Jullière model

The Jullière model describes spin-conserving tunneling between ferromagnetic electrodes using their spin-resolved density of states at the Fermi energy. If $P_i=(n_{i\uparrow }-n_{i\downarrow })/(n_{i\uparrow }+n_{i\downarrow })$ and the tunneling factors are spin independent, summing the two spin channels givesThe last equality uses $R=1/G$. For $P_1=P_2=0.4$, the predicted tunnel magnetoresistance is $0.32/0.84\approx 0.381$, or 38.1 percent.

The motivating experiment compared low-temperature conductance of iron–germanium–cobalt thin-film junctions after preparing parallel and antiparallel magnetizations. The thin separating layer permits quantum tunnelling, while changing magnetic alignment tests the two-channel prediction. Interface states, spin-dependent tunneling amplitudes and finite-bias effects are additional physics outside this simple model.^[ref]