Rb87nuclear-magnetic-resonance study of the cubic to tetragonal phase transition in RbCaF3

Abstract

The static and dynamical phenomena occurring around the structural phase transition at ${T}_{c}\ensuremath{\simeq}195.90\ifmmode\pm\else\textpm\fi{}0.15$ K in RbCa${\mathrm{F}}_{3}$ have been investigated by means of $^{87}\mathrm{Rb}$ Fourier-transform NMR measurements. The second-order shift of the central line due to the static quadrupole perturbation has been related to the electric field gradient arising at the Rb site below ${T}_{c}$ and the temperature dependence of the angle of rotation $\ensuremath{\varphi}$ of the Ca${\mathrm{F}}_{6}$ octahedra has been obtained. The $^{87}\mathrm{Rb}$ spin-lattice relaxation rate above ${T}_{c}$ has been related to the rotational fluctuations of the octahedra induced by the critical-soft-mode branches, from which information on the symmetry and the anisotropy of the fluctuations are derived. The analysis of the results shows: (i) below $T\ensuremath{\simeq}170$ K the temperature dependence of $\ensuremath{\varphi}$ is well described by the classical mean-field approximation, with critical exponent $\ensuremath{\beta}=\frac{1}{2}$ and extrapolated transition temperature ${T}_{0}=220$ K; (ii) above about 170 K a nonclassical critical behavior is evidenced, the apparent critical exponent being not equal to $\frac{1}{3}$, suggesting a possible changeover in the dimensionality of the correlations of the rotations; (iii) the rotational fluctuations appear to be predominantly of ${R}_{25}$ symmetry but strongly anisotropic, i.e., only slightly correlated in adjacent (100) planes as is consistent with the hypothesis of softening of a large portion of the $R\ensuremath{-}M$ branch. Order-of-magnitude estimates for the static angle of rotation as well as for the degree of anisotropy of the fluctuations are also obtained and discussed.