Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

We measured⁸⁷Rb nuclear magnetic resonance (NMR) and³⁵Cl nuclear quadrupole resonance (NQR) Hahn spin-echo magnetization decays in the incommensurate (I) phase of Rb₂ZnCl₄ and, in each case, obtained a Hahn echo decay that was shorter than the Carr-Purcell-Meiboom-Gill decay and one which decayed with a time constant proportional to the cube of the echo time. From these measurements we obtained from both the⁸⁷Rb NMR and³⁵Cl NQR measurements values for the diffusion coefficients that are comparable in magnitude, a fact that strongly supports the existence of slow modulation wave diffusionlike motions in the I phase, since such motions should affect both Rb and Cl ions similarly. In addition, we used⁸⁷Rb two-dimensional exchange-difference NMR to study atomic motions in the incommensurate (I) and paraelectric (P) phases to elucidate the nature of the I-P transition. We measured as a function of the mixing time the frequency shifts of the cross peaks from the main diagonal and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. We interpreted the motions observed in the P phase as normal modes arising from simultaneous reorientations of ZnCl₄ tetrahedra and corresponding Rb ions displacements between two sites. These normal modes freeze out in the I phase and change to the diffusionlike motion of the modulation wave. We also performed³⁵Cl NQR lineshape andT ₁ measurements in K₂ZnCl₄ and obtained conclusive evidence for the presence of a narrow 1q (singly modulated) I phase between 146 and 149 K.