Berry phase effect in anomalous thermoelectric transport

Abstract

We develop a theory of 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 CuCr$_2$Se$_{4-x}$Br$_x$, obtaining quantitative agreement with a recent experiment.