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A conventional and rotating magnetoelectric effect of a half-filledspin-electron model on a doubly decorated square lattice is investigated byexact calculations. An importance of the electron hopping and spatialorientation of the electric field upon a magnetoelectric effect is examined indetail. A critical temperature may display one or two consecutive round maximaas a function of the electric field. Although the rotating magnetoelectriceffect (RME) does not affect the ground-state ordering, the pronounced RME isfound close to a critical temperature of continuous phase transition. It isshown that RME is amplified upon strengthening of the electric field, whichadditionally supports thermal fluctuations in destroying a spontaneousantiferromagnetic long-range order.

Conventional and rotating magnetoelectric effect of a half-filled spin-electron model on a doubly decorated square lattice