Orientation Dependence of the Intrinsic Anomalous Hall Effect in hcp Cobalt

We carry out first-principles calculations of the dependence of the intrinsic anomalous Hall conductivity of hcp Co on the magnetization direction. The Hall conductivity decreases smoothly from 481 S/cm to 116 S/cm as the magnetization is tilted from the c-axis to the ab-plane. This factor-of-four reduction compares well with measurements on single crystals, while the angular average of 226 S/cm is in excellent agreement with the value of 205 S/cm measured in polycrystalline films. The strong anisotropy of the anomalous Hall conductivity is a consequence of spin-orbit induced changes in the electron states near the Fermi level as the magnetization is rotated.