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Timedependent Schwinger boson meanfield theory of supermagnonic propagation in 2D antiferromagnets
by M. D. Bouman, J. H. Mentink
Submission summary
Authors (as registered SciPost users):  Johan Mentink 
Submission information  

Preprint Link:  https://arxiv.org/abs/2306.16382v1 (pdf) 
Date submitted:  20230629 23:00 
Submitted by:  Mentink, Johan 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approaches:  Theoretical, Computational 
Abstract
Understanding the speed limits for the propagation of magnons is of key importance for the development of ultrafast spintronics and magnonics. Recently, it was predicted that in 2D antiferromagnets, spin correlations can propagate faster than the highest magnon velocity. Here we gain deeper understanding of this supermagnonic effect based on timedependent Schwinger boson meanfield theory. We find that the supermagnonic effect is determined by the competition between propagating magnons and a localized quasibound state, which is tunable by lattice coordination and quantum spin value $S$, suggesting a new scenario to enhance magnon propagation.
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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 timedependent SBMFT lacks proper physical introduction. In the beginning of Sec. 3 the authors give few references to the prior publications, which may discuss, the lightmatter Hamiltonian, but they do not sum up their results and do not provide explanations on writing the timedependent 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 selfconsistent 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 steplike f(t) is used. Such a timedependent 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.
Strengths
 well written and nice figures/illustrations
 results and methodology seem sound and are clearly stated
 problem that is addressed is timely and interesting
Report
In the manuscript entitled “Timedependent Schwinger boson meanfield theory of supermagnonic propogation in 2D antiferromagnets”, Bouman and Mentink study timedependent Schwingerboson meanfield theory (SBMFT) and compare it with linear spinwave 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 followup 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:
Requested changes
1) As mentioned above, it is clear that the work is a followup 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.
Report
The paper presents a comprehensive and theoretically wellfounded study of supermagnonic propagation in 2D antiferromagnets. The authors use the timedependent Schwinger boson meanfield theory (SBMFT) to study the dynamics of spin correlations in this context. The paper is wellstructured, 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 magnonmagnon interactions. The use of Schwinger boson meanfield theory to study the spacetime dynamics of spin correlations is a novel approach that provides valuable insights.
The authors have successfully developed a methodology for studying the spacetime dynamics of spin correlations within the framework of timedependent Schwingerboson meanfield theory (SBMFT) in the linearresponse 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 spinwave 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 quasibound state resulting from magnonmagnon 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.
Requested changes
No changes are requested