Polarization Analysis in Mössbauer Reflectometry with Synchrotron Mössbauer Source

Round 1

Reviewer 1 Report

This a good paper setting forth the use of polarization in reflectometry spectra from thin films with Synchrotron Mossbauer radiation. It will be interesting for future workers in the field, admittedly a small community, but nevertheless important for them to have the principles of the analysis set out. Some new results on iron-chromium films are reported.

Author Response

We are grateful to the reviewer for the positive estimation of out work.

We have tried to correct small spelling bugs in the text.

Reviewer 2 Report

The advent of Synchrotron Mössbauer Source (SMS) was a major breakthrough in the application of nuclear resonant scattering of synchrotron radiation. The pure nuclear Bragg reflection of a ⁵⁷FeBO₃ single crystal moved by a conventional Mössbauer drive results in a single-line energy-domain Mössbauer source having nevertheless most of the unique properties of synchrotron radiation including small beam size, high degree of collimation and practically full polarization. During the past two decades, time-domain Mössbauer reflectometry based on the small beam size and the high degree of collimation was widely used to map the magnetic structure of thin films and multilayers. In these studies, the polarization of the synchrotron radiation played a decisive role. When Mössbauer reflectometry is done with SMS, it is an important question how the polarization behaves in such an experiment and which conclusion on the hyperfine structure of the scatterer can be drawn from an additional polarization analysis. Therefore the study described in the manuscript is, doubtless, an important one and deserves to be published. Still, the present version of the paper contain several points that need to be reconsidered and, in the opinion of this reviewer, to be changed before publication.

The abstract starts with claiming that a new experimental technique was tested. This is for sure a vast exaggeration and should be formulated in a much more modest way. In fact, as also shown by references of the manuscript itself, both standing wave technique and polarization analysis in nuclear resonant scattering has been previously used by several groups (including those of the authors). Since, due to hyperfine interaction, nuclear resonant scattering is polarization-dependent, polarization analysis is obvious. The application of a silicon channel-cut crystal as sigma-analyzer is a standard method in x-ray experiments. The polarization dependence of nuclear resonant scattering has already been considered in published computer codes. Therefore the described approach is an excellent unification of well-known methods rather than e new experimental technique.

The term “rotated polarization” used already in the abstract and later at many places of the text is somewhat misleading. Indeed, as properly described in Equations (1) to (4), in the general case, the polarization of the scattering amplitude of the reflected beam is no longer linear. Probably using another term like “changed” or “altered” polarization would be more appropriate. Admittedly, the polarization analysis measures the intensity belonging to a certain rotated component of the scattering amplitude but this doesn’t mean that the whole scattered intensity can be described by a rotated polarization.

The experimental data presented in the manuscript are of quite low quality. This fact is ascribed by the to the surface roughness and imperfections of the cluster-layered film that resulted in a divergence of the reflected beam much exceeding the angular acceptance of the Si (840) analyzer channel-cut. Although this is certainly true, the low statistics of the data shown in Figs. 6, 7, 8b and 8c strongly undermine the conclusion on the improved data interpretation in the case of poorly resolved spectra. It would have been more convincing to demonstrate the efficiency of the presented approach on a sample of much better quality.

In the left column of Fig. 9b, seven fitted field distributions extracted from the experimental spectrum in Fig. 8b is shown. The credibility of this fit can be questioned. Indeed, without presenting the correlation matrix of the fit, it is hard to accept that so many parameters can be determined from the noisy spectrum in Fig. 8b.

Author Response

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

The authors have properly taken into account the comments in the first page of my review. However, probably due to some technical issues of the editorial system, the second page of the report seems not to have reached the authors. Therefore now I am attaching the full report as a pdf file and kindly ask the authors to reflect on the concerns raised in the second page, as well.

Comments for author File: Comments.pdf

Author Response

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Concerning the statement in lines 165-170, the basic problem has now been solved by the authors’ removing the word “theoretical”. Indeed, the real novelty of the paper is the experimental demonstration of the existence of the peak at very low grazing angle in the energy domain.

It is true that no Fresnel formula for an anisotropic mirror is directly available in established optics textbooks. Nevertheless, since the incident wave comes from the vacuum, the principal axis system of the anisotropic semi-infinite medium can be used and then the Θ → 0 limit of the reflectivity can easily be calculated from formulae published in standard textbooks, an example being Eqs. (7.39) and (7.41) in the respective pages 305 and 306 of John David Jackson’s book Classical Electrodynamics (third edition, John Wiley & Sons, Inc.). By doing so, it can be easily seen that r^aa → -1, r^bb → -1, r^ab → 0, r^ba → 0 for Θ → 0.

Of course, the physical reason of the peak appearing in the π → σ scattering is different from that of the peak in the π → π scattering in the sense that, as the authors have just shown, the former one appears also when the electronic scattering is completely switched off (with a shifted position and distorted shape, though). Nevertheless, the reason is the same considering the simple argument that any non-negative real function having the limits 0 both for Θ → 0 and for high values of Θ should necessarily have a maximum in between. But then, mentioning the term “critical angle of the total external reflection” in connection with the peak appearing in the π → σ scattering (cf. lines 18, 180, 464 and 466 of the manuscript) is at least very strange.

I still feel that the role of the standing-wave method is overemphasized in the paper and also the term itself is somewhat misleading since the peaks should be present not only for stratified systems like multilayers but also for a semi-infinite homogenous medium where no standing waves exist, not at least in the commonly used meaning of the word.

Admittedly, my remaining concerns are somewhat questions of taste. Therefore, although I would be happy if the authors took them into account, finally I also can live with leaving the text as is.

In conclusion, I suggest to ask the authors for the mentioned very last minor corrections after which the paper can be published in Condensed Matter.