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In order to better understand the role of possible couplings in determiningthe giant magnetoresistance (GMR) behavior of multilayers, a knowledge of thedependence of the $GMR$ on magnetic field $H$ appears to be useful. Since a fewspecific cases have only been treated theoretically in the literature, it wasdecided to carry out a modeling of the $GMR(H)$ curves offerromagnetic/non-magnetic (FM/NM) multilayers with various interlayercouplings. For simplicity, we focused on a trilayer structure (FM1/NM/FM2)corresponding fairly well to the case of a large number of FM/NM bilayers. Tocarry out the calculations, some fundamental assumptions were made: (i) singledomain FM layer, in plane magnetization; (ii) the magnetization of each layeris the same; (iii) the magnetization vectors rotate in the plane of the layersin an external magnetic field. In order to calculate the $GMR(H)$ function, weneed to know the magnetization process in the trilayer, i.e., the $M(H)$function. Therefore, first we calculate the equilibrium angle $\phi(H)$ betweenthe two magnetization vectors as a function of the field by minimizing thetotal energy of the trilayer. According to most previous theoretical andexperimental works, the angular dependence of the GMR is fairly well describedby the relation $GMR(\phi)\propto (1-\cos\phi)$ and we used this relation toderive the $GMR(H)$ function. Along this line, the $M(H)$ and $GMR(H)$ curveswere calculated for the following cases: (i) pure AF coupling; (ii) pureorthogonal coupling; (iii) AF coupling and orthogonal coupling simultaneouslypresent. As to the calculation of the $GMR(H)$ curves, some of theseconfigurations have not yet been treated formerly or for some specificparameter values only. For those cases for which calculations were reported inthe literature for $M(H)$ and $GMR(H)$, our results agree with previousreports.

Modeling the magnetoresistance vs. field curves of GMR multilayers with  antiferromagnetic and/or orthogonal coupling by assuming single-domain state  and coherent rotation