The concept of a single-domain particle

An attempt to calculate exchange and magnetostatic energies for several discrete atoms, which can only be done for larger interatomic distances, is discussed. All estimations of the single-domain particle size are based on certain approximations which apply to a continuous material, but break down in the limit of discrete atoms. It is shown that when these approximations are eliminated, a very small magnetic particle can never be completely saturated, even though such a state can be a very good approximation to the physical reality. The previous micromagnetic calculations are only approximately valid, which resolves the Brown paradox