Anomalous Hall effect in frustrated magnetics

A comparative analysis of Hall effect in substitutional solid solutions Ho$_{0.5}$Lu$_{0.5}$B$_{12}$, Mn$_{1-x}$Fe$_{x}$Si (0 $\le x\le$ 1) и Eu$_{1-x}$Gd$_{x}$B$_{6}$ ($x<$ 0.04) is carried out at temperatures 2–300 K in magnetic fields up to 8 T. Anomalous Hall effect $\rho_{xy}^{A}\sim\rho_{xx}M$ is identified for the systems with different kinds of magnetic frustration. Linear scaling $\rho_{xy}^{A}\sim\rho_{xx}$, which is detected at resistivity $\rho_{xx}\sim$ 0.01–1 m$\Omega$ cm out from the region of applicability of classical skew-scattering model, is associated with the increase of spin fluctuations amplitude in paramagnetic phases of the investigated compounds with noncollinear magnetic structure. Topological contribution to Hall effect is extracted for Ho$_{0.5}$Lu$_{0.5}$B$_{12}$ и Eu$_{1-x}$Gd$_{x}$B$_{6}$, its amplitude varying from 80 n$\Omega$ cm (для Ho$_{0.5}$Lu$_{0.5}$B$_{12}$) up to 7.5 $\mu\Omega$ cm (for Eu$_{0.97}$Gd$_{0.03}$B$_{6}$).