Non-collinear magnetic structures in the magnetoelectric Swedenborgite CaBaFe4O7 derived by powder and single-crystal neutron diffraction

We would like to thank the referees again for the close inspection of the manuscript.
We have incorporated the requested changes into the resubmitted version and we have created a DOI for the neutron data on an external server. We have furthermore added the DOIs for the references, where possible.

REFEREE 1:

1- Reconsider the statement "One can immediately realize ..." on lines 174-177 at the beginning of section 3.1.3.
We have reformulated this sentence which now better explains how to read the basis vectors in Table 2.

2- Reconsider the caption of Fig. 5.
It is now mentioned that the values are the ones derived from the single-crystal experiments.

3a- Reconsider the first sentence of second paragraph of the Conclusion on lines 332-335.
We prefer to leave the mentioned sentence as it is in order to avoid more speculations. The question of the in-plane component arises even between TN1 and TN2, i.e. not only for the complex low-temperature phase, and with the data at hand we cannot address this issue adequately.

3b- Consider making the data for χ in Fig. 3(a) available.
We can make the data available upon request.

4- Inconsistent grammar in the second line of the caption of Table 1 ("Wyckhoff siteS ... IS").
This has been corrected.

5- Second line of caption of Table 3: remove full stop after "component".
This has been corrected.

6- Line 193: remove full stop in "Figure. 4".
This has been corrected.

7- Second line of caption of Table 5: "analog" is fine in American English, but if the authors meant to write British English (see, e.g., "neighbours" on line 42), they should use "analogous".
This has been corrected.

8- Lines 284/285: "almost insignificant" sounds a bit strange (I think "insignificant" or "almost zero" would work).
This has been corrected.

9- Refs. [22-24] should be cited between Ref. [16] and Ref. [17].
This has been corrected.

10- Double check casing in the references ("Mineral" [8], "K" [15], "Heisenberg" [17], ...).
This has been corrected.

REFEREE 2:

1. Introduction: I did not understand why only minor magnetocrystalline anisotropy is expected for Fe2+ in the tetrahedral coordination. Orbital moment of Fe2+ is not quenched, so the anisotropy is likely. Moreover, the authors themselves resort to the single-ion anisotropy in the Conclusions when they discuss the magnetic structure between TN1 and TN2. This inconsistency may confuse readers and should be avoided.

We agree with the referee that this inconsistency may confuse readers and have therefore reformulated the paragraph in the introduction.

2. Fig. 8b: I could not see the "opposite triangular chirality between two T1 triangles separated by z~0.5", or perhaps I do not quite understand what the authors mean by the "triangular chirality" (is it scalar chirality? or vector chirality?). In my view, the spins rotate counter-clockwise when going around the triangle in the clockwise direction, and this kind of chirality is the same for all the T1 triangles shown in this figure. A clarification along these lines would be helpful.

Note that the part before the quoted passage says: "..., because a spin configuration which yields a 120$^\circ$ alignment on all triangles - which does not explain the experimental data - requires an opposite...", i.e. we refer to a different magnetic structure which is not in agreement with the data. The depicted magnetic structure reveals - as the referee correctly points out - a unique triangular chirality for the T1 triangles.