Thermoelectric transport properties in magnetically ordered crystals

What is it about?

Transport properties of a crystal 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 crystal. The Peltier and Seebeck effects describe the interaction between thermal and electric transport properties. If a magnetic field is applied to the crystal, further effects appear, named after Hall, Righi-Leduc, Nernst and Ettingshausen. These effects exist in all crystals, 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 space-time point groups. The paper gives for all the properties mentioned above the form of the corresponding tensors for all 122 space-time point groups up to second order in the applied magnetic field.

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Why is it important?

The results are presented in Nye notation, which immediately shows how many tensor components are independent, which ones are zero and how the non-zero components are related. In the literature the "magnetic tensor" is traditionally added to the tensor describing the corresponding effect occurring in all space-time point groups. It is shown that, experimentally, the two parts can be determined separately. It follows that information about the form of the tensors is lost if only the sum is considered instead of the two parts. Numerical values given in the literature that illustrate our general results are shown and errors concerning our general results are corrected.