Lorenz number determination of the dissipationless nature of the anomalous hall effect in itinerant ferromagnets

We have measured the thermal Hall conductivity for ferromagnetic Ni and Ni0.97Cu0.03. In the low temprature region (less than or similar to 100 K), we show for the first time that the Wiedemann-Franz law is satisfied even for the anomalous Hall current. While the Hall Lorenz number for the normal part decreases rapidly with temperature, that for the anomalous part shows much less deviation from the free-electron Lorenz number. This evidences the dissipationless nature of the anomalous Hall effect.