Phase transitions of the ferroelectric (ND₄)₂FeCl₅D₂O under a magnetic field

Due to the strong coupling between magnetism and ferroelectricity, (ND₄)₂FeCl₅ .D₂O exhibits several intriguing magnetic and electric phases.  To explain the ferroelectric (FE) phase transitions of (ND₄)₂FeCl₅.D₂O 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, we include higher-order onsite anisotropic spin interactions.  Our theory predicts a new ferroelectric phase sandwiched between the observed FE II and FE III phases in a magnetic field.  This phase may appear with doping.  By emphasizing the importance of the higher-order spin anisotropic interactions, our work provides a framework to understand multiferroic materials with rich phase diagrams.