Tunneling magnetoresistance (TMR) is a dramatic change of the tunneling current in magnetic tunnel junctions when relative magnetizations of the two ferromagnetic layers change their alignment. TMR is a consequence of spin-dependent tunneling. TMR can be understood in terms of Julliere's model, which is based on two assumptions. First, it is assumed that spin of electrons is conserved in the tunneling process. It follows, then, that tunneling of up- and down-spin electrons are two independent processes, so the conductance occurs in the two independent spin channels. According to this assumption, electrons originating from one spin state of the first ferromagnetic film are accepted by unfilled states of the same spin of the second film. If the two ferromagnetic films are magnetized parallel, the minority spins tunnel to the minority states and the majority spins tunnel to the majority states. If, however, the two films are magnetized antiparallel the identity of the majority- and minority-spin electrons is reversed, so the majority spins of the first film tunnel to the minority states in the second film and vice versa.
Second, it is assumed that the conductance for a particular spin orientation is proportional to the product of the effective density of states of the two ferromagnetic electrodes. According to these two assumptions, the TMR can be written as follows:
Julliere's model was used to estimate the magnitude of TMR in magnetic tunnel junctions from the known values of the spin polarization of ferromagnets obtained in experiments on superconductors.
