Magnetoelectric Coupling Based on Protons in Ammonium Sulfate

Most ferroelectric crystals have their own set of unique characteristics, and ammonium sulfate (NH4)2SO4 is no exception. We report on two previously unidentified features in ammonium sulfate: (1) that there are at least two successive transitions instead of one occurring at the Curie temperature TC = 223 K according to dielectric constant measurements, and (2) pronounced step-like anomalies are found in the magnetic susceptibility χ(T) exactly at TC. To explain these results, we take into account that there exists a previously unidentified linear coupling between the magnetic and electric dipole moments of the NH4+ tetrahedra due to their rapid reorientations and distorted geometry, respectively. The magnetic moments are small, 0.0016 μB for every C3 reorientation, which involves three protons (H+) undergoing orbital motion. Nevertheless, short-range correlations exist in the paraelectric phase because the magnetic moments are restricted to only point along 14 possible orientations due to the symmetry and periodic nature of the potential wells. At TC, C2 reorientations (involving four protons) are no longer energetically feasible, so the reduction in the degrees of freedom to 8 further enhances the effect of the magnetic interactions. This triggers long-range ordering of the orbital moments in an antiferromagnetic configuration along the ab-plane, which via Dzyaloshinskii–Moriya interactions ends up canting slightly toward the c-axis direction. Since there exist two types of inequivalent NH4+ groups that reorient at different frequencies with temperature and do not have the same degree of distortion, the emerging polar phase is ferrielectric. This previously unidentified “magneto-protonic” effect can be further extended toward understanding the fundamental causes of the spontaneous polarization in many other ferroelectric crystals as well as provide the missing link toward understanding the enhanced functionalities of many hydrogen-based compounds and organic–inorganic hybrid materials.