Abstract
Due to the strong coupling between magnetism and ferroelectricity, ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ exhibits several intriguing magnetic and electric phases. In this Letter, we include higher-order onsite anisotropic spin interactions to explain the ferroelectric phase transitions of ${({\mathrm{ND}}_{4})}_{2}{\mathrm{FeCl}}_{5}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{D}}_{2}\mathrm{O}$ in a magnetic field and to produce the large weights of high-order harmonic components in the cycloid structure that are observed from neutron diffraction experiments. Moreover, we predict a new ferroelectric phase sandwiched between the FE II and FE III phases in a magnetic field. By emphasizing the importance of the higher-order spin anisotropic interactions, our work provides a framework to understand multiferroic materials with rich phase diagrams.
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