Effective magnetic anisotropy vector field

An effective anisotropy vector field that can be treated as an effective external field has been formulated for uniaxial anisotropies with n-fold symmetry within the plane containing the main axis. A simple method for obtaining the effective field for the two-fold symmetry uniaxial anisotropy and the calculated result according to the method are presented. Then the extension to n-fold symmetry anisotropies is given and the calculated results for four- and six-fold symmetry cases are demonstrated. The tips of those vector fields are found to trace hypocycloids moving oppositely with the rotation of magnetization. The newly introduced effective anisotropy vector field may make a new tool in various analysis of magnetization processes and help understand the effect of anisotropy on magnetization visually