Analytical investigation of spin transfer dynamics using a perpendicular-to-plane polarizer

An analytical investigation of the dynamic properties of spin-transfer torque (STT) devices comprising a perpendicular-to-plane polarizer (PERP) is reported. Several analytical solutions for PERP are derived from Landau-Lifshitz-Gilbert (LLG) equation including the spin-torque term, and proved its validity by comparing with numerical simulations using the single domain model. The critical spin-torque amplitude a_JC is linearly proportional to the in-plane anisotropy field of the sample. It shows a good agreement with simulation assuming single domain except in the case of large positive current where the polarizer magnetization is also excited. Several analytical solutions for precession frequency are derived which showed a good agreement with single domain simulations. The main results reveal that, considering the thermal stability criterion, the switching current density in PERP based structures is larger than that in their longitudinal polarizer counterparts when the cell area is smaller than a certain value. However, the switching is much faster in the PERP. Also, it is found that the precession frequency in PERP based structures can be tuned from about 1 GHz to 20 GHz by only changing the current without any external field.