Dissipationless Anomalous Hall Current in the Ferromagnetic Spinel CuCr${}_2$Se${}_{4-x}$Br${}_x$

Abstract

In a ferromagnet, an applied electric field $\mathbf{E}$ invariably produces an anomalous Hall current ${\mathbf{J}}_H$ that flows perpendicular to the plane defined by $\mathbf{E}$ and $\mathbf{M}$ (the magnetization). For decades, the question whether ${\mathbf{J}}_H$ is dissipationless (independent of the scattering rate), has been keenly debated without experimental resolution. In the ferromagnetic spinel CuCr${}_2$Se${}_{4-x}$Br${}_x$, the resistivity $\rho$ (at low temperature) may be increased 1000 fold by varying $x$(Br), without degrading the $\mathbf{M}$. We show that ${\mathbf{J}}_H/E$ (normalized per carrier, at 5 K) remains unchanged throughout. In addition to resolving the controversy experimentally, our finding has strong bearing on the generation and study of spin-Hall currents in bulk samples.

7 pages, 6 figures