Measurements of the Hall conductivity in MnSi can provide incisive tests of theories of the anomalous Hall (AH) effect, because both the mean free path and magnetoresistance (MR) are unusually large for a ferromagnet. The large MR provides an accurate way to separate the AH conductivity ${\sigma }_{xy}^A$ from the ordinary Hall conductivity ${\sigma }_{xy}^N$. Below the Curie temperature $T_C$, ${\sigma }_{xy}^A$ is linearly proportional to $M$ (magnetization) with a proportionality constant $S_H$ that is independent of both $T$ and $H$. In particular, $S_H$ remains a constant while ${\sigma }_{xy}^N$ changes by a factor of 100 between $5\mathrm{K}$ and $T_C$. We discuss implications of the hidden constancy in $S_H$.

• Received 27 October 2006

DOI:https://doi.org/10.1103/PhysRevB.75.172403