Absence of Spin Frustration in the Kagomé Layers of Cu²⁺ Ions in Volborthite Cu₃V₂O₇(OH)₂·2H₂O and Observation of the Suppression and Re-Entrance of Specific Heat Anomalies in Volborthite under an External Magnetic Field

Round 1

Reviewer 1 Report

The paper addresses an important issue, i.e., the character of magnetism in Volborthite Cu3V2O7(OH)22H2O, whose  kagomé lattice had led to believe that this was an example of magnetically frustrated system.

By means of a joint theoretical and experimental effort, the authors demonstrate that such picture was wrong, and that the behavior of the compound is actually well described by a very different model, based on weakly interacting antiferromagnetic chains of composite the S=1/2 spins.

This research has been carried out carefully and the work is sound, interesting and really well written, I recommend publication in its present form.

Author Response

We thnk Reviewer 1 for the positive comment. No further revison necessary.

Reviewer 2 Report

The authors studied the volborthite Cu3V2O7(OH)2.2H2O and its deuterated analog Cu3V2O7(OD)2.2D2O by magnetic susceptibilities and specific heats measurements in zero magnetic fields and also in the magnetic field range 0-9T. They developed a very weakly interacting (hardly spin-frustrated) antiferromagnetic uniform chains model made up of effective S=1/2 pseudospin units. This model can explain their data well. In addition, the authors also discovered a second specific heat anomaly in a magnetic field above 5.5T, ascribed this to a new magnetic ordering, and proposed a theory to understand the origin of these anomalies.

This manuscript is clear and relevant for the field of spin-frustrated systems. Their data and theory are presented in a well-structured manner. Their results are important and provide new knowledge to the field. The paper should be published in Condensed Matter. There are, however, several points that I believe need to be addressed before the work should be published.

1. Line71-85

When discussing the crystal structure of volborthite, it would be better to reference Fig.1 to help readers to understand the crystal structure and the magnetic structure.

2. Line123-124:

It is not clear to me which phase has U_eff=4eV or U_eff=5eV. Do volborthite and their deuterated analog have the same U_eff? 

3. Line193:

The larger U_eff, then the smaller J_AF. It is not clear to me how the authors choose the U_eff values in the calculations, 4-5eV vs 8-10eV?  How to determine the U_eff values?

4. Line 224:

What is the function form of  \Chi_spin(J_C, g, T)? The authors showed a fit but did not tell the readers what the fitting function looks like.

5. Line320:

To probe the cause for --> To understand the origin of

6. Line 325:

missing comma.

respectively--> respectively.

7. Line332:

which is due most likely to the magnetic ordering of each kagomé layer

-->which is most likely due to the magnetic ordering of each kagomé layer

8. Line359:

What does 'topological constraint' mean? This term is ambiguous. Is it a geometry constraint? What does 'topological' mean? It lacks a definition here.

9. Line 489

remove 'do'

10. Line 495.

I wouldn't recommend the authors to say that the single broad heat capacity anomaly disappears under a magnetic field higher than ~13 T. Such data is not available. The assumption of a symmetric shape is not justified.

Author Response

Details of revision and replies

[1] Changes related to Reviewer 2

Comment 1:

Reply 1:

             In line 73 we added a reference to Fig. 1 .

Comment 2:

Reply 2:

               In our DFT+U calculations for the P21/c phase, we employed both U_eff = 4 eV and U_eff = 5 eV. This was done to make sure that the trends in the calculated spin exchanges J₁ – J₄ do not depend on the value of U_eff. U_eff is related to correlation effects of the 3d⁹ orbitals of Cu²⁺ cation and as such is independent of the choice of anions. However, DFT calculations were only done for the protonated sample.

Comment 3:

Reply 3:

               Our DFT+U calculations employ the energy-mapping analysis, which maps the relative energies of the electronic Hamiltonian onto those of the spin Hamiltonian. The U_eff values of our calculations are chosen to make sure that the electronic structure under consideration is magnetic insulating.

               In Janson et al.’s DFT+U calculations, the U_eff value is chosen to simulate the band dispersion relations. It appears that their approach requires large U_eff values than our mapping analysis does.

Comment 4:

Reply 4:

            Chi_spin(J_C, g, T) cannot be given as an analytical function but rather as a Padé approximant with coefficient given in detail in Ref. [2], Johnston et al.            

            Three lines below equation (2) (line 228) we refer explicitly to Ref. [20].

Comment 5:

Reply 5:

               Use of this wording is a matter of taste. We decided to keep it as is.

Comment 6:

Reply 6:

             The comma has been added.

Comment 7:

Reply 7:

               Use of this wording is a matter of taste. We decided to keep it as is.

Comment 8:

Reply 8:

               The meaning of the wording “topological” was clearly stated immediately below the caption of  Figure 4.

Comment 9:

Reply 9:

               “do” was removed.

Comment 10:

Reply 10:

               The specific heat anomaly above ~5.5 T arises from a magnetic ordering, so it will disappear under high enough external magnetic field. Then, it is of interest to speculate under what field the anomaly vanishes. The energy absorption by volborthite arises from the entropy spectra of Group II and III, so it would be continuous because the binomial distribution is symmetric. Thus, the broad absorption ridge above ~5.5 T is symmetric in shape. Our prediction is based on the condition that the broad absorption ridge is symmetric in shape. In the absence of experimental

               observation, it is important to provide a verifiable prediction.  

[2] Other changes

1. In Introduction

1. Thus, results of Janson et al.’s exact diagonalization based on their trigonal spin lattice model are inappropriate for understanding the physics of volborthite below ~17 K. The

2. In Concluding remarks:

1. “Conversely,” to “However, our work showed that”
2. The last sentence was modified.

3. In References

1. Reference 33 was added.
2. Some typos were corrected for.