= Solution
Eu$^{2+}$ has the half-filled $4f^7$ term with $L=0$. First-order orbital magnetism is therefore quenched already at the ion level, making the dominant moment approximately spin-only. Spin-orbit-induced <magnetocrystalline anisotropy> arises only through weaker admixtures and other small interactions; magnetic dipole interactions can also contribute. This explains why a cubic anisotropy term is allowed by symmetry but numerically weak.
An appropriate insulating local-moment model is a nearly isotropic <Heisenberg model>,
$$
\boxed{H=-\sum_{\langle i,j\rangle}J_{ij}\mathbf S_i\cdot\mathbf S_j
+H_{\rm weak\ anisotropy}+H_{\rm dipolar},\qquad S=7/2,}
$$
with dominant effective ferromagnetic couplings in the sign convention $J_{ij}>0$. The Eu sublattice in rocksalt EuO is face-centered cubic; nearest- and further-neighbor effective exchanges can be retained as needed. Because the solid is not metallic, an itinerant-electron <Stoner model> or a generic free-carrier <RKKY interaction> mechanism is not the natural starting point. Exchange can still arise through virtual hopping and ligand-mediated processes in an insulator; it does not require mobile dc carriers.
Back to article page
