Spin-Orientation Diagrams and Magnetic Anisotropy of Rare-Earth-Iron Ternary Cubic Laves Compounds

The directions of the easy magnetization in the ${\mathrm{Ho}}_x{\mathrm{Tb}}_{1-x}{\mathrm{Fe}}_2$, ${\mathrm{Ho}}_x{\mathrm{Er}}_{1-x}{\mathrm{Fe}}_2$, ${\mathrm{Dy}}_x{\mathrm{Tb}}_{1-x}{\mathrm{Fe}}_2$, ${\mathrm{Dy}}_x{\mathrm{Er}}_{1-x}{\mathrm{Fe}}_2$, and ${\mathrm{Ho}}_x{\mathrm{Tm}}_{1-x}{\mathrm{Fe}}_2$ systems have been determined, as a function of $x$ and temperature by means of the Mössbauer effect in ${}_{}{}^{57}{}_{}{}^{}\mathrm{Fe}$. If the direction of magnetization of each system is described by a ($x,T$) spin-orientation diagram, it is found that the ($x,T$) plane is divided into two or three regions, in each of which the direction of magnetization is along a different major crystal axis. Theoretical calculations based on the assumption that the magnetic crystalline anisotropy is due to the anisotropy of the interaction between the $4f$ electrons of the rare-earth ions with the crystal fields reproduced the general features of the experimental results though small discrepancies remained. Taking into account an additional contribution to the anisotropy attributed to the Fe-Fe interaction improved the agreement between the theoretical and experimental spin-orientation diagrams. From the theoretical fits to the experimental results a value of $(-0.038\mathrm{}\pm 0.003)a_0^{-2\mathrm{}}$ is derived for the ratio of the crystal field parameters $\frac{A_6}{A_4}$. The transitions between the regions of the spin-orientation diagrams are not sharp. Possible reasons for the existence of the transition regions are discussed.