  Based on the exact muffin-tin orbitals (EMTOs), we developed a
first-principles method to calculate the current operators and investigated the
anomalous Hall effect in bcc Fe as an example, with which we successfully
separated the skew scattering contribution from the side jump and intrinsic
contributions by fitting the scaling law with the introduction of sparse
impurities. By investigating the temperature dependence of the anomalous Hall
effect in bulk Fe, we predicted a fluctuated anomalous Hall angle as a function
of temperature when considering only phonons, which, in the future, can be
measured in experiments by suppressing magnon excitation, e.g., by applying a
high external magnetic field.
