Theory of the Relaxation of the Uniaxial Anisotropy Induced by Ionic Migration in Iron-Cobalt Ferrites

The relaxation character of the induced uniaxial anisotropy in Co x Fe 3-x O 4 has been analyzed theoretically, employing several models and taking into account the presence of short range ordering and the detailed micro processes of vacancy migration mechanism. It is shown on mathematical grounds that the relaxation times of the processes are inversely proportional to the density of the cation vacancies, ρ, in the crystal. The accurate solution of the relaxation time can be derived specifically for the range of x =10 -(1.5∼2) . It is {aligned} 1/τ{=}4.65{·}ρ{·}f̄exp(-Q̄/kT). {aligned} The experimental results by Inoue are well described by this equation after putting f =7.5×10 12 sec -1 , and Q =1.0 eV at x =0.063. A theory is presented which takes into account the symmetry of the crystal lattice rigorously. The theory is in excellent agreement with the single crystal results by Palmer. It is pointed out that the cobalt ion neighboring a vacancy is in a trivalent state, and that electron transfer is important in lowering the activation energy of the ionic migration.