Time-dependent Schwinger boson mean-field theory of supermagnonic propagation in 2D antiferromagnets

This is an interesting theoretical work on a topical subject in the field of magnetism. For the most part, the authors do a good job motivating and presenting details of their calculations. Still, in my view, the second part devoted to the time-dependent SBMFT lacks proper physical introduction. In the beginning of Sec. 3 the authors give few references to the prior publications, which may discuss, the light-matter Hamiltonian, but they do not sum up their results and do not provide explanations on writing the time-dependent Hamiltonian (10). In particular, what are typical f(t) and p(delta) relevant to the cited experiments.
The lack of the physical insight into the origin of (10) leaves me puzzled with the subsequent procedure adopted by the authors in their calculations. Namely, the recipe that the self-consistent solution needs to be obtained for each moment of time 't'. This implies that f(t) in (10) is a slowly varying function of time, right? Subsequently, in Sec. 3.2, a step-like f(t) is used. Such a time-dependent perturbation can be presumably realised for quantum gases in optical lattices. Can it be relevant to magnetic solids?

I think the paper deserves publication once the above questions are properly addressed in the text.

- well written and nice figures/illustrations
- results and methodology seem sound and are clearly stated
- problem that is addressed is timely and interesting

In the manuscript entitled “Time-dependent Schwinger boson mean-field theory of supermagnonic propogation in 2D antiferromagnets”, Bouman and Mentink study time-dependent Schwinger-boson mean-field theory (SBMFT) and compare it with linear spin-wave theory. The goal is to develop a detailed understanding of what the authors dubbed (in a previous work) the “supermagnonic effect”, i.e., the fact that spin correlations can propagate faster than the highest magnon velocity. Antiferromagnetic models on two different lattices, the square and honeycomb lattice, are studied in parallel, which helps illustrating the concepts and phenomena.

A better understanding and illustration of the “supermagnonic effect” is clearly interesting and timely; although the work appears to be a follow-up of a previous PRL (Ref. 26 in the manuscript) of the authors with more details, it does seem to contain enough new results and explanations to justify publication in a journal like SciPost Physics. However, I would like to ask the authors to consider the following comments:

1) As mentioned above, it is clear that the work is a follow-up to the previous PRL, which is of course completely fine. However, I think the current introduction does not make very clear what the additional aspects/results/insights in the manuscript at hand are. So it seems important to very clearly distinguish it from the previous work. I understand there is already a paragraph (bottom of page 2, top of page 3) talking about this, but it was not clear to me, e.g., to what extend the SBMFT has already been studied in the previous PRL. Things become clear after reading the PRL, but this should not be necessary.
2) The part of the paper from Eq. (20) to Eq. (27) contains a lot of equations and not too much physics. The authors might want to think about moving part of it to an Appendix or at least cutting a few equations out of the draft.

Finally, I notice the typo “nog longer” on page 2.

The paper presents a comprehensive and theoretically well-founded study of supermagnonic propagation in 2D antiferromagnets. The authors use the time-dependent Schwinger boson mean-field theory (SBMFT) to study the dynamics of spin correlations in this context. The paper is well-structured, and it addresses an important and timely topic in the field of magnonics and spintronics. The manuscript provides a valuable contribution to the understanding of magnon propagation and supermagnonic effects which is an important question in the field of magnonics and ultrafast spintronics - the propagation of coherent magnons with short wavelengths.

The paper offers a thorough analysis of supermagnonic propagation, considering quantum effects and magnon-magnon interactions. The use of Schwinger boson mean-field theory to study the space-time dynamics of spin correlations is a novel approach that provides valuable insights.

The authors have successfully developed a methodology for studying the space-time dynamics of spin correlations within the framework of time-dependent Schwinger-boson mean-field theory (SBMFT) in the linear-response regime. This approach allowed them to explore quantum effects arising from both the discrete lattice structure and the quantum nature of the spins in a unified framework.

One of the central aspects of this study was the investigation of the supermagnonic effect, where spin correlations were found to transiently propagate faster than the highest magnon group and phase velocity. The paper compared the propagation patterns in SBMFT and linear spin-wave theory (LSWT) and found that, while the qualitative features were similar, the propagation velocities at short length and time scales exhibited significant differences.
The study systematically examined the square lattice and honeycomb lattice and varied the quantum spin number (S) to gain a deeper understanding of the supermagnonic effect. It was revealed that the effect is intricately tied to the interplay between propagating magnon pairs, a feature shared with LSWT, and a quasi-bound state resulting from magnon-magnon interactions. The strength of this effect is highly dependent on the quantum nature of the spins, the coordination, and the lattice geometry.

This research could lead to the enhancement of the supermagnonic regime and have implications for experimental detection.

Two minor observations are in order, that the authors may take into consideration:

1) Providing a more accessible explanation of the theory, equations, and their physical interpretations would be helpful for readers who may not be familiar with SBMFT.

2) A more detailed comparison and discussion of how their results align or differ from LSWT could provide additional insights into the significance of their findings.

In conclusion, the paper offers valuable insights into the supermagnonic effect, providing a foundation for future studies and potential applications in the field of magnonics and ultrafast spintronics. Henceforth I recommend publication in SciPost Physics.

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