Dependence of improper ferroelectricity on the preferred orientation of Mn3 spins in CaMn7O12

The improper ferroelectricity of CaMn7O12 is studied by examining the influence of the orientation angle of Mn3 spins on the basis of first-principles density functional theory. We analyze the helicoidal magnetic order induced forces, ionic displacements, and polarization contributions from both atomic and mode- decomposition viewpoints. Our work unambiguously reveals the critical role of the orientation angle of Mn3 spins in determining the improper ferroelectricity of CaMn7O12. The ferroelectric polarization can be reversed by changing the orientation angle of Mn3 spins without switching spin chirality of the helicoidal magnetic order. We demonstrate that the particular helicoidal magnetic order induces remarkable mismatch of the Born effective charges with the lattice symmetry, which leads to the dominant contribution to ferroelectric polarization from purely Raman-type ionic displacements. However, this significant polarization contribution from the purely Raman-type distortion cannot survive in the absence of IR-active ionic displacements.