We observe sharp step-down discontinuities in the magnetic susceptibility of NH4H2PO4 and NH4H2PO4-d 60 (60% deuterated) along the a- and c-axes occurring exactly at their antiferroelectric transition temperatures. For the case of KH2PO4, less pronounced discontinuities occur at the ferroelectric transition temperature. To explain this, we treat the acid protons as individual oscillators that generate current elements that translate to magnetic forces in near resonance with each other. With decreasing temperature, the resonant forces become more commensurate, which amplifies a disproportionate drop off of two types of magnetic forces to eventually trigger the structural phase transitions. For the case of NH4H2PO4, the associated internal magnetic field appears to aid the NH4 + to order at a higher temperature. At 49 K, a shoulder-like anomaly in both NH4H2PO4 and KH2PO4 is attributed to a possible onset of macroscopic quantum tunneling of protons. Our findings bring forth a new category of intrinsic multiferroic systems.

Most ferroelectric crystals have their own set of unique characteristics, and ammonium sulfate (NH 4 ) 2 SO 4 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 T C = 223 K according to dielectric constant measurements, and (2) pronounced steplike anomalies are found in the magnetic susceptibility χ(T) exactly at T C . 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 NH 4 + tetrahedra due to their rapid reorientations and distorted geometry, respectively. The magnetic moments are small, 0.0016 μ B for every C 3 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 T C , C 2 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 NH 4 + 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.