Anomalous-Hall heat current and Nernst effect in the ferromagnet CuCr₂Se_(4-x)Br_x

In a ferromagnet, an anomalous-Hall heat current, given by the off-diagonal Peltier term $\alpha_{xy}$, accompanies the anomalous Hall current. By combining Nernst, thermopower and Hall experiments, we have measured how $\alpha_{xy}$ varies with hole density and lifetime $\tau$ in $\rm CuCr_2Se_{4-x}Br_x$. At low temperatures $T$, we find that $\alpha_{xy}$ is independent of $\tau$, consistent with anomalous-velocity theories. Its magnitude is fixed by a microscopic geometric area ${\cal A}\sim 34 \mathrm{\AA}^2$. Our results are incompatible with some models of the Nernst effect in ferromagnets.