Magnetic Tunnel Junctions (MTJs), usually consist of layered ferromagnet/insulator/ferromagnet systems. The two ferromagnets’ magnetizations can vary independently of each other, due to decoupling provided by the insulating layer. By changing the relative orientation of the ferromagnet alignments from parallel to antiparallel, a large change in the resistance across such a system is observed. 

Here the Left two pictures represent the non-magnetic barrier system, with the RED(BLUE) lines indicating the spin UP(DOWN) channel, and the black region in the middle being an insulating region.  The Right two pictures represent the magnetic barrier system, with the same color scheme.  Notice that there are now split levels in the insulating region.  Delta is the Exchange Splitting.

The resistance change observed when the orientations of the magnetic fields are switched can be used to calculate the Tunnel Magnetoresistance Ratio, and it is defined as:

 (1)

Where Rap and Rp are the resistances of the antiparallel and parallel configurations, respectively. PL is the polarization of electrons from the left ferromagnet, PR is the polarization of electrons from the right ferromagnet, shown here:

  (2)

Even for a idealized situation where the left and right electrodes are half metallic with a perfect interface, at room temperature the system will have a low TMR ratio. To improve this ratio, it may be possible to introduce a ferromagnetic insulator in place of the normal insulator, as shown in fig.1. Experiments have shown possible polarizations of nearly 100%.(3)
To examine this situation, we use Non-equilibrium Green’s Functions with Tight-Binding Hamiltonians to model systems like the one described above. By using this method, charge currents, spin currents, and magnetic moments can be obtained. Recent work has begun to examine new configurations for MTJs utilizing ferromagnetic insulators.

Some results:

Here is a plot of (Spin Up Current + Spin down Current) vs. Bias for two configurations of the magnetization in the non-magnetic insulator system.  The parallel configuration is with both leads magnetized in the positive spin-z direction.  The parallel configuration has the left lead magnetized down, with respect to the magnetization of the right lead, which is up.

Here is a plot of (Spin Up Current + Spin down Current) vs. Bias for two configurations of the magnetization in the Magnetic insulator system.  The parallel configuration is with both leads magnetized in the positive spin-z direction.  The parallel configuration has the left lead magnetized down, with respect to the magnetization of the right lead, which is up.

Notice that there is asymmetry introduced in the curves.  This comes about due to the addition of a quadratic term to the previous linear curves for low bias, from Brinkman's expression for current as a function of bias and barrier levels.(4)  The curves are not perfectly linear due to effects from the shape of the bands.

From the Currents, we can find the resistances, and thereby the TMR.  Here is a plot of the TMR for the non-magnetic and magnetic barriers vs. bias.  The interesting thing to notice here is that there is an increase in TMR at small bias for the Magnetic Insulator system.  This is an exciting result, although coupling between the ferromagnetic barrier and the leads may make this system difficult to acheive.

References:

1.) Ching-Ray Chang and Sui-Pin Chen, Chinese J. Phys. 36, 2-I (1998)

2.) M.G. Chapline, S. X. Wang, J. Appl. Phys. 100, 123909 (2006)

3.) D. C. Worledge, T. H. Geballe, J. Appl. Phys. 88, 9 (2000)

4.) W. F. Brinkman, R. C. Dynes, and J. M. Rowell, J. Appl. Phys. 41, 5 (1970)