On the theory of magnetization in multiferroics: competition between ferro- and antiferromagnetic domains

Many technological applications of multiferroics are based on their ability to reconstruct the domain structure (DS) under the action of small external fields. In the present paper we analyze the different scenarios of the DS behavior in a multiferroic that shows simultaneously ferro- and antiferromagnetic ordering on the different systems of magnetic ions. We consider the way to control a composition of the DS and macroscopic properties of the sample by an appropriate field treatment. We found out that sensitivity of the DS to the external magnetic field and the magnetic susceptibility in a low-field region are determined mainly by the destressing effects (that have magnetoelastic origin). In a particular case of Sr$_{2}$Cu$_{3}$O$_{4}$Cl$_{2}$ crystal we anticipate the peculiarities of the elastic and magnetoelastic properties at $T\approx 100$ K.