In the antiferromagnetic spin system, superexchange leads to the dominant isotropic coupling. One of the high-order effects, due to crystal field, is written as , which is a constant for these spin- high- materials. Another second-order effect is the spin-orbital coupling. This effect will pick up a preferred direction and lead to an term, which also arises due to the lattice distortion in . More complicated terms, like the antisymmetric exchange, can also be generated. For simplicity and clarity, we focus the study on the antiferromagnetic Heisenberg model with an Ising-like anisotropy as in Equation 6.12. The anisotropy parameter h relates to the usual reduced anisotropy energy through . In the past, the anisotropy field model, , has also been included. However, its origin is less clear and, furthermore, the Ising symmetry is explicitly broken.