Single domain (magnetic)

In

Early investigators pointed out that a single-domain particle could be defined in more than one way.[4] Perhaps most commonly, it is implicitly defined as a particle that is in a single-domain state throughout the hysteresis cycle, including during the transition between two such states. This is the type of particle that is modeled by the Stoner–Wohlfarth model. However, it might be in a single-domain state except during reversal. Often particles are considered single-domain if their saturation remanence is consistent with the single-domain state. More recently it was realized that a particle's state could be single-domain for some range of magnetic fields and then change continuously into a non-uniform state.^[5]

Another common definition of single-domain particle is one in which the single-domain state has the lowest energy of all possible states (see below).

Single domain hysteresis

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. The magnitude of this moment is ${\displaystyle \mu =VM_{s}}$, where ${\displaystyle V}$ is the volume of the particle and ${\displaystyle M_{s}}$ is the

The magnetization at any point in a ferromagnet can only change by rotation. If there is more than one magnetic domain, the transition between one domain and its neighbor involves a rotation of the magnetization to form a domain wall. Domain walls move easily within the magnet and have a low coercivity. By contrast, a particle that is single-domain in all magnetic fields changes its state by rotation of all the magnetization as a unit. This results in a much larger coercivity.

The most widely used theory for hysteresis in single-domain particle is the Stoner–Wohlfarth model. This applies to a particle with uniaxial magnetocrystalline anisotropy.

Limits on the single-domain size

Experimentally, it is observed that though the magnitude of the magnetization is uniform throughout a homogeneous specimen at uniform temperature, the direction of the magnetization is in general not uniform, but varies from one region to another, on a scale corresponding to visual observations with a microscope. 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).

), though in the special case of a homogeneous sphere of radius ${\displaystyle r\,\!}$, what nowadays is known as Brown’s fundamental theorem of the theory of fine ferromagnetic particles. This theorem states the existence of a critical radius ${\displaystyle r_{c}\,\!}$ such that the state of lowest free energy is one of uniform magnetization if ${\displaystyle r<r_{c}\,\!}$ (i.e. the existence of a critical size under which spherical ferromagnetic particles stay uniformly magnetized in zero applied field). A lower bound for ${\displaystyle r_{c}\,\!}$ can then be computed. In 1988,