Tunnel magnetoresistance ($\mathrm{TMR}=(R_{\mathrm{AP}}-R_{\mathrm{P}})/R_{\mathrm{P}}$)

Tunnel magnetoresistance is the change in resistance of a magnetic tunnel junction when the relative magnetizations of its two electrodes change. A common convention iswhere P and AP denote parallel and antiparallel alignment. This connects quantum tunnelling to the spin dependence of electronic states in the electrodes.

In the Jullière model, assume spin-conserving tunnelling with spin-independent matrix factors, and let the density of states polarizations at the Fermi energy be $P_i=(n_{i\uparrow }-n_{i\downarrow })/(n_{i\uparrow }+n_{i\downarrow })$. Parallel alignment pairs matching spin channels, while antiparallel alignment pairs opposite channels. Hence $G_{\mathrm{P}}\propto 1+P_1{P}_2$ and $G_{\mathrm{AP}}\propto 1-P_1{P}_2$. Using $R=1/G$ givesThis is a consequence of the stated two-channel model, rather than a universal material law.

M. Jullière's 1975 experiment compared the conductance of iron–germanium–cobalt thin-film junctions with parallel and antiparallel magnetizations at low temperature. The thin separating layer, magnetic preparation of the films and conductance measurement together made relative magnetic orientation an experimentally controllable transport variable.^[ref]

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]