Mössbauer study of static and dynamic critical behavior in Fe

In this paper we present the results of detailed experimental studies on the critical behavior of Fe near its critical temperature $T_c$ (here also Curie temperature $T_C$) using the Mössbauer effect. Using a highly controlled two-stage Mössbauer furnace, we made a careful measurement of the critical exponent $\beta$ and the critical exponent $z$. The value of ${\beta }_{\mathrm{eff}}$ was obtained in both source and absorber experiments and was found to be 0.379(4) for the reduced-temperature range ${10}^{-3\mathrm{}}<~t<~2\times {10}^{-2\mathrm{}}$ and 0.371(8) for ${10}^{-4\mathrm{}}<~t<~2\times {10}^{-2\mathrm{}}$, respectively. We have used correction-to-scaling form in the critical region and have obtained the universal $\beta$ as $\beta =0.367\mathrm{}\left(5\right)\mathrm{}$ and the correction amplitude $A=-0.458\mathrm{}\left(22\right)\mathrm{}$. The results on $\beta$ agree well with theory, bulk measurements on Fe, and most data on other ferromagnets in the universality class $\mathrm{}(n,d)=(3,3)\mathrm{}$. The value $z$ was measured as $z=1.93\mathrm{}\left(19\right)\mathrm{}$, which is inconsistent with the theory of short-range exchange interactions and neutron scattering results in Fe, but in agreement with previous hyperfine studies on Ni and Fe, and a recent hypothesis on the dynamic behavior in the asymptotic critical region. We have also investigated the possible magnetization dependence of the isomer shift in Fe and obtained negative results, both within 2 K of the Curie point, and in a wide region above and below the Curie point. These findings, like the $\beta$ measurements, are based on both source and absorber experiments. They disagree with Preston's observations near $T_c$. By studying the Mössbauer line intensities we observed a magnetostrictive reorientation of ferromagnetic domains as a function of temperature. This behavior is similar to that observed in some Fe alloys under the influence of compressive strain as well as temperature variation.