Based on rigorous results for both the antiferromagnetic Heisenberg mo
del and the Hubbard model, we construct some layered crystal lattices,
and show rigorously that the interlayer magnetic coupling (IMC) betwe
en magnetic layers separated by a non-magnetic or antiferromagnetic sp
acer is oscillatory with a period of two monolayers in the interlayer,
and independent of the magnetic layer thickness. Our findings provide
a possible way to find or construct some magnetic superlattices as we
ll as to understand the mechanism of the IMC.