Mössbauer Spectra of Mixed Crystals; Diamagnetically Substituted Yttrium Iron Garnet in the Critical Region

There is a range of temperature where the Mössbauer spectra of ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}_{}^{3+}{}_{}{}^{}$ in diamagnetically substituted magnetically ordered iron oxides show broad lines and may be reproduced by local-molecular-field theory. The lines can exhibit a well-defined structure if the number of neighboring cation sites is less than six, and the spectra can then be used to determine whether the cation distribution is random. Such is the case for ${\mathrm{Y}}_3{\left({\mathrm{Fe}}_{1-x}{\mathrm{Sc}}_x\right)}_2{\left[\mathrm{Fe}\right]}_3{\mathrm{O}}_{12}$ with $x=0.10\mathrm{} \mathrm{and} 0.25$. The site preferences of other trivalent cations in yttrium iron garnet (YIG) are measured, including ${\mathrm{Rh}}^{3+}$ which goes onto $a$ sites. At higher temperatures, central peaks appear in the spectra of mixed oxides, and they grow at the expense of the magnetically split spectrum until it finally disappears at $T_c$. The spectra of ${\mathrm{Y}}_3{\left({\mathrm{Fe}}_{0.75}{\mathrm{Sc}}_{0.25}\right)}_2{\left[\mathrm{Fe}\right]}_3{\mathrm{O}}_{12}$ were studied in and around this broad critical region. An applied field produces increased hyperfine splitting, which is correlated with the static magnetic susceptibility. The mixed spectra cannot be explained by a range of ordering temperatures in different parts of the crystal, or by independent relaxation of the ionic spins. Short-range collective behavior is indicated, with coupled moments of $({10}^2-{10}^4){\mu }_B$ around $T_c$. A computer study of the geometry of the random lattice shows that there is no tendency to form localized clusters of the right size. The short-range order is probably evanescent.