  A conventional and rotating magnetoelectric effect of a half-filled
spin-electron model on a doubly decorated square lattice is investigated by
exact calculations. An importance of the electron hopping and spatial
orientation of the electric field upon a magnetoelectric effect is examined in
detail. A critical temperature may display one or two consecutive round maxima
as a function of the electric field. Although the rotating magnetoelectric
effect (RME) does not affect the ground-state ordering, the pronounced RME is
found close to a critical temperature of continuous phase transition. It is
shown that RME is amplified upon strengthening of the electric field, which
additionally supports thermal fluctuations in destroying a spontaneous
antiferromagnetic long-range order.
