The effective field is the local field felt by the magnetization. It can be described informally as the derivative of the magnetic energy density with respect to the orientation of the magnetization, as in:
where dE/dV is the energy density. In variational terms, a change dm of the magnetization and the associated change dE of the magnetic energy are related by:
Since m is a unit vector, dm is always perpendicular to m. Then the above definition leaves unspecified the component of H that is parallel to m. This is usually not a problem, as this component has no effect on the magnetization dynamics.
From the expression of the different contributions to the magnetic energy, the effective field can be found to be: