Twist of rhombohedra, spin helix, and “giant” polarization in a CaMn7O12 multiferroic crystal

Abstract

A qualitative assessment of axial vector Γ_z in invariant P_z(McurlM)Γ_z proposed earlier for the description of the thermodynamic potential of a CaMn₇O₁₂ multiferroic material with electric polarization P_z along the z axis of the helix of magnetic moments M has been performed based on the fan-shaped structure of the atomic cell of the crystal. The dependence of Γ_z on the permanent dipole moment of MnO₆ octahedra (rhombohedra), which are inevitably distorted in the paraelectric phase due to the structural transformation, on the mechanical stiffness of the crystal lattice, and on the projected area of the cross section of rhombohedra with bevels undergoing a shift has been determined from dimensional considerations. It has been demonstrated how these factors contribute to the twist of rhombohedra.