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Muonium reaction in MgO: A showcase for the final steps of ion implantation
by Rui C. Vilão, Ali Roonkiani, Apostolos G. Marinopoulos, Helena V. Alberto, João M. Gil, Ricardo B. L. Vieira, Robert Scheuermann and Alois Weidinger
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Apostolos Marinopoulos · Rui Vilão |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202504_00035v1 (pdf) |
| Date submitted: | April 24, 2025, 12:02 p.m. |
| Submitted by: | Vilão, Rui |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Experimental |
Abstract
We present an in-depth investigation of the implantation of positive muons in magnesium oxide (MgO). Muonium, the positive muon plus an electron is an analogue of the hydrogen atom. This study describes the final stage of the implantation process, from muon diffusion over the potential barrier and the stopping by an inelastic reaction to the final embedding of the muon into the lattice structure. A special aspect is a relatively long-lived intermediate configuration which lasts for several hundred nanoseconds or more and is accessible to muon spin spectroscopy. The model presented here provides a framework for the analysis of the general case of ion implantation.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
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That said, the main objective of the study is the introduction and validation of the doorway model would benefit from a more rigorous and comprehensive foundation. At present, the model's description appears to rely on assumptions that are not sufficiently supported by the presented experimental data or theoretical analysis. In particular, the physical mechanisms and associated timescales underlying the model remain speculative, and the current first-principles calculations do not fully substantiate the proposed conclusions or their quantitative alignment with the experimental observations.
While the study explores an interesting and potentially impactful idea, I believe that further experimental validation and more detailed theoretical modeling are necessary to support the claims made. I encourage the authors to address these issues in a revised version, which could significantly strengthen the manuscript. However, in its current form, I do not recommend the manuscript for publication.
The concern is;
There is insufficient and unambiguous evidence to support the claim that the transient state proposed in the model is long-lived. Only a qualitative experimental estimate was provided. Furthermore, there is a lack of compelling evidence for the values of the fixed parameters used in fitting the thermal spike. The authors have also reported significant uncertainties in their analysis of the various phases. In addition, no definitive proof has been presented to demonstrate that the muon is halted at the transient state due to an inelastic reaction. The evidence provided relies primarily on classical, assumed estimates of phonon-induced charge density fluctuations, with no direct simulations to substantiate the muonium effects.
Given that the authors have already utilized first-principles calculations to determine muon localization sites, and considering the novel nature of the proposed processes, it would be beneficial for the authors to undertake the challenging task of employing appropriate methodologies for studying dynamic processes. This would not only help validate both the short-lived and long-lived processes proposed, but also provide stronger support for the model's overall validity.
Recommendation
Ask for major revision
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Requested changes
1- Why do the authors call their suggested intermediate muonium configuration "doorway state", and no longer "transition state"? To me, that sounds more like a linguistic quibble, but perhaps I missed something. In other words, what is the difference between the doorway and the tranistion state model of ref. [31]? Is it the "inelastic reaction" used in the doorway state? But this looks more like adding more details to what is happening during the time the muon spends in the transition state.
2- what is the origin of the missing fraction in Fig. 4? The authors explain it only later in the discussion in chapter 4. I would prefer to get already an indication about the origin of the missing fraction in the description of Fig. 4.
3- In lines 163/164, the authors write that the "apparent peak in the amplitudes [of the Mu lines] at around T = 100 K will be discussed in connection with Fig. 4". However, there is no discussion about this peak in connection with Fig. 4 on page 7. I am curious to see the interpretation of the authors of this peak.
4- what is the parameter C in Eq. 3?
5- ref. [24]: Advances in Physics 72(4), 409 (2023)
6- ref. [58] does not seem to be the proper reference for the Swiss Muon Source. Ref. [58] refers to one of the beamlines of the SmuS.
Recommendation
Ask for minor revision
We thank the referee for the careful review of the paper and the comments. We now reply to the comments and indicate our proposed changes:
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“Doorway model” expresses more clearly than “transition state model” the entrance character of the initial reactions: The passage through the “doorway” by the inelastic reaction and the formation of an initial configuration through which all other reactions proceed. We will add a corresponding sentence in the paper.
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We will add in the description of Fig. 4 in the main manuscript: “About 20 % fraction is missing. It is attributed to muon spin polarization loss due to rapid fluctuations of the hyperfine interaction in the initial hot phase after the muon stopping.”
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We will add the following in the manuscript when introducing Fig. 4, before the last paragraph of section 2: “As mentioned in the experimental section, the observed muonium amplitudes show a peaking slightly above 100 K. We note that the increase is parallel to the increase of diamagnetic-like fraction, suggesting that both states are formed in the same process. The decrease of the muonium fraction at temperatures above about 120 K may either be due to a decrease of the formation probability or to dephasing effects which are rather strong at these high frequencies.”
4 – C is a constant fitting parameter. It is related to the coupling strength of the muonium electron with the phonons, but no details can be given here. We will add this in the main text.
5 – We will correct this and apologize for the wrong citation.
6 – We will replace this reference by the PSI webpage.
Author: Rui Vilão on 2025-06-17 [id 5577]
(in reply to Report 2 on 2025-06-08)We thank the referee for reviewing this manuscript and for his comments, but we disagree with his/her assessment. We believe that the experimental data presented in this work, together with joint calculations, constitute a solid, serious, novel and impactful contribution to the field of muon/ion implantation in solids. This paper is a contribution to the discussion, but it is not meant as the final solution of the problem. We kindly ask the referee to reconsider his/her assessment and to agree to acceptance of the paper.
We now reply to specific comments of the referee:
Comment of referee 2
There is insufficient and unambiguous evidence to support the claim that the transient state proposed in the model is long-lived. Only a qualitative experimental estimate was provided.
Our comment
The fast component is long-lived, otherwise it would not be experimentally observed. A precise determination of the lifetime is out of the scope of this work, but the experimental evidence is unambiguous.
Comment of referee 2
Furthermore, there is a lack of compelling evidence for the values of the fixed parameters used in fitting the thermal spike.
Our comment
The thermal spike concept is used here only to account for the levelling-off of the formation probability at low temperatures. It is not a major issue in this connection and is therefore a secondary point that does not affect the main model.
Comment of referee 2
The authors have also reported significant uncertainties in their analysis of the various phases.
Our comment
The determination of the phases is very uncertain for high frequency signals. We therefore do not discuss the phases explicitly in this paper.
Comment of referee 2
In addition, no definitive proof has been presented to demonstrate that the muon is halted at the transient state due to an inelastic reaction. The evidence provided relies primarily on classical, assumed estimates of phonon-induced charge density fluctuations, with no direct simulations to substantiate the muonium effects.
Our comment
For an interaction of the muon with the lattice it is necessary that the muon stays a certain time at a place. This requirement is fulfilled during the slowing down, first at the top of the diffusion barrier. We give a classical consideration at what energy the sufficiently long stay time is reached, but this is of course only a qualitative estimate.
Comment of referee 2
Given that the authors have already utilized first-principles calculations to determine muon localization sites, and considering the novel nature of the proposed processes, it would be beneficial for the authors to undertake the challenging task of employing appropriate methodologies for studying dynamic processes. This would not only help validate both the short-lived and long-lived processes proposed, but also provide stronger support for the model's overall validity.
Our comment
Simulations such as those asked by the referee are out of the scope of the present paper and would represent alone a major contribution to the difficult field of simulation of the final stages in ion implantation physics.