Due to the strong coupling between magnetism and ferroelectricity, ${\left({\mathrm{ND}}_4\right)}_2{\mathrm{FeCl}}_5·{\mathrm{D}}_2\mathrm{O}$ 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 ${\left({\mathrm{ND}}_4\right)}_2{\mathrm{FeCl}}_5·{\mathrm{D}}_2\mathrm{O}$ 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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• Ferroelectricity
• Magnetic anisotropy
• Magnetic phase transitions
• Phase diagrams
• Ferroelectrics
• Heisenberg model
• Variational wave functional methods