmagnetic impurities, CsCo c Mg 1- c Cl 3 (c=1, 0.95, 0.9, 0.85, 0.6 and 0.4), were performed. The concentration dependence of the spin dynamics showed that although the solitons and the spin-wave continuum state were stable for a small amount of nonmagnetic impurities, they vanished at c=0.8. We also observed the coexistence of Ising-cluster excitations and intra-cluster excitations at low temperatures. These results can be well interpreted by a theory incorporated with next-nearest-neighbor interactions in the chain.
Inelastic neutron scattering is used to study transverse-polarized magnetic excitations in the quasi-one-dimensional S=1/2S\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/2S=1/2 antiferromagnet BaCu2Si2O7{\mathrm{BaCu}}_{2}{\mathrm{Si}}_{2}{\mathrm{O}}_{7}BaCu2​Si2​O7​, where the saturation value for the N\'eel order parameter is ${m}_{0}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.12{\ensuremath{\mu}}_{\mathrm{B}}$ per spin. At low energies the spectrum is totally dominated by resolution-limited spin-wave-like excitations. An excitation continuum sets in above a well-defined threshold frequency. Experimental results are discussed in the context of current theories for weakly interacting quantum half-integer-spin chains.
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