Interlayer exchange coupling in perovskite-type magnetic trilayers

The interlayer exchange coupling constant of ferromagnetic trilayers made of perovskite oxides has been calculated by using a tight-binding model for ${e}_{g}$ orbitals of Mn and Ni ions in $\mathrm{La}\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_{3}∕\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{3}∕\mathrm{La}\mathrm{Ba}\mathrm{Mn}{\mathrm{O}}_{3}$. We show that the extended ${e}_{g}$ band model, which includes the second nearest neighbor hoppings, reproduces experimental results well for suitable settings of the Fermi level. However, both oscillation period and intensity are shown to be sensitive to the position of the Fermi level. The results may be examined experimentally by replacing La with Sr or Ca to alter the electron number in $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{3}$.