Observation of single antiferromagnetic magnon modes in the tunnelling transistors of spin-1/2 Kitaev system a-RuCl3

Referee: [Abstract and inelastic-tunneling results] The central attribution of selected inelastic tunneling features below TN to single magnon modes of the zigzag order lacks quantitative support: no explicit energy matching to the bulk magnon dispersion or density of states from neutron scattering, no lineshape modeling, and no error analysis or fitting procedure are described (Abstract and results section on inelastic features).

Authors: We agree that more explicit quantitative support strengthens the attribution. In the revised manuscript we have added a direct comparison table matching the observed inelastic peak positions (with experimental uncertainties from multiple devices) to single-magnon energies extracted from published bulk neutron-scattering dispersion relations. Lorentzian lineshape fits are now shown with fitting parameters and residuals reported in the supplementary information; the fitting procedure is described in the methods. A full magnon density-of-states calculation is not performed here as it lies beyond the experimental scope, but we cite the relevant neutron literature for the continuum and note this as a future direction. revision: yes

Referee: [Low-temperature inelastic spectra] Alternative explanations (phonons, interface states, strain-induced modes, or modified thin-film dispersions) are not excluded by magnetic-field dependence, thickness-series comparison, or temperature scaling that would track the bulk zigzag order (results section on low-temperature inelastic spectra).

Authors: We have expanded the discussion to address each alternative explicitly. Phonon energies from Raman data on RuCl3 do not coincide with the observed features, and the inelastic signals appear only below TN with temperature scaling that follows the bulk zigzag order parameter. Interface states are minimized by hBN encapsulation, as evidenced by the clean semiconducting behavior and absence of mid-gap states at higher temperatures. Strain effects are discussed as unlikely given the van der Waals assembly method. We have added magnetic-field sweeps showing suppression of the features at fields consistent with bulk TN reduction. Thickness dependence is shown for 1L–3L devices with consistent feature positions; a broader series including thicker films is acknowledged as desirable but limited by current fabrication yield and is noted for future work. revision: partial

Referee: [Discussion of thin-film limit] The claim that films of three layers and below retain bulk-like zigzag order and its single-magnon continuum relies on qualitative similarity rather than a direct, falsifiable test against neutron-derived energies or a control experiment on thicker films (discussion of thin-film limit).

Authors: The revised discussion now includes explicit numerical matching of the inelastic energies to neutron-derived magnon values, making the comparison falsifiable. The temperature onset of the features coincides with the bulk TN range, providing an additional consistency check. While direct neutron scattering on these mesoscopic samples is not feasible, the electrical probe itself constitutes the falsifiable test in the thin-film limit. We have clarified that the work focuses on the atomically thin regime and does not claim to replace scattering techniques; a sentence has been added noting that future heterostructure studies could extend the comparison. revision: yes