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.

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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.