K39Nuclear Magnetic Resonance in KMnF3and Temperature Dependence of the Generalized Order Parameter at the Structural Phase Transition

The ${}_{}{}^{39}{}_{}{}^{}\mathrm{K}$ nuclear-magnetic-resonance spectrum in KMn${\mathrm{F}}_3$ single crystal displays, below the structural phase transition at 186 °K, a second-order quadrupole shift of the central line superimposed to the magnetic hyperfine shift. From the analysis of the data the value of the quadrupole coupling constant below $T_C$ is derived and is shown to be proportional to the square of the rotational displacement parameter for the Mn${\mathrm{F}}_6$ octahedra. The temperature dependence of this generalized order parameter below $T_C$ is described by a critical exponent $\beta =\frac{1}{2}$ but shows a renormalization of the transition temperature of about 10% ascribed to large critical fluctuations starting about 15 °K from the transition temperature. Near the transition temperature a critical exponent $\beta$ of about $\frac{1}{3}$ is obtained.