Temperature dependence of the interlayer exchange coupling in magnetic multilayers:: An ab initio approach

The temperature dependence of interlayer exchange coupling (IEC) is studied theoretically within the asymptotic theory with preasymptotic corrections included, and by employing an ab initio approach based on the Green function formulation of the IEC. In this paper an efficient method for calculating integrals involving the Fermi-Dirac distribution by representing the occurring integrands by a sum of complex exponentials is discussed. In particular a method which allows us to extract separately the temperature-dependence of the short-period (SPO) and long-period (LPO) oscillations in the case of Co/Cu/Co(001) trilayers from computed values is suggested. Furthermore, a detailed discussion of predictions of asymptotic theory is given. It is found that in the limit of a large spacer thickness N ab initio calculations confirm the results of asymptotic theories for SPO for a variety of trilayer geometries, namely, that the oscillation amplitudes depend on the temperature T as cNT/sinh(cNT). On the other hand, for the case of the LPO this simple form does not apply. We explain this behavior by large preasymptotic corrections necessary for the LPO. The combined effect of the temperature and the disorder in the spacer is also discussed.