Molecular Field Coefficients of Substituted Yttrium Iron Garnets

By fitting the Néel theory of ferrimagnetism to previously reported magnetic moment‐temperature data for several $$\{{\mathrm{Y}}_3{\mathrm{\}[R}}_x{\mathrm{Fe}}_{\text{2−x}}{\mathrm{](Q}}_y{\mathrm{Fe}}_{\text{3−y}}){\mathrm{O}}_{12}$$ compositions, where R and Q represent diamagnetic octahedral and tetrahedral substitutions, i.e., Sc³⁺, In³⁺, Ga³⁺, and Al³⁺, the molecular field coefficients were determined to have the following linear relations with the levels of substitution: $$\begin{array}{c}{N}_{\mathrm{dd}}\text{=−30.4(1−043x),}\\ N_{\mathrm{aa}}\text{=−65.0(1−042y),}\\ N_{\mathrm{ad}}\text{=97.0(1−0.125x−0.127y)\hspace{0.17em}}\mathrm{mole}/{\mathrm{cm}}^3,\end{array}$$ for x≤0.70 and y≤1.95. Since both intrasublattice coefficients are affected only by substitutions in the opposite sublattice, a strong similarity to Geller's random canting concepts is apparent. Below the antiferromagnetic transitions it is demonstrated that a clear correlation exists between the decrease in sublattice moment from canting and the reduction in magnitude of the molecular field constant. For both sublattices, the antiferromagnetic transition occurs when N_dd, N_aa∼−20 mole/cm³. This observation lends further credence to the notion that canting sets in immediately upon substitution. To demonstrate the applicability of the above results, magnetic moment‐temperature curves are computed for compositions of {Y₃} [Mg_x²⁺Fe_2−x] (Si_x⁴⁺Fe_3−x) O₁₂ and are shown to compare very favorably with experiment, thus providing a method for predicting the behavior of a wide variety of substituted garnet compositions.