Peer review of: Gapless spin liquid in a square-kagome lattice antiferromagnet (2017)

RR2
Reviewers' comments:
Reviewer #1 (Remarks to the Author):
  Gapless spin liquid in a square-kagome lattice antiferromagnet
 by
 M.Fujihala et al.
 In the first-round referee's reports on the submitted original manuscript,
 there were several interesting comments and questions requiring further studies and changes of the
 paper.
 In particular,
 the authors were asked
 to provide further evidence for the absence of structural disorder,
 to rule out the spin glass behavior,
 to rethink again about the INS data and to redo theoretical DMRG calculations for the scattering
 intensity,
 to rephrase statements in several places of the manuscript,
 to modify the list of references,
 as well as
 to remove typos.
 I think, the authors have provided satisfactory answers to all referee's comments
 and the revised version of the paper may be published in Nature Communications.
 However, there are still some small mistakes
 (e.g.,
 p.6/21: Supplementary Information Sec. II -> Supplementary Information Sec. III;
 p.8/21: finite temperature lanczos -> finite temperature Lanczos;
 p.11/21: luttinger liquid -> Luttinger liquid;
 p.13/21: references 19 and 21, the list of authors must be checked;
 p.19/21: Supplementary Information Sec. II -> Supplementary Information Sec. III;
 p.2/5, Fig.S1: figure capture looks unfinished
 etc.).
 Reviewer #2 (Remarks to the Author):
 I would like to thank the authors for their careful and detailed responses to my questions. They have
 answered all the points that I raised, and I am happy to recommend this manuscript for publication in
 Nature Communications.
 There is just one point that I would like the authors to check before the paper is finally accepted. The
 authors note that their model [Fig. 5c] appears inconsistent with their neutron-scattering data,
 because the model shows a main peak at Q = 1.3 A^-1 whereas the data show the main peak at Q =
 0.8 A^-1. I would like the authors to double-check that the x-axis units of Fig. 5c are correct: are they
 definitely Q (A^-1) and not the reciprocal-lattice units (dimensionless) favoured by theorists? A
 confusion between these units would cause the x-axis of the calculation to be stretched by a factor
 a/(2*pi) = 1.6, which would exactly explain the apparent discrepancy with the experimental data.
 (I apologise if the authors already checked this!)

 Reviewer #3 (Remarks to the Author):
 I found the comments of Referee 2 to be very important and completely agree with him/her. I do not
 think the authors have adequately addressed the questions raised, especially about having 2% free-
 spins but yet having the Cu layers structurally perfect. I think 2% impurity spins can screw up
 everything. This is also my concern 1 in my previous report.
 For the issue in MuSR experiment, I do not think the authors have understood it completely. Why the
 initial total asymmetry is smaller measured in DR. They claim that the reason is that they used a
 smaller pellet in DR. This is totally wrong! The initial asymmetry does not depend on the size of
 sample. If the sample is smaller, then the signal from the background will be larger, so that the
 dashed line in Figure S3 would be higher. The total asymmetry should not be changed.
 For the specific heat measurements, now in Figure 2 (c), the lattice contribution is much smaller than
 the measured one even at high temperatures. Previously, they have a <i>T</I> linear term in the
 lattice contribution. I do not think the <i>T</I> linear can be simply deleted. One needs to know
 where it is from and understand it. In addition, the entropy calculated is much smaller than R ln2, it
 seems that the authors do not understand it as well.