Interlayer exchange coupling in complex magnetic multilayers

We extend the hole confinement model of Edwards et al. to the problem of two kinds of complex magnetic sandwich structures. One is the magnetic sandwich covered on both sides by nonmagnetic films(case 1) and the other is that covered by magnetic films(case 2). The interlayer exchange coupling and the angular dependence of coupling energy in the two cases are investigated systematically. For case 1, our results show that the magnetic and outer nonmagnetic films influence significantly the oscillation behavior of exchange coupling and the appearance of noncollinear exchange coupling is very sensitive to the thickness of magnetic and outer nonmagnetic layers. Our results also show that the nonoscillatory component of the coupling generally varies with the thickness of magnetic(outer nonmagnetic) films and the results in the case where the thickness of both magnetic(outer nonmagnetic) films vary simultaneously are significantly different from that in the case where the thickness of one of the two magnetic(outer nonmagnetic) films is fixed while the other is varied, which is qualitatively in agreement with the experimental measurements. For case 2, the exponential dependence of exchange coupling on the thickness of the intermagnetic layer has been obtained, similar to the Parkin's experimental results for giant magnetoresistance.