[1] The possibility of single domain particles received little attention until two developments in the late 1940s: (1) Improved calculations of the upper size limit by Charles Kittel and Louis Néel, and (2) a calculation of the magnetization curves for systems of single-domain particles by Stoner and Wohlfarth.
[2][3] The Stoner–Wohlfarth model has been enormously influential in subsequent work and is still frequently cited.
If a particle is in the single-domain state, all of its internal magnetization is pointed in the same direction.
It therefore has the largest possible magnetic moment for a particle of that size and composition.
Domain walls move easily within the magnet and have a low coercivity.
Uniform of direction is attained only by applying a field, or by choosing as a specimen, a body which is itself of microscopic dimensions (a fine particle).
[4] The size range for which a ferromagnet become single-domain is generally quite narrow and a first quantitative result in this direction is due to William Fuller Brown, Jr. who, in his fundamental paper,[6] rigorously proved (in the framework of Micromagnetics), though in the special case of a homogeneous sphere of radius
, what nowadays is known as Brown’s fundamental theorem of the theory of fine ferromagnetic particles.
(i.e. the existence of a critical size under which spherical ferromagnetic particles stay uniformly magnetized in zero applied field).
In 1988, Amikam A. Aharoni,[7] by using the same mathematical reasoning as Brown, was able to extend the Fundamental Theorem to the case of a prolate spheroid.
[9] Eventually, the same result has been shown to be true for metastable equilibria in small ellipsoidal particles.
[10] Although pure single-domain particles (mathematically) exist for some special geometries only, for most ferromagnets a state of quasi-uniformity of magnetization is achieved when the diameter of the particle is in between about 25 nanometers and 80 nanometers.
[11][b] The size range is bounded below by the transition to superparamagnetism and above by the formation of multiple magnetic domains.
The frequency of jumps has a strong exponential dependence on the energy barrier, and the energy barrier is proportional to the volume, so there is a critical volume at which the transition occurs.