Ferrimagnetic Resonance in Single Crystals of Cobalt-Substituted Manganese Ferrite

Abstract

The results of microwave resonance measurements of the $g$ factor and the first- and second-order anisotropy fields $K_1\mathrm{/M}$ and $K_2\mathrm{/M}$ are summarized for crystals with the nominal composition ${\mathrm{Co}}_x{\mathrm{Mn}}_{\text{1−x}}{\mathrm{Fe}}_2{\mathrm{O}}_4$ , where $\text{0\hspace{0.17em}≤\hspace{0.17em}x\hspace{0.17em}≤\hspace{0.17em}0.10}$ . In the region ${\text{150°K<T<300°K\hspace{0.17em}Δ(K}}_1\mathrm{/M)\hspace{0.17em}=\hspace{0.17em}Ax}$ , ${\mathrm{\Delta (K}}_2\mathrm{/M)\hspace{0.17em}=\hspace{0.17em}-Bx}$ and $\mathrm{g\hspace{0.17em}=\hspace{0.17em}a+bx}$ . ${\mathrm{\Delta (K}}_1\mathrm{/M)}$ is the cobalt contribution to $K_1\mathrm{/M}$ ; similarly for ${\mathrm{\Delta (K}}_2\mathrm{/M)}$ . The results for $K_1\mathrm{/M}$ are in agreement with published values determined statically on the same crystals. For $\text{T\hspace{0.17em}=\hspace{0.17em}290°K}$ , 260°K, 230°K, 200°K, 170°K, and 140°K, $B$ is 510, 1790, 4600, 10 300, 22 400, and 50 000, respectively. At 260°K the values for $a$ and $b$ are 2.003 and 0.41 respectively, at 9400 Mc; at 17 000 Mc the values are 1.992 and 0.42. For the lower frequency at 170°K the values are 2.004 and 0.64. The two microwave frequencies were used only above 77°K; in this range the $g$ values are isotropic to better than 0.5%. At 4.2°K the effect of the cobalt upon the variation of resonance field with direction in a (110) plane cannot be accurately described by $K_1\mathrm{/M}$ and $K_2\mathrm{/M}$ . The results are compared with the successful theory for the cobalt ion substituted into ${\mathrm{Fe}}_3{\mathrm{O}}_4$ . It appears that modification of the original model is necessary to take into account the differing environment of the cobalt ion when substituted into ${\mathrm{MnFe}}_2{\mathrm{O}}_4$ .