Quantitative model for switching asymmetry in perpendicular MTJ: A material-device-circuit co-design

A physics based switching model for perpendicular magnetic tunnel junction (p-MTJ) device is presented by combining (a) 4×4 tunneling conductance matrix derived using non-equilibrium Green's function (NEGF) formalism and (b) 4×4 ferromagnetic conductance matrix derived using 4 component spin diffusion equation. It provides qualitative as well as quantitative agreement with switching voltages in spin torque experiments and further explains the pattern of asymmetry i.e. Vc, ap-> p < Vc, p-> ap observed in most of the switching experiments and Vc, ap-> p > Vc, p-> ap observed in our measured data. Starting at the materials and phenomena level of abstraction, our model provides a unique quantitative machinery for device engineers to model p-MTJ circuits and architectures.