Spontaneous Anomalous and Spin Hall Effects Due to Spin-Orbit Scattering of Evanescent Wave Functions in Magnetic Tunnel Junctions

We theoretically investigated the anomalous Hall effect (AHE) and spin Hall effect (SHE) transversal to the insulating spacer I, in magnetic tunnel junctions of the form F/I/F where the F’s are ferromagnetic layers and I represents a tunnel barrier. We considered the case of purely ballistic (quantum mechanical) transport. These effects arise because of the asymmetric scattering of evanescent wave functions due to the spin-orbit interaction in the tunnel barrier. The AHE and SHE we investigated have a surface nature due to the proximity effect. Their amplitude is of first order in the scattering potential. This contrasts with ferromagnetic metals wherein these effects are of second (side-jump scattering) and third (skew scattering) order in these potentials. The value of the AHE current in the insulating spacer may be much larger than that in metallic ferromagnetic electrodes. For the antiparallel orientation of the magnetizations in the two F electrodes, a spontaneous Hall current exists even at zero applied voltage.

Figure 1

Schematic illustration of a MTJ. The F’s are the ferromagnetic layers, and I the insulating spacer. Arrows denote the direction of magnetizations in the electrodes, for parallel (P) and antiparallel (AP) orientations. The bottom curve schematically illustrates the dependence of density of states ($\nu$ is in arbitrary units) of spin up tunnelling electrons on the distance from the interface for P and AP orientations.

Figure 2

Schematic illustration of the AHE and SHE in a MTJ due to spin-orbit scattering on impurities. $\otimes$ and $\odot$ denote the direction of magnetizations and electron spins. The thickness of the lines are proportional to Hall currents for the given projection of spin.