Due to the strong coupling between magnetism and ferroelectricity, $(mathrm{ND}_4)_2mathrm{FeCl}_5cdotmathrm{D}_2mathrm{O}$ exhibits several intriguing magnetic and electric phases. In this letter, we include high-order onsite spin anisotropic interactions in a spin model that successfully captures the ferroelectric phase transitions of $(mathrm{ND}_4)_2mathrm{FeCl}_5cdotmathrm{D}_2mathrm{O}$ under a magnetic field and produces 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. Our results emphasize the importance of the high-order spin anisotropic interactions and provide a guideline to understand multiferroic materials with rich phase diagrams.
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