Strain-controlled anomalous hall conductivity of 3d transition metals

The Anomalous Hall Effect (AHE) is a phenomenon that consists of the emergence of an anomalous transverse velocity when an electric current is passed through a ferromagnetic material. Here, we studied the dependence of strain and local magnetization on the intrinsic anomalous Hall conductivity (AHC) in 3d transition metals Fe-bcc, Co-fcc, Co-hcp, and FeCo. For the Fe-bcc case, the AHC shows a slight decrease in the compressive strain, this being associated with the magnetization dependence with the lattice constant. For tensile strain, AHC decreases fast, at approximately 70%, even when the local magnetic moment has increased slightly. This decrease seems to be related to the changes of the electronic band structure and Berry curvature above the equilibrium lattice constant. With the increase of positive deformation (traction), the AHC in Co-hcp and Co-fcc decrease down to a strain of 5%, while for negative deformation (compression) AHC increases, also associated with magnetization dependence with lattice constant, but not on all the strain range. Finally, the AHC in FeCo material behaves as a contribution from both precursors. Our analysis shows that the intrinsic AHC is complexly dependent on the band structure and Berry curvature changes to the strain and total magnetization. It is expected that this fundamental study will help to exploit strain engineering strategies on a future generation of sensor spintronic devices based on 3d transition metals.