Single-ion anisotropy ($D(S_j^z{)}^2$)

Single-ion anisotropy is an orientation-dependent local spin energy, commonly $D(S_j^z{)}^2$. It differs from a linear Zeeman magnetic field term. For a classical planar spin, positive $D$ penalizes the out-of-plane component; for a spin-half quantum degree of freedom this particular square is constant.