The Role of Cation Vacancy in Magnetic Annealing of Iron-Cobalt Ferrites

The kinetics of magnetic annealing effects in iron-cobalt ferrites is studied, based on a vacancy migration mechanism. First, a formal theory is developed, which makes clear the existence of a distribution of relaxation times in the phenomena. In order to get the distribution function of the relaxation time as a function of vacancy concentration and diffusion constants, a calculation based on a rather stochastic approach has been given. It is assumed that the dispersion in the relaxation time comes principally from the time required for the vacancies to migrate throughout the entire crystal lattice. The distribution function obtained is ${\mathrm{f(\tau )\hspace{0.17em}=\hspace{0.17em}W\rho \tau /\tau }}_0\times \exp {\mathrm{(-W\rho \tau /\tau }}_0)$ , where $\rho$ is the density of vacancies, ${\tau }_0$ is the mean relaxation time for the migration of a single vacancy, and $W$ is a constant which depends on the lattice type, degree of short range ordering, and so on. On using this function the formation and the annihilation of the degree of directionality $S_u$ is expressed as ${\mathrm{\Delta S}}_u{\mathrm{\hspace{0.17em}=\hspace{0.17em}\int }}_0^{\infty }\mathrm{f(\tau )\Delta S(\tau )d(}\log \mathrm{\tau )}$ , ${\mathrm{\Delta S(\tau )\hspace{0.17em}=\hspace{0.17em}[S(\tau )-S}}^e{\mathrm{(T)](-\Delta t/\tau }}_0)$ . A quantitative calculation of the annihilation process of the magnetic annealing anisotropy in isothermal annealing accords exactly with the experimental results for iron-cobalt ferrites. There is a short discussion of the equilibrium density of vacancies in iron-cobalt ferrites using the results of our statistical thermodynamical study of the same system. Discussions of several theoretical and experimental results of iron-cobalt ferrites recently carried out in Japan are also presented. From our results we conclude that the decrease in the degree of oxidation simply makes the scale of the time constant of the relaxation process longer, therefore it is not consistent with the suggestion previously made that only cobalt ions near vacancies can rearrange rapidly.