Proton ordering and conduction in TlH ₂PO ₄ with a paraelectric-antiferroelectric mixed order

We have studied proton ordering and proton conduction in a TlH ₂PO ₄ single crystal associated with the recently identified intermediate paraelectric-antiferroelectric mixed phase with a phase boundary temperature T _s = 327 K. According to the ¹H nuclear magnetic resonance rotatingframe spin-lattice relaxation measurements, proton ordering takes place at T _s rather than at the structural phase transition temperature T _c = 230 K. Distinct temperature dependencies of the electrical conductivity were observed below and above T _s, indicating that proton conduction in the system is dictated by the proton and the electric dipole orders.