Title: Magnetic Ordering of Ammonium Cations in NH$_4$I, NH$_4$Br and NH$_4$Cl

Abstract: The different types of magnetism arise mainly from how electrons move and interact with each other. In this work, we show how protons (H$^+$) also exhibit magnetic behavior. We measured the magnetic susceptibility of the ammonium halides and identified pronounced increases at 232 K, 233 K and 243 K for NH$_4$I, NH$_4$Br and NH$_4$Cl, respectively, which all coincide to the geometric ordering of its ammonium cations. With extensive literature establishing the fact that the ammonium cations exhibit rotational motion even towards the lowest temperatures, we take into account that the orbital motion of the protons carries a magnetic moment and find it to be larger than that of the paired electrons. Consequently, the structural phase transitions are magnetically-driven as the system attempts to lift 8-fold energy degeneracies of the proton orbitals via Jahn-Teller distortions. Our findings identify that NH$_4$$^+$ cations are capable of comprising magnetism which appears to be ubiquitous in ammonia-based molecular solids.