Reply to the ‘Comment on “Magnetostructural correlations in isolated trinuclear iron(III) oxo acetate complexes”’ by M. Antkowiak, G. Kamieniarz and W. Florek, Phys. Chem. Chem. Phys., 2018, 20, DOI: 10.1039/C8CP04691C

The comments by Antkowiak et al.¹ on our own recent contribution² are well received. We appreciate them pointing out their own work^3,4 on spin frustration in odd-numbered ring arrangements as derived as an application of the Lieb–Mattis formalism^5,6 which in turn is based on the ubiquitous Heisenberg Hamiltonian. In our own modelling we have relied on a more recently outlined scheme⁷ that was prepared to understand a particular case of spin frustration. It is beneficial to see that our current understanding is well embedded into a larger framework.

A particular question addressed by Antkowiak et al. in the first part of the comment is whether spin magnetic interactions can induce a geometrical distortion in the present case. They assume that this cannot be the case in the absence of spin–orbit interaction. They have seemingly overlooked that in the hypothetical equilateral case of J₁₂ = J₁₃ = J₂₃, the S = 1/2 ground state is spatially degenerate and that therefore a magnetic Jahn–Teller distortion has to be expected. This distortion is probably somewhat overestimated when performing a geometry optimization on a UDD broken symmetry configuration. Nevertheless, our hypothesis holds as it stands: spin frustration leads to distortion. In the present case, this is connected with spatial degeneracy.

In the second part of the comment Antkowiak et al. point out that ground states of different spin will result, based on the difference in the magnetic coupling constants that we have reported. This finding is reported in the last two columns of Table 3 of our paper. It is noteworthy that for n = 0 and n = 3, where the ground state has spin S = 1/2, the second lowest state is also an S = 1/2 state which lies 4 (J–J*) above, and these two would become degenerate if all three coupling constants were equal (J = J*). This splitting demonstrates the energy gain by the magnetic Jahn–Teller distortion.

At this instance we are able to announce further experimental work, that shall be published in the near future: through the application of gas phase X-ray induced magnetic circular dichroism (XMCD)^8,9 measurements on isolated [Fe₃O(OAc)₆(Py)_n]⁺ we have determined spin- and orbital moments for the cases n = 0–3. The experimental spin moments are in good agreement with our predictions² and with those of Antkowiak et al.¹

Conflicts of interest

There are no conflicts to declare.

References

1. M. Antkowiak, G. Kamieniarz and W. Florek, Comment on “Magnetostructural correlations in isolated trinuclear iron(III) oxo acetate complexes” by J. Lang et al, Phys. Chem. Chem. Phys., 2018 10.1039/C8CP04691C.
2. J. Lang, et al., Magnetostructural correlation in isolated trinuclear iron(III) oxo acetate complexes, Phys. Chem. Chem. Phys., 2018, 20(24), 16673–16685.
3. G. Kamieniarz, W. Florek and M. Antkowiak, Universal sequence of ground states validating the classification of frustration in antiferromagnetic rings with a single bond defect, Phys. Rev. B: Condens. Matter Mater. Phys., 2015, 92(14), 140411.
4. W. Florek, M. Antkowiak and G. Kamieniarz, Sequences of ground states and classification of frustration in odd-numbered antiferromagnetic rings, Phys. Rev. B, 2016, 94(22), 224421.
5. E. Lieb and D. Mattis, Ordering energy levels of interacting spin systems, J. Math. Phys., 1962, 3(4), 749.
6. E. Lieb and D. Mattis, Theory of ferromagnetism and ordering of electronic energy levels, Phys. Rev., 1962, 125(1), 164.
7. D. N. Hendrickson, Spin Frustration in Polynuclear Complexes, in Research Frontiers, in Magnetochemistry, ed. C. J. O’Connor, World Scientific Co. Pte. Ltd, Singapore, 1993, pp. 87–108.
8. S. Peredkov, et al., Spin and Orbital Magnetic Moments of Free Nanoparticles, Phys. Rev. Lett., 2011, 107(23), 233401.
9. J. Meyer, et al., The spin and orbital contributions to the total magnetic moments of free Fe, Co, and Ni clusters, J. Chem. Phys., 2015, 143(10), 104302.

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Footnote

† Present address: Universität Stuttgart, Institut für Organische Chemie, 70569 Stuttgart, Germany.

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