Stability Diagrams of a Tunnel Nanoheterostructure in the Free-Electron Approximation

One of important characteristics of a magnetic tunneling junction (MTJ) nanoheterostructure that is used as magnetic random access memory (MRAM) cell and is switched by the spin transfer torque (STT) effect is its stability diagram, which determines the range of values of the external magnetic field and applied voltage under which a cell is in one of two stable states. To numerically construct such diagrams, one usually uses the solution of the Landau–Lifshitz dynamic equation in the single-domain approximation along with phenomenological constants that determine the values of spin torque in the material. In the present paper, the problem of spin-dependent electron transfer in an MTJ structure is considered, whose solution in the free-electron approximation allows one to calculate the values of spin torque for a given material in any magnetic configuration of the system and apply them to the integration of the Landau–Lifshitz equation. The method used allows one to more precisely reproduce the shape of the stability diagram and predict the critical values of the magnetic field and voltage necessary to switch an MTJ-based MRAM cell.