External electric field driven modification of the anomalous and spin Hall conductivities in Fe thin films on MgO(001)

Abstract

The effects of applying external electric fields to the anomalous and spin Hall conductivities in Fe thin-film models with different layer thicknesses on MgO(001) are investigated by using first-principles calculations. We observe that, for the considered systems, the application of positive electric field associated with the accumulation of negative charges on the Fe side generally decreases (increases) the anomalous (spin) Hall conductivities. The mapping of the Hall conductivities within the two-dimensional Brillouin zone shows that the electric-field-induced modifications are related to the modification of the band structures of the atoms at the interface with the MgO substrate. In particular, the external electric field affects the Hall conductivities via the modifications of the ${d}_{xz},{d}_{yz}$ orbitals, in which the application of positive electric field pushes the minority-spin states of the ${d}_{xz},{d}_{yz}$ bands closer to the Fermi level. Better agreement with the anomalous Hall conductivity for bulk Fe and a more realistic scenario for the electric field modification of Hall conductivities are obtained by using the thicker layers of Fe on MgO (${\mathrm{Fe}}_{3}$/MgO and ${\mathrm{Fe}}_{5}$/MgO).