Linear magnetization dependence and large intrinsic anomalous Hall effect in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Fe</mml:mi><mml:mn>78</mml:mn></mml:msub><mml:msub><mml:mi>Si</mml:mi><mml:mn>9</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">B</mml:mi><mml:mn>13</mml:mn></mml:msub></mml:mrow></mml:math> metallic glasses

The origin of the anomalous Hall effect (AHE) in ferromagnetic metallic glasses (MGs) is far from well understood due to the disordered atomic structure. Here, we report that the AHE is found in ${\mathrm{Fe}}_{78}{\mathrm{Si}}_{9}{\mathrm{B}}_{13}$ MGs, and the anomalous Hall conductivity $({\ensuremath{\sigma}}_{\mathrm{AH}})$ has a linear dependence with magnetization $({M}_{z})$, which is a feature of intrinsic mechanism contribution rather than extrinsic mechanism contribution. Moreover, the ${\ensuremath{\sigma}}_{\mathrm{AH}}$ normalized by ${M}_{z}$ is independent of longitudinal conductivity (${\ensuremath{\sigma}}_{xx}$), which also indicates the characteristic of the nondissipative intrinsic mechanism. This intrinsic contribution could be understood from the density of Berry curvature integrated over occupied energies proposed recently for aperiodic materials, and the linear magnetization dependence can be understood from the fluctuations of spin orientation at the finite temperature. In such case, Berry curvature is proportional to spin magnetization in different orientations. Our results indicate experimental signatures to distinguish the intrinsic mechanism in ferromagnetic MGs and confirm that the intrinsic ${\ensuremath{\sigma}}_{\mathrm{AH}}$ has a large value $(505--616\phantom{\rule{0.16em}{0ex}}{\mathrm{Scm}}^{\ensuremath{-}1})$ in the ${\mathrm{Fe}}_{78}{\mathrm{Si}}_{9}{\mathrm{B}}_{13}$ MGs.