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Due to the strong coupling between magnetism and ferroelectricity,$(\mathrm{ND}_4)_2\mathrm{FeCl}_5\cdot\mathrm{D}_2\mathrm{O}$ exhibits severalintriguing magnetic and electric phases. In this letter, we include high-orderonsite spin anisotropic interactions in a spin model that successfully capturesthe ferroelectric phase transitions of$(\mathrm{ND}_4)_2\mathrm{FeCl}_5\cdot\mathrm{D}_2\mathrm{O}$ under a magneticfield and produces the large weights of high-order harmonic components in thecycloid structure that are observed from neutron diffraction experiments.Moreover, we predict a new ferroelectric phase sandwiched between the FE II andFE III phases in a magnetic field. Our results emphasize the importance of thehigh-order spin anisotropic interactions and provide a guideline to understandmultiferroic materials with rich phase diagrams.

Phase transitions of the ferroelectric $(\mathrm{ND}_4)_2\mathrm{FeCl}_5\cdot\mathrm{D}_2\mathrm{O}$ under a magnetic field