Strength of the symmetry spin-filtering effect in magnetic tunnel junctions
We developed a general theory that allows us to predict the power factor n in the asymptotics of the tunneling magnetoresistance (TMR), TMR Nn, in the limit of large number of the tunnel barrier layers, N, for a magnetic tunnel junction (MTJ) system that has the so-called symmetry spin-filtering properties. Within this theory the only information required to determine n is the knowledge of the symmetries of the wave functions of the bulk electrode and barrier materials at the Γ point in the in-plane surface Brillouin zone. In particular, we show that for a MTJ that has the in-plane square symmetry only three values for the power factor are allowed: n=0,1, and 2 for the asymptotics of the TMR enhanced due to the symmetry spin-filtering mechanism. To verify our theory we performed the density functional theory calculations of transmission functions and TMR for a Fe/MgO/Fe MTJ which confirm predicted values of the power factor n=0,1, or 2 in specific ranges of energies (in particular, n=1 at the Fermi energy).