= Tunnel magnetoresistance
{title2=$\mathrm{TMR}=(R_{\rm AP}-R_{\rm P})/R_{\rm P}$}
<Tunnel magnetoresistance> is the change in resistance of a <magnetic tunnel junction> when the relative magnetizations of its two electrodes change. A common convention is
$$
\mathrm{TMR}=\frac{R_{\rm AP}-R_{\rm P}}{R_{\rm P}},
$$
where 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 $G_{\rm P}\propto1+P_1P_2$ and $G_{\rm AP}\propto1-P_1P_2$. Using $R=1/G$ gives
$$
\mathrm{TMR}=\frac{2P_1P_2}{1-P_1P_2}.
$$
This 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.<Tunneling between ferromagnetic films by M. Jullière>[1975, abstract and experimental description of Fe–Ge–Co junctions, parallel/antiparallel states and the model]{ref}
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