Ab Initio Theory of the Scattering-Independent Anomalous Hall Effect

We report on first-principles calculations of the side-jump contribution to the anomalous Hall conductivity (AHC) directly from the electronic structure of a perfect crystal. We implemented our approach for a short-range scattering disorder model within the density functional theory and computed the full scattering-independent AHC in elemental bcc Fe, hcp Co, fcc Ni, and $L{1}_0$ FePd and FePt alloys. The full AHC thus calculated agrees systematically with experiment to a degree unattainable so far, correctly capturing the previously missing elements of side-jump contributions, hence paving the way to a truly predictive theory of the anomalous Hall effect and turning it from a characterization tool to a probing tool of multiband complex electronic band structures.

Figure 1

The dependence of the intrinsic and side-jump (inset) conductivities on the strength of the Coulomb repulsion $U$ of valence $d$ electrons in fcc Ni for different directions of the magnetization in the crystal.

Figure 2

Angle-resolved conductivity $d\sigma /d\Omega$ in units of $\mathrm{S}/\mathrm{cm}$ as a function of direction in the BZ. $d\sigma /d\Omega$ corresponds to all contributions to $\sigma$ from inside the inner sphere in the BZ within the solid angle element $d\Omega$. (a) ${\sigma }^{\mathrm{int}}$ for Ni [001], (b) ${\sigma }^{\mathrm{sj}}$ for Ni [001], (c) ${\sigma }^{\mathrm{sj}}$ for Ni [110], (d) ${\sigma }^{\mathrm{sj}}$ for Fe [001].