Using the constrained-path Monte Carlo method, we studied the magnetic prop
erties of the two-dimensional periodic Anderson model for electron fillings
between 1/4 and 1/2. We also derived two effective low-energy theories to
assist in interpreting the numerical results. For 1/4 filling, we found tha
t the system can be a Mott or a charge-transfer insulator, depending on the
relative values of the Coulomb interaction and the charge-transfer gap bet
ween the two noninteracting bands. The insulator may be a paramagnet or ant
iferromagnet. We concentrated on the effect of electron doping on these ins
ulating phases. Upon doping we obtained a partially saturated ferromagnetic
phase for low concentrations of conduction electrons, if the system were a
charge-transfer insulator, we would find that the ferromagnetism is induce
d by the well-known Ruderman-Kittel-Kasuya-Yosida interaction. However, we
found a novel correlated hopping mechanism inducing the ferromagnetism in t
he region where the nondoped system is a Mott insulator. Our regions of fer
romagnetism spanned a much smaller doping range than suggested by recent sl
ave boson and dynamical mean-field theory calculations, but they were consi
stent with that obtained by density-matrix renormalization group calculatio
ns of the one-dimensional periodic Anderson model.