 Jullière model

ID: julliere-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 ↑} - n_{i ↓}) / (n_{i ↑} + n_{i ↓})

and the tunneling factors are spin independent, summing the two spin channels gives

G_{P} \propto 1 + P_{1} P_{2}, G_{AP} \propto 1 - P_{1} P_{2}, TMR = \frac{R _{AP} - R _{P}}{R _{P}} = \frac{2 P _{1} P _{2}}{1 - P _{1} P _{2}} .

The last equality uses

R = 1/ G

. For

P_{1} = P_{2} = 0.4

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]

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