Layer thickness and angular dependence of spin transfer torque in ferromagnetic trilayers

We investigate the spin transfer torque arising from a perpendicular-to-plane current in a ferromagnetic (FM)-nonmagnetic-FM trilayer. Our analysis is based on the spin drift-diffusion model, modified for the case of noncollinear magnetization, i.e., with arbitrary angle theta between the magnetization orientation of the two FM layers. By solving the electrochemical potential and spin accumulation across the trilayer, we obtain the theta dependence of the magnetoresistance and spin transfer torque in the free FM layer. The optimal magnetization orientation theta(max) and the corresponding maximum torque tau(max) are investigated as a function of the FM layer thicknesses. Based on the analysis, we propose that (i) the free (fixed) FM layer thickness be set at approximately the transverse (longitudinal) spin relaxation lengths, and (ii) the relative FM orientation be biased at some intermediate angles instead of the conventional collinear configuration, in order to maximize the current-induced magnetization switching effect. (c) 2007 American Institute of Physics.