An explicit derivation of a relation between magnetization M and saturation magnetization Ms

An explicit relationship between a magnetization vector M and its saturation magnetization M_s is derived using the definition of M along with assumptions of the continuum exchange theory. The obtained expression is found to be an extension of the commonly used fixed-length constraint and represents the continuous analog of it for the elementary moment per unit volume. The derivation of this relation is carried out in detail and important potential implications relating to equations for M are also highlighted.