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Timedependent Schwinger boson meanfield theory of supermagnonic propagation in 2D antiferromagnets
by M. D. Bouman, J. H. Mentink
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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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Report
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.
Author: Johan Mentink on 20241005 [id 4838]
(in reply to Report 2 on 20231026)
Answer 21
We thanks the referee for the positive assessment of our research.
In the previous PRL, we already identified that the origin must be quantum fluctuations by studying the dependence on the spin value S using SBMFT. Here, we study more systematically the dependence on quantum fluctuations with the same SBMFT by investigating not only the dependence on S but also the dependence on the lattice coordination z. This gap making is now made explicitly in the introduction text.
Answer 22
We agree with the referee that Eqs. (2027) do not contain key physical insight themselves. They comprise merely the result of technical derivations and convenient notation to derive the results analytically. Therefore, we followed the advice of the referee to move these results to the appendix.
We corrected the typo 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
Author: Johan Mentink on 20241005 [id 4839]
(in reply to Report 1 on 20231023)
We thank the referee for the positive assessment of our manuscript. To make the physics resulting from the SBMFT theory more accessible, we decided to focus on the qualitatively new results that are captured beyond LSWT. Hence we have moved Eqs. (2027) of Sec. 3.1 to an appendix since they comprise merely technical derivations (see also the feedback from referee 2) .
We have further highlighted the physical effects by adding a paragraph at the end of Sec. 3.1 to explain the difference with LSWT. Unlike LSWT, the SBMFT includes magnonmagnon interactions. When taking these interactions into account, the twomagnon spectrum changes qualitatively: instead of being a (renormalized) sum of noninteracting magnons, the excitation of interacting magnonpairs causes the emergence of a quasibound state. These changes are captured in SBMFT by the timedependent correction to the bond order parameter, but are missing in LSWT.
Author: Johan Mentink on 20241005 [id 4837]
(in reply to Report 3 on 20231108)We thank the referee for the positive assessment of our paper. To better assess the physical origin of equation (10), we now started with introducing the general lightmatter hamiltonian and explicitly review previous publications that have derived them. Subsequently, we specialize to the formulation given in Eq.(10), which is merely a technical convenience for the systematic derivation of the linearresponse SBMFT.
In addition, in the same introduction paragraph of Sec. 3, we elaborated on the physical motivation for the form of the function f(t): for solids, the most relevant function for f(t) is a function which mimicks timeenvelope of a femtosecond laser pulse (eg a Gaussian in time). Since the laser pulse can perturb the exchange interaction only modestly (at most by a few percent of the unperturbed exchange interaction), we focus on the derivation in the linearresponse regime.
The theoretical linear response formalism itself would be valid for any shape of the function f(t). For laserinduced spin dynamics, we are mostly interested in impulsive perturbations. These are characterized by a pulsewidth $\tau$ that is much shorter than the subsequent time scale of the induced dynamics of the system. For the present case, in which the response features oscillations with maximum frequency $\omega_{max}$, this comprises the regime $\tau \omega_{max}\ll 1$.
In numerical simulations, impulsive perturbations can be conveniently implemented by a square pulse $f(t)=1$ for $0< t \leq \tau$. Below we are interested in the shorttime dynamics for which the supermagnonic effect is observed. In this regime, the dynamics induced by a single step function $f(t)=\Theta(t)$ was found to closely resemble the square pulse protocol adopted in an earlier publication [G. Fabiani and J.H. Mentink, SciPost Phys. 7, 004 (2019)]. Therefore the step function is used to investigate the supermagnonic effect.