MICROMAGNETICS OF UNEVEN ULTRATHIN-FILM TRILAYERS

For ferromagnetic sandwiches where two iron layers are separated by a middle layer, the strength of the coupling sharply varies with each ch ange in the thickness of the middle layer. If the interfaces were shar p on the atomic scale, one could observe this directly, or else one ca n use micromagnetics to take into account the actual morphology of les s than ideal interfaces as shown by Slonczewski. As an approximation t he average magnetization in each layer is found from a phenomenologica l energy that contains the competition between bilinear and biquadrati c exchange constants that depend on surface roughness. More detailed m icromagnetic calculations using relaxation methods to treat spatial va riations of the magnetization in each layer are given for Fe-Cr-Fe san dwiches. The approximate calculations give jumps in the magnetization at critical fields, but these are smeared out in the more detailed cal culations. For the special case of equivalent layers, the phenomenolog ical expression for the energy can be used to obtain analytic expressi ons for the field dependence of the magnetization. (C) 1996 American I nstitute of Physics.