The nature of magnetic and anisotropic properties of yttrium iron garnets with substitutional Ce3+, $Sm^{3+}$, $Nd^{3+}$ and $Tm^{3+}$ ions

A great body of experimental data on the magnetic and anisotropic properties of yttrium iron garnets doped with $Ce^{3+}$, $Sm^{3+}$, $Nd^{3+}$, and $Tm^{3+}$ ions have been considered. The data obtained are compared with the available theoretical concepts concerning anisotropy and magnetostriction of ferrimagnetics. The possible nature of magnetic anisotropy in these compounds is suggested. It is shown that for all the ferrites studied, the magnetic anisotropy at small concentrations of rare-earth ions can be explained within the framework of the single-ion model, whereas at high concentrations the two-ion model must be used because the anisotropic exchange interaction between pairs of magnetic ions must be taken into account.