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Thermoelectric transport properties in magnetically ordered crystals. Further corrigenda and addenda
aMultiscale Materials Experiments, Research with Neutrons and Muons, Paul Scherrer Institut, Forschungsstrasse 111, Villigen PSI, CH-5232, Switzerland
*Correspondence e-mail: hans.grimmer@psi.ch
Further corrigenda and addenda for the article by Grimmer [Acta Cryst. (2017), A73, 333–345] are reported. New figures in the supporting information show how the restrictions on the forms of galvanomagnetic and thermomagnetic tensors are related to those on corresponding thermoelectromagnetic tensors.
Keywords: thermoelectricity; transport properties; magnetic order; galvanomagnetic effects; thermomagnetic effects.
Thermoelectric transport properties in magnetically ordered materials.
What is it about?
Transport properties of a material like electric or heat conductivity are generally not the same in all directions. The direction dependence can be described by a tensor, the form of which depends on the point group of the material. The Peltier and Seebeck effects describe the interaction between thermal and electric transport properties. If a magnetic field is applied to the material, further effects appear, named after Hall, Righi-Leduc, Nernst and Ettingshausen. These effects exist in all materials, also in dia- and paramagnetic ones, where the spins are not ordered. Considering magnetically ordered materials one has to deal also with the spontaneous Hall, Righi-Leduc, Nernst and Ettingshausen effects (which occur if no magnetic field is applied) and how they change in a magnetic field. These effects are described by tensors invariant under space inversion but changing sign under time inversion, called "magnetic tensors", which do not vanish only for materials belonging to at most 69 of the 122 crystallographic space-time point groups. In case of polycrystalline materials, also the 16 cylindrical and the 5 spherical limit space-time point groups are of interest. Magnetic tensors do not vanish only for materials belonging to at most 10 of the 21 limit point groups. The paper gives for all the properties mentioned above the form of the corresponding tensors for all 122 crystallographic and all 21 limit space-time point groups up to second order in the applied magnetic field. For a cylindrical group the restrictions on the form of the tensors are the same as for the corresponding hexagonal group. For a spherical group, however, fourth rank tensors satisfy an additional restriction compared to the corresponding cubic group.
Why is it important?
The figures given in the supporting information present the results in Nye notation, which immediately shows how many tensor components are independent, which ones are zero and how the non-zero components are related. These figures not only correct errors in the figures contained in the original paper [Acta Cryst. (2017) A73, 333-345]; they extend the results to the limit point groups and, exchanging full and empty circles for certain tensor components, clearly show how the restrictions on the forms of galvanomagnetic and thermomagnetic tensors are related to the restrictions on the corresponding thermoelectromagnetic tensors.
Corrigenda. Corrections to Grimmer (2017![[Grimmer, H. (2017). Acta Cryst. A73, 333-345.]](../../../../../../logos/arrows/a_arr.gif "Grimmer, H. (2017). Acta Cryst. A73, 333-345.")
) are needed in Figs. 4(c) and 6(c) for the fourth-rank tensors containing components marked in blue and in Fig. 6(b) for in magnetic form class 4′. The corrections are included in the figures in the supporting information.
Addenda. For even tensors (invariant under space inversion and time inversion 1′), the galvanomagnetic tensors ρ and the thermomagnetic tensors k are symmetric in the first two indices if the rank is even and antisymmetric if the rank is odd, whereas the thermoelectromagnetic tensors Σ are general for all ranks. For magnetic tensors (invariant under
and changing sign under 1′), ρ and k are antisymmetric in the first two indices if the rank is even and symmetric if the rank is odd, whereas the tensors Σ are general for all ranks. The intrinsic symmetry of these tensors has been discussed in more detail by Gallego et al. (2019
).
Exchanging and
for certain components, new figures are obtained that clearly show how the forms of the tensors for ρ and k are related to those for Σ. The forms of the tensors for the limit point groups described in Grimmer (2019
) are included in the supporting information in Figs. 1–6.
Supporting information
The tensors describing the thermoelectric transport properties considered, a table of the 69 crystallographic and 10 limit space-time point groups for which magnetic tensors can exist, and corrected figures 1-6. DOI: https://doi.org/10.1107/S2053273320000881/ib5088sup1.pdf
References
Gallego, S. V., Etxebarria, J., Elcoro, L., Tasci, E. S. & Perez-Mato, J. M. (2019). Acta Cryst. A75, 438–447. Web of Science CrossRef IUCr Journals Google Scholar
Grimmer, H. (2017). Acta Cryst. A73, 333–345. Web of Science CrossRef IUCr Journals Google Scholar
Grimmer, H. (2019). Acta Cryst. A75, 409. CrossRef IUCr Journals Google Scholar
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