Mössbauer studies of the static and dynamic critical behavior of the layered antiferromagnets RbFeF4and KFeF4

Detailed ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$ Mössbauer studies of the static and dynamic critical behavior of the layered antiferromagnets RbFe${\mathrm{F}}_4$ and KFe${\mathrm{F}}_4$ are reported. All measurements were performed on single crystals with the direction of the $\gamma$ rays perpendicular to the magnetic layers. Both systems undergo a second-order phase transition at the Néel temperature $T_N=133.57\mathrm{}\left(2\right)\mathrm{}$ K for RbFe${\mathrm{F}}_4$ and $T_N=135.79\mathrm{}\left(2\right)\mathrm{}$ K for KFe${\mathrm{F}}_4$. Special attention was given to a careful evaluation of reliable values for the critical indices. In the asymptotic critical region below $T_N$, the temperature dependence of the hyperfine field $H$ is well described by the power law $H\propto t^{\beta }$, where $\beta$ is the static critical exponent of the order parameter, and $t=\frac{1-T}{T_N}$ is the reduced temperature. The following asymptotic values for $\beta$ were found: $\beta =0.316\mathrm{}\left(3\right)\mathrm{}$ for RbFe${\mathrm{F}}_4$ in the range $5\times {10}^{-4\mathrm{}}<t<\mathrm{}{10}^{-2\mathrm{}}$ and $\beta =0.151\mathrm{}\left(3\right)\mathrm{}$ for KFe${\mathrm{F}}_4$ in the range $3.8\times {10}^{-4\mathrm{}}<t<\mathrm{}5.7\mathrm{}\times {10}^{-2\mathrm{}}$. These results indicate that RbFe${\mathrm{F}}_4$ shows a three-dimensional critical behavior, in contrast to KFe${\mathrm{F}}_4$, where the magnetic transition is essentially two dimensional in nature. The present values for $\beta$ disagree considerably with the nonasymptotic values previously reported by other groups. Just above $T_N$ a characteristic line broadening $\Delta \Gamma$ due to critical spin fluctuations is observed. At the critical point $\Delta \Gamma$ diverges as $\Delta \Gamma \propto {\left|t\right|}^{-w}$, where the exponent $w$ involves, besides two static exponents, the dynamic exponent $z$. In the critical region ${10}^{-4\mathrm{}}<\left|t\right|<\mathrm{}{10}^{-3\mathrm{}}$, the following values for $w$ and the corresponding values for $z$ were obtained: $w=0.81\mathrm{}\left(6\right)\mathrm{}$, $z=2.15\mathrm{}\left(19\right)\mathrm{}$ for RbFe${\mathrm{F}}_4$ and $w=0.91\mathrm{}\left(5\right)\mathrm{}$, $z=1.29\mathrm{}\left(9\right)\mathrm{}$ for KFe${\mathrm{F}}_4$. These values are compared to those predicted by the current theory of critical dynamics. At $T_N$ the center shift and the quadrupole splitting show a pronounced anomaly that appears to be associated with the onset of magnetic ordering.