Magnetoelectric effect and magnetic dynamics in the Gd$_2$CuO$_4$ antiferromagnet

The magnetoelectric effect and the magnetic dynamics in Gd$_2$CuO$_4$ have been studied using a phenomenological approach and group-theory methods. Vector order parameters are introduced based on four magnetic sublattices. Invariant products of the order parameters are determined, from which the thermodynamic potential density is constructed. Using the spin-wave representation, the calculations can be significantly simplified and the ground orientation magnetic state can be presumably determined. The magnetic dynamics is described by the Landau–Lifshitz equations, from which the antiferromagnetic resonance frequency and the dynamic susceptibilities, namely, magnetic, antiferromagnetic, magnetoelectric, and antiferroelectric susceptibilities are found. The frequency and the susceptibility are shown to be controlled by applied electric field.