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.