  We present a systematic study of quantum fluctuations in the C-type and
A-type antiferromagnetic (AF) phases in cubic lattices and in bilayer systems.
Using the linear spin-wave theory, we show that the spin stiffness and the
quantum corrections to the order parameter and energy obtained for C-AF and
A-AF phases decrease with the increasing number of ferromagnetic bonds.
Therefore, the quantum spin effects in LaMnO_3 and in LaVO_3 are rather small,
suggesting the magnetic moments of 3.91 and 1.89 Bohr's magneton, respectively.
They cannot explain the strong reduction of the magnetic order parameter
observed in cubic vanadates.
