Ferroelectric atomic displacement in multiferroic tetragonal perovskite Sr_{1/2}Ba_{1/2}MnO_{3}

Abstract

We investigate the crystal structure in multiferroic tetragonal perovskite Sr_{1/2}Ba_{1/2}MnO_{3} with high accuracy of the order of 10^{−3} Å for an atomic displacement. A large atomic displacement of the Mn ion from the centrosymmetric position, comparable with the off-centering distortion in the tetragonal ferroelectric BaTiO_{3}, is observed in the ferroelectric phase (T_{N}≤T≤T_{C}). In stark contrast, in the multiferroic phase (T≤T_{N}), the atomic displacement for the Mn ion is suppressed, but those for O ions are enlarged. The atomic displacements in the polar crystal structures are also analyzed in terms of the ferroelectric modes. In the ferroelectric phase, the atomic displacements are decomposed into dominant positive Slater, negative Last, and small positive Axe modes. The suppression of Slater and Last modes, the sign change of the Last mode, and the enlargement of the Axe mode are found in the multiferroic phase. The ferroelectric distortion is well reproduced by a first-principles calculation based on the Berry phase method, providing additional information on competing mechanisms to induce the ferroelectric polarization, electronic p-d hybridization versus magnetic exchange striction. The quantitative comparison between the experimental result and the theoretical calculation leads to a better understanding of the ferroelectric polarization in the multiferroic phase.