Berry-Phase Effect in Anomalous Thermoelectric Transport

We develop a theory of the Berry-phase effect in anomalous transport in ferromagnets driven by statistical forces such as the gradient of temperature or chemical potential. Here a charge Hall current arises from the Berry-phase correction to the orbital magnetization rather than from the anomalous velocity, which does not exist in the absence of a mechanical force. A finite-temperature formula for the orbital magnetization is derived, which enables us to provide an explicit expression for the off-diagonal thermoelectric conductivity, to establish the Mott relation between the anomalous Nernst and Hall effects, and to reaffirm the Onsager relations between reciprocal thermoelectric conductivities. A first-principles evaluation of our expression is carried out for the material ${\mathrm{CuCr}}_2{\mathrm{Se}}_{4-x}{\mathrm{Br}}_x$, obtaining quantitative agreement with a recent experiment.

Figure 1

The wave packet description of a charge carrier whose center is $({\mathit{r}}_c,{\mathit{k}}_c)$. A wave packet generally possesses two kinds of motion: the center of mass motion and the self-rotation around its center. Both of them contribute to the local current density as given in Eq. (2).

Figure 2

The intrinsic anomalous Nernst conductivity ${\alpha }_{xy}$ (divide by the temperature $T$) of ${\mathrm{CuCr}}_2{\mathrm{Se}}_{4-x}{\mathrm{Br}}_x$ as a function of the Br content $x$. The calculated curve is compared with experimental results (●) extracted from Ref. 9.