Cycloid manipulation by electric field inBiFeO3films: Coupling between polarization, octahedral rotation, and antiferromagnetic order

Abstract

The room temperature multiferroic ${\mathrm{BiFeO}}_{3}$, by far the most studied experimentally, exhibits outstanding ferroelectric properties with a cycloidal magnetic order in the bulk and many unexpected advantages for possible applications in spintronics, sensor techniques, and photovoltaics. To consider ferroelectric and magnetic phase transitions in multiferroic ${\mathrm{BiFeO}}_{3}$ under electric field, we suggest the Ginsburg-Landau-like approach based on the symmetry and $\mathbf{P}\ensuremath{-}\ensuremath{\omega}\ensuremath{-}\mathbf{L}$ coupling, where the order parameters are: $\mathbf{P}$ is the electric polarization, $\ensuremath{\omega}$ is the axial vector of antidistorsion (describing a rotation of the oxygen octahedrons), and $\mathbf{L}$ is the antiferromagnetic vector. The theoretical model is consistent with experiment and ab initio calculations data. We give the complete set of numerical coefficients of the model and explore the behavior of $\mathbf{P}$ and $\ensuremath{\omega}$ vectors in strong electric field. The proposed approach is particularly promising for the analysis of magnetoelectric phenomena whose length scale is significantly larger than the length of the cell used in ab initio calculations. The considered cycloid problem is the clear example of such a system. Electric field-induced transformations of cycloid are exemplified on an epitaxial ${\mathrm{BiFeO}}_{3}$ film grown on the (001)-oriented substrate. We show that the jump of vectors $\mathbf{P}$ and $\ensuremath{\omega}$ in the field $E=6$ MV/m is accompanied by a jump of a cycloid spin rotation plane. This effect is of particular interest for spintronics and nanoelectronics.