Magnetic Structures of ${\mathrm{Er}}_2$${\mathrm{O}}_3$ and ${\mathrm{Yb}}_2$${\mathrm{O}}_3$

The magnetic structure of ${\mathrm{Er}}_2$ ${\mathrm{O}}_3$ and ${\mathrm{Yb}}_2$ ${\mathrm{O}}_3$ have been determined by analysis of neutron diffraction data on powders and single crystals. Noncollinear antiferromagnetic structures were found, with the moment direction related to the local symmetry axis. For ${\mathrm{Er}}_2$ ${\mathrm{O}}_3$, the moment on the $C_2$ site is $(5.36\mathrm{}\pm 0.08){\mu }_B$ and at the $C_{3i}$ site the moment is $(6.06\mathrm{}\pm 0.23){\mu }_B$. For ${\mathrm{Yb}}_2$ ${\mathrm{O}}_3$, the corresponding moments are $(1.86\mathrm{}\pm 0.06){\mu }_B$ and $(1.05\mathrm{}\pm 0.06){\mu }_B$. The Néel points are 3.4°K for ${\mathrm{Er}}_2$ ${\mathrm{O}}_3$ and 2.3°K for ${\mathrm{Yb}}_2$ ${\mathrm{O}}_3$. Calculations of the dipole-dipole energies for the observed structures indicate that the dipole forces are not sufficient to explain the structures. The dependence of the long-range magnetic order on the reduced temperature is the same in both systems. Good agreement with this temperature dependence was obtained by assuming a biquadratic exchange interaction and making a simple molecular-field approximation.