Electric-field-induced structural and magnetic transformations in BiFeO$_3$ multiferroics

The influence of an electric field on the structural changes and related transformation of the magnetic subsystem in a BiFeO$_3$ multiferroic material has been investigated in the framework of the phenomenological model based on the Ginzburg–Landau theory. The hysteresis dependences of the electric polarization, the counter-rotation of oxygen octahedra, the magnetization, and the antiferromagnetic vector have been obtained as a function of the electric field applied along the crystallographic directions [110] and [001] of the pseudocubic structure. The model parameters are consistent with the results of the ab initio calculations of the structural and magnetic transitions in this material. It has been shown that, in the region of the existence of a spatially modulated spin state, an abrupt change in the polarization vector leads to a stepwise transformation of the antiferromagnetic structure. Within the proposed approach, the electric-field-controlled change in the spin structure of the multiferroic material is adequately described in the range of weak and strong magnetic fields.