${\mathrm{Rb}}^{87}$ Quadrupole Coupling and the Ferroelectric Transition in Rb${\mathrm{H}}_2$As${\mathrm{O}}_4$

The quadrupole-induced shifts of the ${\mathrm{Rb}}^{87}$ ½ → -½ NMR transition have been studied as a function of temperature and crystal orientation, and the electric-field-gradient (EFG) tensors at the Rb sites in Rb${\mathrm{H}}_2$As${\mathrm{O}}_4$ have been determined. In the ferroelectric phase there are two physically nonequivalent ${\mathrm{Rb}}^{87}$ EFG tensors ($A$ and $B$) which are related by the symmetry operations of the orthorhombic space group. In addition, each line is split into two components ($A$, $A^{\prime }$ and $B$, $B^{\prime }$) because of domain effects. The ${\mathrm{Rb}}^{87}$ quadrupole coupling constant equals 5.76 MHz at 108°K, and the asymmetry parameter is $\eta ==0.85\mathrm{}$. The paraelectric EFG tensor is nearly, though not exactly, equal to the average of the two ferreolectric ones ($A$ and $B^{\prime }$, or $A^{\prime }$ and $B$) from oppositely polarized domains. The anomalous decrease in the quadrupole coupling constant of ${\mathrm{Rb}}^{87}$ with decreasing temperature in the paraelectric phase throws some light on the atomic motion as well as proton-lattice coupling and suggests that the Rb nuclei take part in collective atomic fluctuations which might represent an overdamped quasispin-wave ferroelectric mode.