Interlayer exchange coupling between two ferromagnets with finite thickness separated by a nonmetallic spacer

Interlayer exchange coupling (IEC) between two ferromagnets (FM's) separated by a nonmetallic spacer is analyzed theoretically within the free-electron approximation. Particular attention is paid to the influence of FM thickness dFM on IEC and the variation of Fermi energy with the alignment of two FM's. The results show that (1)dFM strongly influence the IEC such that, only when dFM is not large, the barrier height and molecular field are both small, the IEC may oscillate with the spacer thickness owing to the quantum-size effect; otherwise, the IEC does not oscillate, but exhibits an exponential behavior in most spacer thickness; $(2)$ as an oscillatory function of dFM with multiple periods, the IEC has a negative nonoscillatory term, which will become zero when the molecular field is comparatively small; $(3)$ the Fermi energy has little difference between the parallel and antiparallel alignments of the two FM's, which correlates with the IEC to some extent. Particularly, with the increasing of dFM, this correlation becomes stronger.