The bilinear and intrinsic biquadratic coupling in magnetic metallic trilayers

We find the exact Green's functions of the Anderson s-d mixing model for ma gnetic trilayers with arbitrary spin canting angle between two ferromagneti c layers within the mean-field theory of the on-site Coulomb repulsion. A b ilinear exchange coupling and an intrinsic biquadratic coupling which does not vanish in the limit of flat interfaces is obtained by those Green's fun ctions. It is shown that both of these couplings oscillate in the experimen tal range of the spacer thickness only when the s-d mixing is strong enough . When the mixing strength is large enough one finds that the oscillation p eriod of the intrinsic biquadratic term is equal to half of the correspondi ng one for the bilinear term. We also find that the temperature dependence of those interlayer couplings is considerably enhanced with the decrease of the Hubbard coupling. It is also shown that the biquadratic coupling falls off much more rapidly with increasing temperature than the bilinear one.