  We theoretically investigated Anomalous Hall Effect (AHE) and Spin Hall
Effect (SHE) transversally to the insulating spacer O, in magnetic tunnel
junctions of the form F/O/F where F are ferromagnetic layers and O represents a
tunnel barrier. We considered the case of purely ballistic (quantum mechanical)
transport, taking into account the assymetric scattering due to spin-orbit
interaction in the tunnel barrier. AHE and SHE in the considered case have a
surface nature due to proximity effect. Their amplitude is in first order of
the scattering potential. This contrasts with ferromagnetic metals wherein
these effect are in second (side-jump scattering) and third (skew scattering)
order on these potentials. The value of AHE voltage in insulating spacer may be
much larger than in metallic ferromagnetic electrodes. For the antiparallel
orientation of the magnetizations in the two F-electrodes, a spontaneous Hall
voltage exists even at zero applied voltage. Therefore an insulating spacer
sandwiched between two ferromagnetic layers can be considered as exhibiting a
spontaneous ferroelectricity.
