A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moments of the atoms are aligned with one another and they point in the same direction. When cooled below a temperature called the Curie temperature, the magnetization of a piece of ferromagnetic material spontaneously divides into many small regions called magnetic domains. The magnetization within each domain points in a uniform direction, but the magnetization of different domains may point in different directions. Magnetic domain structure is responsible for the magnetic behavior of ferromagnetic materials like aluminium, iron, cobalt, nickel, copper, silver, gold and their alloys, and ferrimagnetic materials like ferrite. This includes the formation of permanent magnets and the attraction of ferromagnetic materials to a magnetic field. The regions separating magnetic domains are called domain walls, where the magnetization rotates coherently from the direction in one domain to that in the next domain. The study of magnetic domains is called micromagnetics. Magnetic domains form in materials which have magnetic ordering; that is, their dipoles spontaneously align due to the exchange interaction. These are the ferromagnetic, ferrimagnetic and antiferromagnetic materials. Paramagnetic and diamagnetic materials, in which the dipoles align in response to an external field but do not spontaneously align, do not have magnetic domains.
Development of domain theory Magnetic domain theory was developed by French physicist Pierre-Ernest Weiss who, in 1906, suggested existence of magnetic domains in ferromagnets. He suggested that large number of atomic magnetic moments (typically 1012-1018) were aligned parallel. The direction of alignment varies from domain to domain in a more or less random manner, although certain crystallographic axis may be preferred by the magnetic moments, called easy axes. Weiss still had to explain the reason for the spontaneous alignment of atomic moments within a ferromagnetic material, and he came up with the so-called Weiss mean field. He assumed that a given magnetic moment in a material experienced a very high effective magnetic field He due to the magnetization of its neighbors. In the original Weiss theory the mean field was proportional to the bulk magnetization M, so that H e = α M {\displaystyle H_{e}=\alpha M} where α {\displaystyle \alpha } is the mean field constant. However this is not applicable to ferromagnets due to the variation of magnetization from domain to domain. In this case, the interaction field is
H e = α M s , {\displaystyle H_{e}=\alpha M_{s},}
where M s {\displaystyle M_{s}} is the saturation magnetization at 0K. Later, the quantum theory made it possible to understand the microscopic origin of the Weiss field. The exchange interaction between localized spins favored a parallel (in ferromagnets) or an anti-parallel (in anti-ferromagnets) state of neighboring magnetic moments
Domain structure
Why domains form The reason a piece of magnetic material such as iron spontaneously divides into separate domains, rather than exist in a state with magnetization in the same direction throughout the material, is to minimize its internal energy. A large region of ferromagnetic material with a constant magnetization throughout will create a large magnetic field extending into the space outside itself (diagram a). This requires a lot of magnetostatic energy stored in the field. To reduce this energy, the sample can split into two domains, with the magnetization in opposite directions in each domain (diagram b). The magnetic field lines pass in loops in opposite directions through each domain, reducing the field outside the material. To reduce the field energy further, each of these domains can split also, resulting in smaller parallel domains with magnetization in alternating directions, with smaller amounts of field outside the material. The domain structure of actual magnetic materials does not usually form by the process of large domains splitting into smaller ones as described here. When a sample is cooled below the Curie temperature, for example, the equilibrium domain configuration simply appears. But domains can split, and the description of domains splitting is often used to reveal the energy tradeoffs in domain formation.
Size of domains As explained above a domain which is too big is unstable, and will divide into smaller domains. But a small enough domain will be stable and will not split, and this determines the size of the domains created in a material. This size depends on the balance of several energies within the material. Each time a region of magnetization splits into two domains, it creates a domain wall between the domains, where magnetic dipoles (molecules) with magnetization pointing in different directions are adjacent. The exchange interaction which creates the magnetization is a force which tends to align nearby dipoles so they point in the same direction. Forcing adjacent dipoles to point in different directions requires energy. Therefore, a domain wall requires extra energy, called the domain wall energy, which is proportional to the area of the wall. Thus the net amount that the energy is reduced when a domain splits is equal to the difference between the magnetic field energy saved, and the additional energy required to create the domain wall. The field energy is proportional to the cube of the domain size, while the domain wall energy is proportional to the square of the domain size. So as the domains get smaller, the net energy saved by splitting decreases. The domains keep dividing into smaller domains until the energy cost of creating an additional domain wall is just equal to the field energy saved. Then the domains of this size are stable. In most materials the domains are microscopic in size, around 10−4 - 10−6 m.
Magnetic anisotropy
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