In a hexagonal system the  axis is an axis of sixfold rotation symmetry. The energy density is, to fourth 
order,
The uniaxial anisotropy is mainly determined by these first two terms. Depending on the values  and , there are four different kinds of anisotropy (isotropic, easy axis, easy plane and easy cone):
* : the ferromagnet is isotropic.
*  and : the  axis is an easy axis.
*  and : the basal plane is an easy plane.
*  and : the basal plane is an easy plane.
* : the ferromagnet has an easy cone (see figure to right).
The basal plane anisotropy is determined by the third term, which is sixth-order. The easy directions are projected onto three axes in the basal plane.
Below are some room-temperature anisotropy constants for hexagonal ferromagnets. Since all the values of  and  are positive, these materials have an easy axis.
Higher order constants, in particular conditions, may lead to first order magnetization processes FOMP.