Linear Magnetization Dependence of the Intrinsic Anomalous Hall Effect

The anomalous Hall effect is investigated experimentally and theoretically for ferromagnetic thin films of Mn₅Ge₃. We have separated the intrinsic and extrinsic contributions to the experimental anomalous Hall effect and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long-wavelength fluctuations of the spin orientation at finite temperatures. The quantitative agreement between theory and experiment is remarkably good, not only near 0 K but also at finite temperatures, up to about ∼240  K (0.8T_C).