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> ----------------------------------------------------------------------
> Report of the First Referee -- BN13654/Kent-Dobias
> ----------------------------------------------------------------------
>
> The work deals with a purely phenomenological model for the “hidden”
> order parameter if URu2Si2, with particular emphasis on the expected
> elastic properties. The work might eventually be suitable for Phys.
> Rev. B, but some aspects are not clear to me.
>
> The main result is Fig. 2, where the behavior around TN is difficult
> to see. I suggest to add zooms on that crucial T-range, where it seems
> to me that there is a qualitative difference between model and
> experiments. The justification given by the Authors (“mean field
> theory—which is based on a small-eta expansion—will not work
> quantitatively far below the transition where eta has a large nonzero
> value and higher powers in the free energy become important”) does not
> look plausible as the disagreement does not appear to develop slowly
> as T decreases, but appears immediately below TN, where eta is small.
The disagreement between the theory at low temperature is largely resolved by
the addition of an additional interaction in the mean-field free energy of the
form ε²η². In a new appendix, we have worked through the mean field modulus
implied with this new interaction and a fit is now shown in Fig. 2 as a thin
black line.
> Is it not clear how discriminatory is the agreement above TN in 2a, 2b
> and 2c. Are calculation results robust over a wide range of fitting
> parameters, or does the agreement result from a fine-tuning? (e.g.,
> the presence of a maximum at 120 K in 2b).
[Not exactly sure what this means.]
> Is it possible to say something about the c/a ratio, which displays a
> non-trivial T-dependence?
[Not sure what this means either. Is this asking about the ratio of lattice constants?]
> At last, I understand that the model is meant to be purely
> phenomenological, but given the plethora of publications on URu2Si2
> over 30 years, where any conceivable order parameter has been proposed
> as candidate, the Authors should make a connection between their
> abstract OP and possible physical realizations. For instance, in the
> simplest framework of localized f-electrons, what ionic moments would
> fit the present proposal?
[Mike, can you help with this?]
> ----------------------------------------------------------------------
> Report of the Second Referee -- BN13654/Kent-Dobias
> ----------------------------------------------------------------------
>
> In this paper, possible elastic properties of URu2Si2 are studied with
> focusing on the long-standing hidden order (HO) problem. The authors
> introduce a generic form of the free energy density for the elastic
> energy, a modulated order parameter, and their mutual coupling, and
> analyze the temperature dependences of the elastic constants by
> minimizing the free energy. It is shown that the B1g component
> exhibits a remarkable softening with decreasing temperature and a cusp
> singularity at the HO transition point, and these results are compared
> with recent ultrasound experiments. From the comparison, the authors
> conclude that the HO phase of URu2Si2 originates from the modulated
> B1g order parameter.
>
> In the course of evaluation, the referee does not recommend the paper
> to be published in PRB, mainly based on the following reason.
>
> 1) The scheme for the coupled strains in this paper is quite standard
> within the mean-field treatment and does not provide a novel
> theoretical advance.
>
> 2) One can generically expect several sources for softening elastic
> constants. For example, the authors in ref.25 also succeeded in the
> quantitative fits in the framework of a 4f crystal field model for T >
> T_HO. Thus, the fitting is not regarded as the decisive evidence on
> the validity of the model.
[Not sure how to respond to this; Brad?]
> 3) The agreement of C[B1g] in the region T<T_HO is poor, though only
> the cusp at T_HO seems qualitatively consistent with the experiment.
> Moreover, the referee expects that even a cusp structure in the
> elastic constants is not unique to this model; it can be obtained from
> more general models beyond the linear coupling (4), within the
> mean-field level. Therefore, the referee thinks that this analysis
> does not lead uniquely to the authors' arguments on the realization of
> the B1g order parameter.
The disagreement between the theory at low temperature is resolved by the
addition of an additional interaction in the mean-field free energy of the form
ε²η², now shown in Fig. 2 as a thin black line.
While terms like this provide cusp-like features in the modulus for each strain
symmetry, they cannot explain the 1/ΔT softening seen in the high-temperature
phase, since their contribution to the response function is zero above T_c.
> 4) The most important point in the HO problem is the microscopic
> identification of symmetry breaking and the order parameter. In spite
> of the long history in research over almost 40 years, there is no
> experimental evidence of the formation of any superlattice structure
> at least at ambient pressure. So, the proposed modulated order is not
> consistent with the absence or identification of symmetry breaking.
> The authors do not provide any resolution on that point which is the
> most relevant in this problem.
The articles below, also cited in our work, all provide experimental evidence
for the formation of superlattice structure along the c-axis at ambient
pressure.
[I pulled these from our citation on the estimate for q_*. Do they actually
provide the evidence we need? Can someone who knows more about these techniques
elaborate?]
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.111.127002
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.43.12809
https://journals.jps.jp/doi/10.1143/JPSJ.79.064719
https://www.nature.com/articles/nphys522
|
