= Jullière model
{c}
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 gives
$$
G_{\mathrm P}\propto1+P_1P_2,\qquad G_{\mathrm{AP}}\propto1-P_1P_2,\qquad\mathrm{TMR}=\frac{R_{\mathrm{AP}}-R_{\mathrm P}}{R_{\mathrm P}}=\frac{2P_1P_2}{1-P_1P_2}.
$$
The last equality uses $R=1/G$. For $P_1=P_2=0.4$, the predicted <tunnel magnetoresistance> is $0.32/0.84\approx0.381$, 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.<Tunneling between ferromagnetic films by M. Jullière>[1975, Fe–Ge–Co junction measurements and polarization model]{ref}
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