Thermodynamic, Dynamic, and Transport Properties of Quantum Spin Liquid in Herbertsmithite from an Experimental and Theoretical Point of View
, Alfred Z. Msezane 2, Miron Ya. Amusia 3,4, John W. Clark 5,6, George S. Japaridze 2, Vladimir A. Stephanovich 7 and Yulya S. Leevik 8Round 1
Reviewer 1 Report
The manuscript "Thermodynamic, dynamic and transport properties of quantum spin liquid in herbertsmithite from experimental and theoretical point of view", by. V. R. Shaginyan, et al., seems to provide an interesting review of the subject. Hereafter, I list few suggestions to improve the overall presentation.
1. Do not the authors think that a figure illustrating the very structure of herbertsmithite would be appreciated by the readers of e review article?
2. There is a paragraph, "Then, the FCQPT ... electric current", that is repeated identical, in Sec. 2 (lines 119-128) and in Sec. 2 (lines 136-144). The repetition puzzles the reader, as no new information is conveyed the second time, so the authors should either suppress the repeated paragraph, or at least formulate it in such a way as to convey new information.
3. The captions of most figures are not satisfactory, as they should serve to guide the reader. For instance, the horizontal and vertical lines in Fig. 4 are unexplained, whereas in Fig. 5 the reader notices that some values of the field (0T, 1T, 3T), appear more than once, under different symbols, with no further explanation of the meaning of these multiple occurrences.
4. Am I missing something, or the label of the horizontal axis in Figs. 6,7,8 should be ωN rather than EN?
With the above remarks taken into account, I suggest that the manuscript may be accepted for publication.
Author Response
We thank the referees for their time and reports that improve significantly our review.
The text of our review was extensively revised. All the referees’ criticism was taken into account. We highlighted by yellow our revisions that correspond to the referees’ criticism.
The corresponding file is QSL_Herb_MDPI_R_Mark.
1. Do not the authors think that a figure illustrating the very structure of herbertsmithite would be appreciated by the readers of e review article?
We have added Fig. 1, page 3.
2. There is a paragraph, "Then, the FCQPT ... electric current", that is repeated identical, in Sec. 2 (lines 119-128) and in Sec. 2 (lines 136-144). The repetition puzzles the reader, as no new information is conveyed the second time, so the authors should either suppress the repeated paragraph, or at least formulate it in such a way as to convey new information.
The repetition is eliminated.
3. The captions of most figures are not satisfactory, as they should serve to guide the reader. For instance, the horizontal and vertical lines in Fig. 4 are unexplained, whereas in Fig. 5 the reader notices that some values of the field (0T, 1T, 3T), appear more than once, under different symbols, with no further explanation of the meaning of these multiple occurrences.
We have explained the lines in Fig. 4 and the appearance of the values of magnetic fields. Now these are Figs. 6 and 7.
4. Am I missing something, or the label of the horizontal axis in Figs. 6,7,8 should be ωN rather than EN?
Yes, the mention is correct. We have corrected the formulas.
Reviewer 2 Report
The authors present a review about herbertsmithite including experimental and theoretical viewpoints. When reading the manuscript, it turned out that this is not a really unbiased collection of existing experimental data, but more a defence of the theory of the authors, which was published in Ref. 9, 11, 12, 13, 14, 16, 27, 28. Therefore, I could not really recommend this paper as a review. On the other side, the authors present a thorough analysis of available data in light of their theory. The paper might be suitable for publication, if the authors can clarify which part of this analysis is new and was not published before in the mentioned references. Furthermore, the authors should avoid any statement in the abstract, which could be misinterpreted in the sense, that in this paper new and own experimental data are presented (“Based on experimental data…”), as the work of the authors is purely theoretical, if I understood that correctly.
Author Response
We thank the referees for their time and reports that improve significantly our review.
The text of our review was extensively revised. All the referees’ criticism was taken into account. We highlighted by yellow our revisions that correspond to the referees’ criticism.
The corresponding file is QSL_Herb_MDPI_R_Mark.
The authors present a review about herbertsmithite including experimental and theoretical viewpoints. When reading the manuscript, it turned out that this is not a really unbiased collection of existing experimental data, but more a defence of the theory of the authors, which was published in Ref. 9, 11, 12, 13, 14, 16, 27, 28. Therefore, I could not really recommend this paper as a review. On the other side, the authors present a thorough analysis of available data in light of their theory. The paper might be suitable for publication, if the authors can clarify which part of this analysis is new and was not published before in the mentioned references. Furthermore, the authors should avoid any statement in the abstract, which could be misinterpreted in the sense, that in this paper new and own experimental data are presented (“Based on experimental data…”), as the work of the authors is purely theoretical, if I understood that correctly.
We agree that we do not present lot of new results in our review, for a review paper is not indented to.
Nonetheless, some of our suggestions, like the influence of impurities or the value of magnetic field to measure the behavior of the optical conductivity under the application of magnetic field, are new.
We believe that our review is a really unbiased collection of existing experimental data, for we consider the main experimental data, explaining them. Of course, we cannot observe all available data and explain them. It is impossible to do in a short review. The main item of our review is to clarify the existence of quantum spin liquid in herbertsmithite and to inspire the further experimental work.
Yes, our review is theoretical work and we stressed this point in the abstract.
Reviewer 3 Report
The paper describes a theoretical approach based on the Landau Fermi liquid (LFL) in order to understand the thermodynamic and optical properties of quantum spin liquids. While the LFL commonly applies to metals, here the concept is extended to insulating materials where the spin degrees of freedom remain disordered at low temperatures, suggesting possibility of low-lying spin excitations. From the theoretical point of view it is very important whether these spinons have a gap or not, and experimental results yield conflicting interpretations.
Much effort is devoted to discuss a set of magnetic field dependent susceptibility and specific heat experiments, and also some NMR results, collapsing the data on natural scales. The comparison to the presented theoretical framework provides reasonable agreement. This is taken as evidence that the response is due to gapless spinons, in close similarity to heavy fermion LFL.
The reader can follow the main message, and the results of this work should be reported. Though, the authors should include some improvements, as written below:
1) Discussion is focused mostly on bulk susceptibility and specific heat measurements, which are both sensitive to the intrinsic response of kagome spins and, at the same time, to the contribution of impurities, and potential other extrinsic contributions. To that end, these two experimental probes cannot disentangle between these contributions. The strongest evidence for a spin gap is found in NMR results reported in Ref. 17. As a microscopic probe, the 17-O Knight shift can distinguish between intrinsic and extrinsic contributions as it measures the local spin susceptibility, with the result that the kagome spins exhibit a spin gap. The Knight shift in fact shows that the susceptibility vanishes towards T=0 (Fig. 4B in Ref. 17), in agreement with the expectation in line 233 of the present manuscript. The authors should take notice of the NMR result in the text, and soften the claims about the non-existence of a gap -- simply because susceptibility and specific heat results may pick up different contributions at once, complicating a clear assignment of each.
2) Since there is considerable discussion about impurities, disorder in general should be discussed more in detail. Recently, there has been considerable work on several triangular-lattice spin liquid candidates regarding disorder [Sci. Adv. 3, e1601594 (2017); Nat. Phys. 13, 117–122 (2017), PRB 97, 245134 (2018); PRB 98, 205141 (2018), Crystals 2018, 8, 190]. How would the temperature-field dependence of the maximum in susceptibility and specific heat look like for impurities? The authors should at least mention the broad discussion in other materials classes about disorder in spin liquids and, ideally, include such a comparison to underpin their statements about irrelevance of disorder/impurities in herbertsmithite.
3) I wonder about the relation of the presented model to U(1) gauge theory [PRL 95, 036403 (2005); PRL 99, 156402 (2007)]. The predictions for the optical conductivity seem to produce a quadratic frequency dependence in both cases. To what extent is the lattice symmetry (kagome vs. triangular) relevant for this frequency dependence?
4) line 32: remove 'have'
5) lines 36-38: In the current version the frequent usage of the word 'gap' makes it
difficult to follow whether it is about spin or charge. The wording
should be improved for a better readability. It should be first clearly stated that there is a 3 eV charge gap [PRB 96, 241114(R) (2017)], making it an electrical insulator. Then it should be contrasted to the 'metallic-like' thermodynamic properties and the controversy of a spin gap (see point (1) above), which is crucial for the understanding of the ground state of herbertsmithite.
6) Fig. 3: presenting two data sets on top of each other does not allow to separate which data set is from Herbertsmithite and which is from YbRh2Si2. Instead it would be better to separate into two individual plots, one for each material, showing two panels in horizontal arrangement, for instance.
Given the points above are adequately addressed, I can support publication of this manuscript.
Author Response
We thank the referees for their time and reports that improve significantly our review.
The text of our review was extensively revised. All the referees’ criticism was taken into account. We highlighted by yellow our revisions that correspond to the referees’ criticism.
The corresponding file is QSL_Herb_MDPI_R_Mark.
1) Discussion is focused mostly on bulk susceptibility and specific heat measurements, which are both sensitive to the intrinsic response of kagome spins and, at the same time, to the contribution of impurities, and potential other extrinsic contributions. To that end, these two experimental probes cannot disentangle between these contributions. The strongest evidence for a spin gap is found in NMR results reported in Ref. 17. As a microscopic probe, the 17-O Knight shift can distinguish between intrinsic and extrinsic contributions as it measures the local spin susceptibility, with the result that the kagome spins exhibit a spin gap. The Knight shift in fact shows that the susceptibility vanishes towards T=0 (Fig. 4B in Ref. 17), in agreement with the expectation in line 233 of the present manuscript. The authors should take notice of the NMR result in the text, and soften the claims about the non-existence of a gap -- simply because susceptibility and specific heat results may pick up different contributions at once, complicating a clear assignment of each.
We have added a comment on the 17-O Knight shift and stressed that herbertsmithite is to be considered as an integral system. We have also softened our claims about the existence of the spin gap. On the other hand, we wish to attract attention to new experiments that can clarify the gap item.
2) Since there is considerable discussion about impurities, disorder in general should be discussed more in detail. Recently, there has been considerable work on several triangular-lattice spin liquid candidates regarding disorder [Sci. Adv. 3, e1601594 (2017); Nat. Phys. 13, 117–122 (2017), PRB 97, 245134 (2018); PRB 98, 205141 (2018), Crystals 2018, 8, 190]. How would the temperature-field dependence of the maximum in susceptibility and specific heat look like for impurities? The authors should at least mention the broad discussion in other materials classes about disorder in spin liquids and, ideally, include such a comparison to underpin their statements about irrelevance of disorder/impurities in herbertsmithite.
We have added the references and Figs. 8 (a) and (b) to clarify the role of impurities forming the maximum in susceptibility.
3) I wonder about the relation of the presented model to U(1) gauge theory [PRL 95, 036403 (2005); PRL 99, 156402 (2007)]. The predictions for the optical conductivity seem to produce a quadratic frequency dependence in both cases. To what extent is the lattice symmetry (kagome vs. triangular) relevant for this frequency dependence?
The lattice symmetry can hardly form the frequency dependence, for the conductivity is measured at the low frequencies when the wavelength is bigger than the corresponding lattice size.
4) line 32: remove 'have'
This word is removed.
5) lines 36-38: In the current version the frequent usage of the word 'gap' makes it difficult to follow whether it is about spin or charge. The wording should be improved for a better readability. It should be first clearly stated that there is a 3 eV charge gap [PRB 96, 241114(R) (2017)], making it an electrical insulator. Then it should be contrasted to the 'metallic-like' thermodynamic properties and the controversy of a spin gap (see point (1) above), which is crucial for the understanding of the ground state of herbertsmithite.
The necessary comments are added.
6) Fig. 3: presenting two data sets on top of each other does not allow to separate which data set is from Herbertsmithite and which is from YbRh2Si2. Instead it would be better to separate into two individual plots, one for each material, showing two panels in horizontal arrangement, for instance.
We have added Fig. 5 showing the data sets related to YbRh2Si2.
Reviewer 4 Report
Review report for condensedmatter-538837
The manuscript by V. R. Shaginyan et al. reviews experimental and theoretical studies of herbertsmithite, and focus is placed on evidence that supports a particular perspective advocated by the authors, namely the topological fermion condensation (FC). The authors argue that spinons in QSL form the flat band in a similar way that the valence electrons in heavy fermion metals form the conduction flat bands. With this motivation in mind, the authors established similar scaling behavior of magnetic susceptibility and specific heat in QSL and heavy fermion metals. Based on this similarity and the underlying theoretical considerations in the framework of fermion condensation, the authors argue in favor of a gapless QSL in herbertsmithite. The authors further consider impurity effects in the gapless QSL and suggest that QSL can be stabilized by inhomogeneities at nanoscale.
Overall, I find the discussion intriguing and the manuscript worth to be published in Condensed Matter. I want to point out though, while the fermion condensation provides an interesting phenomenological framework for certain heavy fermion systems with flat bands, the underlying physics of flat bands in various frustrated lattices at large is far from clear and has attracted a lot of attention recently. However, within the framework of FC, I do find the scaling analysis and authors’ predictions on optical conductivity elegant and may inspire future studies.
About the impurity effect, it is indeed a very challenging problem especially to experimentalists. Controlled doping dependence study in a clean system is a must for any unambiguous interpretation of the results. Unfortunately, as the authors also point out, it is extremely difficult to isolate thermodynamic signatures from dynamics in herbertsmithite. In this aspect, similar systems where impurity effects can be studied more systematically is invaluable. The authors might want to include discussions of a recent study of impurity effects in the doped Shastry-Sutherland system [Shi et al, Nat. Commun. 10, 2439 (2019)], where impurities were found to play nontrivial roles in the ground states and the magnetization process of the doped quantum magnet.
I do have some regretful feelings about the English and the overall presentation of the manuscript. For example, in the abstract, the sentence “In this respect, the implications of…are controversial in their implications” can certainly be improved. In the previous sentence, “most perspective material” should probably be “most prospective material”. Also, a lot of the references are missing the journal names.
In conclusion, I recommend the manuscript for its publication in Condensed Matter. I believe the manuscript would be in a better form if the English can be improved.
Author Response
We thank the referees for their time and reports that improve significantly our review.
The text of our review was extensively revised. All the referees’ criticism was taken into account. We highlighted by yellow our revisions that correspond to the referees’ criticism.
The corresponding file is QSL_Herb_MDPI_R_Mark.
About the impurity effect, it is indeed a very challenging problem especially to experimentalists. Controlled doping dependence study in a clean system is a must for any unambiguous interpretation of the results. Unfortunately, as the authors also point out, it is extremely difficult to isolate thermodynamic signatures from dynamics in herbertsmithite. In this aspect, similar systems where impurity effects can be studied more systematically is invaluable. The authors might want to include discussions of a recent study of impurity effects in the doped Shastry-Sutherland system [Shi et al, Nat. Commun. 10, 2439 (2019)], where impurities were found to play nontrivial roles in the ground states and the magnetization process of the doped quantum magnet.
We have added the reference and a brief discussion.
I do have some regretful feelings about the English and the overall presentation of the manuscript. For example, in the abstract, the sentence “In this respect, the implications of…are controversial in their implications” can certainly be improved. In the previous sentence, “most perspective material” should probably be “most prospective material”. Also, a lot of the references are missing the journal names.
In conclusion, I recommend the manuscript for its publication in Condensed Matter. I believe the manuscript would be in a better form if the English can be improved.
We have improved the English and revised the text and added a number of references.
Round 2
Reviewer 2 Report
I am still not convinced that this paper is an unbiased review. But I leave it with the editors, to decide if this article qualifies as that.
Author Response
We thank the referee for the report and time. We have taken into account the criticism and with accordance of the editor recommendation added to the Abstract and Introduction phrase: “The review mostly deals with an historical perspective of our theoretical contributions on this subject, based on the theory of fermion condensation closely related to the emergence (due to geometrical frustration) of dispersionless part in the fermionic quasiparticle spectrum, so-called flat bands.” Our corrections are highlighted in PDF file of our review by yellow color.
Reviewer 3 Report
The authors have answered my questions and the discussion has improved, also aided by the new figures, so the paper can be published. Just one last comment:
Reference [2] is misplaced in line 40 as it is not on herbertsmithite but belongs to the discussion about triangular-lattice compounds on page 16. In addition to Ref. [1], in line 40 one could add a reference to [J. Phys. Condens. Matter 29, 095802 (2017)].
Author Response
We thank the referee for the report and time. We have taken into account the criticism: The mentioned reference is moved on p. 16, while the other reference is added.
