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.
@article{arxiv.cond-mat/0211095,
title = {Spin stiffness and quantum fluctuations in C-type and A-type antiferromagnets},
author = {M. Raczkowski and A. M. Oles},
journal= {arXiv preprint arXiv:cond-mat/0211095},
year = {2009}
}