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

Reviewers' comments: 
Reviewer #1 (Remarks to the Author): 

In this paper, the authors report about the first compound, KCu6AlBiO4(SO4)5Cl, which is of 
relevance to the square-kagome-lattice quantum Heisenberg antiferromagnet. They synthesized 
KCu6AlBiO4(SO4)5Cl, determined its crystal structure, and then report a set of experimental results 
supported by theoretical calculations to check whether a gapless quantum spin liquid state is realized 
in this compound as T → 0. More specifically, they measured the zero-field magnetic susceptibility χ(T), 
the magnetization curve M(H), the zero-field specific heat C(T), and performed the muon spin 
relaxation and inelastic neutron scattering measurements to provide evidence for a gapless quantum 
spin liquid state at T = 0 in this material. From theoretical side, the authors estimated the exchange 
couplings for the square-kagome-lattice quantum Heisenberg antiferromagnet, J1 = 135 K, J2 = 162 K, 
and J3 = 115 K, and the g-factor, g = 2.11, which can reproduce the experimental data for magnetic 
susceptibility and magnetization curve, although fail to explain the inelastic neutron scattering 
experiment. 

In my opinion, this is an interesting paper which deserves to be published in Nature Communications. 
Search for solid-state realizations of a quantum spin liquid state is rather hot 
topic nowadays and the communication about a real-life square-kagome-lattice S = 1/2 Heisenberg 
antiferromagnet sounds very exciting. The reported results are novel and, in my opinion, 
they may influence thinking in quantum magnetism community and inspire new theoretical and 
experimental studies. 

However, I have to advise the authors to consider the following points. 

• First of all, they must mention somehow that theoreticians studied this model at least since 2002, 
i.e., before the paper by I. Rousochatzakis et al. (2013) [19]. I mean the following important papers: 
R. Siddharthan and A. Georges, Square kagome quantum antiferromagnet and the eight-vertex model, 
Phys. Rev. B 65, 014417 (2002) and J. Richter, J. Schulenburg, P. Tomczak, and D. Schmalfuß, The 
Heisenberg antiferromagnet on the square-kagome lattice, Condensed Matter Physics 12, 507 (2009); 
unfortunately, both papers are missed. By the way, in the latter paper one can find the ground-state 
magnetization curve as it follows from ED (N = 24...54) for the J1 = J2 = J3 case (Fig. 5), which looks 
similar to what is shown in Fig. 5(b) for slightly different values of J1, J2, and J3 (J2 = 1.2J1, J3 = 
0.85J1). Furthermore, the case J2 ≠ J3 was studied in Phys. Rev. B 88, 094426 (2013). The high-field 
regime is related to the localized-magnon physics. 

• I noticed some small things which have to be checked. 

Page 6/19, I guess, “As shown in Fig. 3(g), the increase of” has to be replaced by “As shown in Fig. 
3(f), the increase of” and “as shown in Fig. 3(h). In” by “as shown in Fig. 3(g). In”. 

Page 7/19, The authors say: “As shown in Fig. 4(a), streak-like excitation at at Q = 0.8 ̊A^{−1} ... at 
5 K.” However, in the figure caption they say: “INS spectra at 4 K”. Moreover, I cannot see the streak-
like excitation at Q = 0.8 ̊A^{−1} in Fig. 4(a). 

Page 13/19, reference 33, the title is missed. 

Page 18/19, figure 4(e), I guess, the label for the x axis should be “E (meV)” instead of “Intensity 
(a.u.)”. 


Reviewer #2 (Remarks to the Author): 

This manuscript presents an experimental study of a newly-synthesised quantum spin liquid candidate 
based on the mineral atlasovite, in which magnetic Cu2+ ions occupy a potentially frustrated lattice 
known as square-kagome. The authors show - via a combination of bulk magnetic, muon-spin 
relaxation, and inelastic neutron measurements - that this material has net antiferromagnetic 
interactions and does not exhibit long-range magnetic ordering down to ~60 mK. They also claim that 
the magnetic excitation spectrum indicates gapless, spinon-like, excitations. 

I think this manuscript describes a significant experimental advance in the field of frustrated 
magnetism. To the best of my knowledge, there are no other experimental realisations of candidate 
QSLs on this magnetic lattice, although it has been studied theoretically. The manuscript presents a 
comprehensive experimental study using a range of experimental techniques. The paper also contains 
quantum-theoretical modelling, although the link between theory and experiment is somewhat 
incomplete. Overall, the paper is clearly written and I think can be suitable for Nature Communications. 

However, there are several important aspects of the manuscript that, in my opinion, would require 
improvement before the paper can be accepted for publication. I summarise these below: 

(1) The authors make several comments about the absence of structural disorder in this material. 
However, this assertion is only supported by a qualitative chemical argument: " Furthermore, the 
Cu2+ ions and nonmagnetic ions have different valence numbers [...] avoiding site mixing..", and 
seems potentially inconsistent with their susceptibility measurements that show "impurity" or 
"paramagnetic" spins. In my view, more analysis is required to quantify the amount of structural 
disorder in this material, especially since it has not been reported before. First, the authors should 
attempt to refine site-disordered models against their synchrotron X-ray data. Second, the authors 
should give the values of the atomic displacement parameters obtained from their Rietveld refinement. 
These can often indicate the presence of positional disorder, if they are unusually large. 

(2) As part of their basic characterisation, I think the authors should present magnetic susceptibility 
data collected under both field-cooled and zero-field cooled protocols. Any difference between these 
two measurements would normally be indicative of (partial) spin freezing. It is important to rule this 
out in a QSL candidate, and I think that using several complementary techniques here would make the 
manuscript more convincing. 

(3) The authors state: "These INS data are consistent with a gapless continuum of spinon excitations." 
(p.7) 
However, a neutron experiment can only place an upper bound on the size of any gap, because of the 
finite energy resolution of the instrument. To provide quantitative information, the authors should 
quantify the maximum gap consistent with their measurements, e.g. by performing fits to an 
appropriate function (e.g. damped harmonic oscillator) including the effects of instrumental resolution. 

(4) In the INS data shown in Fig. 4, I found it surprising that the phonon modes at high Q seem to 
occur at the same energies as the magnetic modes at low Q. Can the authors comment on this? For 
example, is it possible that the magnetic excitations are strongly coupled to the lattice? Could the 
authors perform DFT calculations of the phonon scattering, to determine more accurately the 
components of the scattering that are purely magnetic? 

(5) The authors state "We succeeded in reproducing the magnetic susceptibility and magnetization 
curve with the J1-J2-J3 SKL model with J1 =135K, J2 =162K, J3 =115K and g=2.11..." 
The agreement of this interaction model with the bulk susceptibility data is indeed convincing. 
However, the authors do not give uncertainties on these exchange interactions, or discuss the 
procedure they used to estimate them. I am also surprised that bulk measurements contain enough 
information to determine three exchange parameters accurately. I think the authors should perform 
further calculations to identify the region(s) of parameter space consistent with their experimental 
data, and hence provide meaningful confidence intervals on the parameter values they report. 

(6) The authors show the calculated Q-dependence of the magnetic scattering intensity from their 
model in Fig. 5c, and claim it is inconsistent with their experimental data. However, it hard to tell the 
extent of this disagreement, because the calculation is of single-crystal scattering whereas the data 
are powder averaged. I think it would be more informative to powder-average the calculation and 
integrate it over 0.5 < E < 1.5 meV, so that it can be compared directly to the experimental data 
shown in Fig. 4g. 

(7) The first sentence of the concluding paragraph states: "We have synthesized a SKL spin-1/2 
antiferromagnet [... with] a negligibly weak interlayer coupling." (p.8) 
This is a strong statement and I am not convinced it is justified by the evidence shown here. The 
authors note that their model excluding inter-layer coupling does not account for the experimental INS 
data, which suggests that further interactions are actually important. The authors did not investigate 
the effect of including interlayer coupling in their model, so the claim that it is "negligible" seems 
unproven. I think further calculations are needed here. 

(8) The authors claim: "The INS spectrum exhibits a streak-like gapless excitation and flat 
dispersionless excitation, consistent with powder-averaged spinon excitations." (p.7) 
It is not clear to me how a flat dispersionless excitation is consistent with spinon excitations, which are 
actually strongly dispersive in 1D magnets (see e.g. Nature Physics 9, 435–441 (2013)). The authors 
should justify this claim with references and/or calculations. 

Some more minor points: 
(A) I think it should be clarified near the start of the manuscript that all experiments were performed 
on powder samples. (This is just to prevent possible confusion - I do not see it as a problem.) 

(B) "As the released magnetic entropy around T ∗ is only 8 % of the expected total entropy, this peak 
cannot be explained by local singlet-triplet excitations in the VBC state." (p.5) 
The authors should state, or reference, what entropy release would they expect for a singlet-triplet 
excitation - otherwise it is not clear why 8% is inconsistent with this scenario. 

(C) "The excitation persist up to at least T = 30 K (see Fig. S3), which confirms the low-dimensional 
nature of the magnetic scattering." (p.7) 
The persistence of structured magnetic excitations over a wide temperature range is actually seen in 
many frustrated magnets, including 3D examples such as antiferromagnetic pyrochlores. I therefore 
think this sentence should therefore be rephrased. 

(D) The manuscript contains several typos; a few examples are: 
p.2 "excitatios" --> "excitations" 
p.5 "the the" --> "the" 
p.5 "Currie-Wiess" --> Curie-Weiss 
This is not an exhaustive list, and the manuscript would require checking by authors and editors if it is 
accepted. 


Reviewer #3 (Remarks to the Author): 

The authors report the first experimental results of the quantum spin liquid (QSL) state on a square-
kagame lattice (SKL) quantum antiferromagnet 
KCu<sub>6</sub>AlBiO<sub>4</sub>(SO<sub>4</sub>)<sub>5</sub>Cl. The evidences from 
magnetic susceptibility, magnetization, heat capacity, muon spin relaxation, and inelastic neutron 
scattering are presented and reveal the formation of a gapless QSL at very low temperatures. As a 
new material, these results are very interesting. However, I have some comments: 

The authors claimed that the Cu<sub>2+</sub> ions and nonmagnetic ions have different valence 
numbers in this SKL, so that the site mixing can be avoided. It is better to show the experimental 
evidence that there is no disorder in this SKL, because this is very important for the study on spin 
liquid. Looking at the INS spectra, the not very clear continuum can also be induced by the effect of 
disorder. 

It is very strange that the ZF-uSR spectra measured at 5K using a DR is different than that in 
<sup>4</sup>He cryostat. I don’t think the authors have fully understand it. In addition, the author 
didn’t pay attention to the fact that the total initial Asy measured in DR is much smaller than that is 
measured in <sup>4</sup>He cryostat. Is it possible that the sample changed after being measured 
in one cryostat? These issues should be addressed. 

In Fig. 2 (c), the temperature dependence of the total specific heat measured at zero field is shown. 
However, the nonmagnetic contribution was assumed to include a <i>T</i> linear term, what is that 
contribution? No labels for the inset of Fig. 2 (c). 

To conclude, I think the material and the experimental results are interesting. However, with the those 
not clear issues I mentioned above, this manuscript does not qualify the standard of Nature 
Communications.