Magnetoelectric effect and toroidal ordering in Ga2−x FexO3

The field dependence of the magnetoelectric effect and longitudinal magnetostriction of Ga2−x FexO3 single crystals is studied in magnetic fields up to 200 kOe in the temperature range from 4.2 to 300 K. It is shown that the magnetoelectric effect in these materials is determined mainly by the toroidal moment T and is not related to magnetostriction, as was previously theorized. A new method for determining the toroidal moment by measuring the electric polarization in a strong magnetic field is proposed. The value of the toroidal moment of the unit cell in Ga1.15Fe0.85O3 is calculated: T=(T a ,0,0), where T a =24.155µ B Å per unit cell. Experimental data are analyzed using a theory of toroidal spin ordering, which gives good agreement with experiment.