Sharp spectroscopic fingerprints of disorder in an incompressible magnetic state

Disorder significantly impacts the electronic properties of conducting quantum materials by inducing electron localization and thus altering the local density of states and electric transport. In insulating quantum magnetic materials, the effects of disorder are less understood and can drastically impact fluctuating spin states like quantum spin liquids. In the absence of transport tools, disorder is typically characterized using chemical methods or by semi-classical modeling of spin dynamics. This requires high magnetic fields that may not always be accessible. Here, we show that magnetization plateaus – incompressible states found in many quantum magnets – provide an exquisite platform to uncover small amounts of disorder, regardless of the origin of the plateau. Using optical magneto-spectroscopy on the Ising-Heisenberg triangular-lattice antiferromagnet K$_2$Co(SeO$_3$)$_2$ exhibiting a 1/3 magnetization plateau, we identify sharp spectroscopic lines, the fine structure of which serves as a hallmark signature of disorder. Through analytical and numerical modeling, we show that these fingerprints not only enable us to quantify minute amounts of disorder but also reveal its nature – as dilute vacancies. Remarkably, this model explains all details of the thermomagnetic response of our system, including the existence of multiple plateaus. Our findings provide a new approach to identifying disorder in quantum magnets.

💡 Research Summary

This paper introduces a novel method for detecting and quantifying minute amounts of disorder in insulating quantum magnets by exploiting magnetization plateaus—states of incompressibility where the total spin‑z component is conserved. The authors focus on the Ising‑Heisenberg triangular‑lattice antiferromagnet K₂Co(SeO₃)₂ (KCSO), which exhibits a robust 1/3 magnetization plateau (the up‑up‑down, UUD, phase) between 2 T and 17 T at low temperature. Using far‑infrared magneto‑optical spectroscopy (FIRMS) in Faraday geometry at 5 K, they observe two dominant absorption modes and three weaker satellite modes that appear only within the plateau.

Standard theoretical tools—linear spin‑wave theory (LSWT), Landau‑Lifshitz dynamics (LLD), and exact diagonalization (ED)—successfully describe the two main modes as single‑spin‑flip excitations (one on an “up” spin, one on a “down” spin) and also capture triple‑spin‑flip bound‑state and continuum features. However, none of these clean‑system models can account for the satellite peaks.

To explain the satellites, the authors develop a “disorder‑bond” model in which the nearest‑neighbor exchange constants are locally reduced: J′zz = Jzz(1 − dzz) and J′xy = Jxy(1 − dxy). Analytic treatment shows that a single‑spin‑flip excitation can split into two distinct energies depending on whether the flipped spin is adjacent to a weakened bond. The energy shifts are ±Jzz dzz/2, with an additional quantum correction proportional to Jxy dxy that scales with the defect density. By fitting the satellite positions, they extract dzz ≈ 0.94 and dxy ≈ 0.94, indicating that the affected bonds are essentially missing rather than merely weakened.

The most natural microscopic origin of a missing bond is a magnetic‑site vacancy (absence of a Co²⁺ ion). The disorder‑bond framework interpolates between three limiting cases: (i) a weakened‑bond model (small d), (ii) a broken‑bond model (d → 1), and (iii) a vacancy model (complete removal of a spin site). Monte‑Carlo simulations of a dilute vacancy concentration (~2.3 %) reproduce not only the satellite intensities observed in FIRMS but also a secondary magnetization plateau with m < 1/3 that appears in magnetization and heat‑capacity measurements.

From the linear fits to the main modes, the authors obtain precise magnetic parameters: Jzz = 2.88 meV, Jxy = 0.20 meV, and an effective g‑factor gz = 7.45, in excellent agreement with prior neutron‑scattering and bulk magnetization studies but with higher precision.

The key insights are: (1) Incompressible plateau states amplify the response of spins near defects because those spins become locally compressible, leading to sharp spectroscopic fingerprints; (2) The multiplicity and energy splitting of spin‑flip excitations serve as a unique diagnostic of the nature (weak bond vs. vacancy) and concentration of disorder; (3) Optical magneto‑spectroscopy provides a low‑field, high‑resolution probe of disorder in quantum magnets, circumventing the need for ultra‑high magnetic fields required to reach full saturation.

Overall, the work establishes magnetization plateaus as a powerful platform for disorder detection, demonstrates that even sub‑percent vacancy concentrations can be identified via satellite modes, and offers a quantitative framework that links spectroscopic signatures to microscopic defect models. This approach opens new avenues for characterizing disorder in candidate quantum spin‑liquid materials and other frustrated magnets where disorder can masquerade as exotic quantum phenomena.