Field Dependence of the Intrinsic Domain Magnetization of a Ferromagnet

In this paper, the variation of the intrinsic domain magnetization of a ferromagnetic with the external magnetic field, is obtained. The basis of the treatment is the exchange interaction model amplified by explicit consideration of the dipole-dipole interaction between the atomic magnets. Approximations appropriate to low temperatures and equivalent to those used by Bloch in his derivation of the ${T}^{1}$ law, are introduced. The resultant expression for the intrinsic volume susceptibility decreases slowly with increasing field; at high fields the functional dependence is as the inverse square root of the field. The variation with temperature is linear; at room temperature and for fields of about 4000 gauss, the order of magnitude of the (volume) susceptibility is ${10}^{\ensuremath{-}4}$. The results are compared with experiment and satisfactory agreement is found.