Symmetry and magnetically driven ferroelectricity in rare-earth manganitesRMnO3(R=Gd,Tb,Dy)

Abstract

This work investigates the magnetically driven ferroelectricity in orthorhombic manganites $R\mathrm{Mn}{\mathrm{O}}_{3}$ ($R=\mathrm{Gd}$, Dy, or Tb) from the point of view of the symmetry. The method adopted generalizes the one used to characterize the polar properties of displacive modulated structures to the case of an irreducible magnetic order parameter. The symmetry conditions for magnetically induced ferroelectricity are established, and the Landau-Devonshire free energy functionals are derived from general symmetry considerations. The ferroelectric polarization observed in $\mathrm{Dy}\mathrm{Mn}{\mathrm{O}}_{3}$ and $\mathrm{Tb}\mathrm{Mn}{\mathrm{O}}_{3}$ at zero magnetic field is explained in terms of the symmetry of a reducible magnetic order parameter. The polarization rotation induced in these compounds by external magnetic fields and the stabilization of a ferroelectric phase in $\mathrm{Gd}\mathrm{Mn}{\mathrm{O}}_{3}$ are accounted for by a mechanism in which magnetization and polarization are secondary order parameters that are not directly coupled but compete with each other through their coupling to competing primary modulated order parameters.