The anomalous Hall heat current and Nernst effect in the ferromagnetic spinel $\rm CuCr_2Se_{4-x}Br_x$

In a ferromagnet, the anomalous Hall current has been demonstrated to be independent of the electron lifetime $\tau$ [1], which provides a strong support for Karplus and Luttinger's anomalous-velocity theory based on the intrinsic spin-orbit interaction. Inspired by the fact that a heat flow accompanies a charge current, we studied the anomalous Nernst effect (ANE) in the ferromagnetic spinel $\rm CuCr_2Se_{4-x}Br_x$ with x ranging from 0 to 1.0. Combining with other transport parameters measured on the same sample, at low temperatures, we uncovered a simple relation for the off-diagonal Peltier conductivity tensor $\rm \alpha_{xy}$, which is a quantity directly relating to the anomalous Hall heat current. We found that $\rm \alpha_{xy}=C {\it N}_F T$ [2], where C is a constant independent of $\tau$, ${\it N}_F$ is the D.O.S. at the Fermi energy, and T is the temperature. This simple relation turns out to be consistent with the prediction based on the anomalous-velocity theory. Therefore, our observation provides another strong support for the anomalous-velocity theory in a ferromagnet. The AHE and ANE can then be understood in a unified picture. * Supported by funds from the U.S. National Science Foundation under grant DMR 0213706. [1]Lee, {\it et al}., Science 303, 1647 (2004). [2]Lee, {\it et al}., PRL 93, 226601 (2004).