Magnetic Annealing Effect in Cobalt-Substituted Magnetite Single Crystals

The effect of magnetic annealing at 375°K on the room-temperature anisotropy of a series of six single crystals in the composition series ${\mathrm{Co}}_x{\mathrm{Fe}}_{3-x}{\mathrm{O}}_4$, in the range of $x$ values between 0.0 and 0.15, is investigated. The anneal-induced anisotropy is shown to be represented by the equation $W_U=-F{\Sigma }_i{{\alpha }_i}^2{{\beta }_i}^2-G{\Sigma }_{i>j}{\alpha }_i{\alpha }_j{\beta }_i{\beta }_j$, where ${\alpha }_i$ and ${\beta }_i$ are direction cosines of the magnetization during measurement and during the annealing process, respectively. $F$ and $G$ are shown to vary with $x$ in a regular fashion: $F\approx 10.1\times {10}^6{x}^2$ erg/cc and $G\approx 9.25\times {10}^{6}x$ erg/cc. These results cannot be explained by the Néel orientation-ordering model or by the precipitate model of magnetic annealing. A new model, involving cobalt ions individually rather than in pairs or larger agglomerates, is introduced.