Temperature dependence of the exchange energy and critical field for antiferromagnetically coupled thin films and superlattices

We calculate the temperature dependence of the antiferromagnetic exchange energy and critical magnetic field for a model ferromagnet/paramagnet/ferromagnet (FM/PM/FM) sandwich and a model (FM/PM/FM${)}_{\mathrm{\infty }}$ superlattice. The temperature dependence is assumed to originate from fluctuations in the spin angular momentum of the FM components, rather than from electronic effects in the PM components. The spins are taken to be localized and coupled via near-neighbor ferromagnetic exchange within the ferromagnets, while spins on outermost layers are coupled to their counterparts across the paramagnetic spacer by a weaker antiferromagnetic exchange. The latter is shown to renormalize with temperature T through a surface-spin–surface-spin correlation function. This correlation function is calculated in the spin-wave region of temperature. For the superlattice, the fractional decrease in critical field and in antiferromagnetic exchange is proportional to T lnT except at extremely low T, where there is a ${\mathit{T}}^{3/2}$ dependence. For the sandwich, a linear dependence on T is found, with a coefficient that depends logarithmically on the dipole energy. Again, a ${\mathit{T}}^{3/2}$ dependence is found as T→0. We compare these results with related calculations and discuss the experimental implications.