Abstract: A microscopic theory of magnetoelectric (ME) effects in multiferroic RCrO3 compounds, where R is a non-magnetic ion (R = Y, La, Lu and Eu) is presented. Taking into account the influence of polar lattice displacements on symmetric and antisymmetric exchange interactions, two types of coupling between the magnetic and the ferroelectric subsystems are defined. The first magnetoelectric interaction is biquadratic with respect to the spin and pseudo-spin operators. The second, called antisymmetric, is induced by the appearance of spontaneous polarization in RCrO3. The built-in microscopic model describes the occurrence of a temperature-dependent spin-reorientation (SR) transition and defines it as continuous (continuous rotation of the magnetic spins in the zx -plane within a given temperature interval). The emergence of additional polarization as a consequence of a magnetic phase transition has been proven theoretically. This is due to the induction of an antisymmetric magnetic interaction of type Dzyaloshinsky-Moriya (DM) interaction, which is a consequence of the occurrence of spontaneous polarization in these compounds. The influence of magnetoelectric interactions on the magnetic and ferroelectric subsystems has been investigated. The behaviour of magnetization at the application of an external electric field is qualitatively explained with the renormalization of the exchange symmetric and antisymmetric magnetic interactions by the spontaneous polarization PS. The dependence of spontaneous polarization on the direction of external magnetic field was explained by the occurrence of feedback between PS and magnetization. It has been established that the width of the temperature interval ??SR, in which the SR transition takes place, decreases with the increase of the value of the external magnetic field. The method of Greenís function is used for the numerical calculations.

Keywords: multiferroics, magnetoelectric interactions, Greenís functions, spin-reorientation transition, induced Dzyaloshinsky-Moriya interaction.