The magnetic behavior of the perpendicular exchange-spring bilayer and multilayer, constituted of a hard and a soft phase that are exchange-coupled on a nanometric scale, is analyzed by a one-dimensional micromagnetic model leading to a complete magnetic phase diagram in terms of layer thicknesses. The validity of the one-dimensional assumption for the perpendicular situation is demonstrated. The phase diagram provides information on the type of demagnetization processes and the critical fields at which nucleation and reversal take place, depending on the intrinsic properties of the chosen soft and hard materials. An analytical expression of the reversal field is deduced for relatively large thicknesses. Moreover, the effect of a reduced interlayer coupling is also taken into account, leading to slight modifications of both the magnetic phase diagram and the hysteresis loops. A series of Fe/FePt bilayers, prepared by sputtering, has been used to evaluate the predictions of the model, which has also been tested with the available literature data on FeRh/FePt bilayers. Both systems have a particular relevance for potential applications in magnetic recording as well as magnetic microelectromechanical systems.
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