Variable variance Preisach model for multilayers with perpendicular magnetic anisotropy

We present a variable variance Preisach model that fully accounts for the different magnetization processes of a multilayer structure with perpendicular magnetic anisotropy by adjusting the evolution of the interaction variance as the magnetization changes. We successfully compare in a quantitative manner the results obtained with this model to experimental hysteresis loops of several ${[\mathrm{CoFeB}/\mathrm{Pd}]}_n$ multilayers. The effect of the number of repetitions and the thicknesses of the CoFeB and Pd layers on the magnetization reversal of the multilayer structure is studied, and it is found that many of the observed phenomena can be attributed to an increase of the magnetostatic interactions and subsequent decrease of the size of the magnetic domains. Increasing the CoFeB thickness leads to the disappearance of the perpendicular anisotropy, and such a minimum thickness of the Pd layer is necessary to achieve an out-of-plane magnetization.