The theory of magnetic tunnel junctions
Within this work an investigation into the tunnelling magnetoresistance (TMR) will be presented. A base numerical model is developed to describe the tunnelling through a magnetic tunnel junction (MTJ) so that a simple analytic model can be compared. These models have been extended to the crystalline barrier MTJs. This numerical model was based upon an enhanced Wentzel-Kramers-Brillouin (EWKB) method to describe the tunnelling current density. By correctly considering realistic MTJ parameters, the key result was found to be the correct handling of the effective masses in of the three MTJ layers. The extracted barrier-heights of 3.5-4eV is much higher than found previously and closer to the half band-gap result expected. It is then clear that the correct treatment of the parameters produces a far more realistic result. The key parameter which can be extracted from the I-V characteristics is the product b m*d V , where m* is the effective mass of the barrier, d is the effective barrier thickness and Vb is the effective barrier height. The analytic solution is a transparent model in which the key material parameters are visible and simple enough to be applied by experimental researchers to MTJs. The accurate modelling of both the prefactor and exponent are crucial to estimating the TMR. A simplified analytic result was produced that is in good agreement with numerical and experimental results. The numerical and analytic model are then extended to describe the TMR through a crystalline Fe(001)/MgO(001)/Fe(001) trilayer system. The calculation is based on the free-electron-like numerical solution providing a functional dependence of the TMR. The results were found to be in excellent agreement with the ab initio models and experiment. Furthermore a simplified analytic expression shows the TMR is dependent on the band-widths of the tunnelling electron states, the coupling and the thickness of the barrier. These models will be of great benefit to both experimental and theoretical researchers.