Elementary Mechanisms of Magnetization in Mixed Oxides of Iron and Cobalt

Abstract

The magnetic properties of mixed ferrites of iron and cobalt of the general class, [$x{\mathrm{Fe}}_{2}{\mathrm{O}}_{3},(1\ensuremath{-}x)\mathrm{CoO}$], where $x$ is the molar fraction, varying from 0.5 to 0.6, are studied. Depending on the conditions of preparation, a small amount of the trivalent iron may also transform into the bivalent form. These materials not only possess remarkable magnetic properties but are particularly amenable to a theoretical as well as experimental study of the fundamental mechanisms involved in orientation in a magnetic field, coercive force, remanence, initial susceptibility, law of approach to saturation, and the energies of magnetization. An attempt has been made to correlate all these factors for these materials.An x-ray examination shows that these materials consist of only a single phase. Direct evidence concerning the mechanism of orientation by annealing in a magnetic field has been obtained. A study of the magnetostriction as a function of composition, density, and temperature---both on oriented and non-oriented materials---permits us to investigate the important factors affecting the fundamental mechanism of magnetization. These materials reveal an unusual characteristic in that the values for magnetostriction are very high ($\ensuremath{\lambda}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$) and their dependence on temperature is very great ($\ensuremath{\lambda}\ensuremath{\sim}{10}^{\ensuremath{-}4}$ at 20\ifmmode^\circ\else\textdegree\fi{}C and 3\ifmmode\times\else\texttimes\fi{}${10}^{\ensuremath{-}4}$ at -196\ifmmode^\circ\else\textdegree\fi{}C). The basic phenomena can thus be readily characterized.As for the coercive force, we place emphasis on the fact that the value of ${H}_{c}$ depends on the density. When the density, $\ensuremath{\delta}$, of the materials is less than 2.9 (theoretical density is 5.1), the value of ${H}_{c}$ for a given temperature is independent of $\ensuremath{\delta}$ which strongly suggests rotations as the only elementary mechanism. Between -80\ifmmode^\circ\else\textdegree\fi{}C and room temperature, we have shown that ${H}_{c}$ is effectively only a function of the magnetoelastic energy. At temperatures lower than this, the phenomena are more complicated and one must consider as well the magnetocrystalline energy in order to account for the values of ${H}_{c}$ encountered. If the density is between 2.9 and 5.1, ${H}_{c}$ depends on $\ensuremath{\delta}$ and, therefore, on the relative volume of voids. Accordingly, it is probable that, in this case, wall displacements also contribute to the properties and we have shown that ${H}_{c}$ is approximately proportional to the square of the volume of voids.We next give a theoretical study of the remanent magnetization. The value of the ratio $\frac{{I}_{r}}{{I}_{s}}$, with a mechanism of orientation which places the magnetic vectors along cubic axes nearest the direction of the field, is in good agreement with our experimental results, at least to -80\ifmmode^\circ\else\textdegree\fi{}C. Below this temperature, other phenomena intervene which we shall discuss.A theoretical and experimental study of the initial susceptibility both on oriented and non-oriented materials has made it possible for us to discern the particular mechanisms which affect the orientation, the coercive force, and the remanence. The ratio $\frac{{\ensuremath{\chi}}_{\mathrm{oriented}}}{{\ensuremath{\chi}}_{\mathrm{n}\mathrm{o}\mathrm{n}\ensuremath{-}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{d}}}$ has been confirmed.An investigation of the law of approach has proved that in all cases Weiss's law, ${\ensuremath{\sigma}}_{H}={\ensuremath{\sigma}}_{\ensuremath{\infty}}[1\ensuremath{-}(\frac{a}{H})]$, is confirmed. The value of "$a$" depends on the relative volume of voids and on $\ensuremath{\lambda}$.A study of the energy of magnetization as a function of temperature on both oriented and non-oriented materials has afforded a supplementary proof of the interconnection between the different mechanisms.Finally, we give a r\'esum\'e of the principal magnetic characteristics of these mixed oxides.