Theory of the spin polarization of field-emitted electrons from nickel

We calculate the spin polarization of field-emitted electrons from nickel in the framework of the Stoner-Wohlfarth-Slater theory of band magnetism. As was first proposed by Hertz and Aoi for the case of tunneling, we find that the $s-d$ hybridization plays an important role and we give a more quantitative treatment of this effect. The crystal wave functions are described as linear combinations of plane waves and tight-binding $d$ wave functions. In a first approximation the contribution of the $d$ states to the emitted current is neglected; the problem of the matching of the wave functions at the crystal boundary can then be solved exactly and, using the band parameters of Zornberg, very large positive spin polarizations are obtained. Next, the contribution of the $d$ electrons is included in a semiphenomenological way and reasonable agreement with experiment is obtained without invoking any many-body effects. The dependence of the spin polarization on crystallographic direction is investigated. This makes it necessary to consider the case of high-index directions for which field emission may be dominated by surface scattering. The final results compare well with the preliminary measurements of Campagna et al.