Temperature effects of the magnetic tunnel junctions with periodic grating barrier

We have developed a tunneling theory to describe the temperature dependence of tunneling magnetoresistance (TMR) of the magnetic tunnel junctions (MTJs) with periodic grating barrier. Through the Patterson function approach, the theory can handle easily the influence of the lattice distortion of the barrier on the tunneling process of the electrons. The lattice distortion of the barrier is sensible to the temperature and can be quite easily weakened by the thermal relaxation of the strain, and thus the tunneling process of the electrons gets changed highly with the variation of the temperature of the system. That is just the physical mechanism for the temperature dependence of the TMR. From it, we find that the decrease of TMR with rising temperature is mostly carried by a change in the antiparallel resistance ($R_{AP}$), and the parallel resistance ($R_{P}$) changes so little that it seems roughly constant, if compared to the $R_{AP}$, and that, for the annealed MTJ, the $R_{AP}$ is significantly more sensitive to the strain than the $R_{P}$, and for non-annealed MTJ, both the $R_{P}$ and $R_{AP}$ are not sensitive to the strain. They are both in agreement with the experiments of the MgO-based MTJs. Other relevant properties are also discussed.