# Magnetic domains

Magnetic domains

A magnetic domain describes a region within a material which has uniform magnetization. This means that the individual moments of the atoms are aligned with one another. In most materials, domains do not naturally exist. The materials have to be exposed to a magnetic field, which will cause the individual moments to try and align with the field, which will eventually nucleate domains. The regions separating magnetic domains are called domain walls where the magnetisation rotates coherently from the direction in one domain to that in the next domain.

Development of Domain Theory

Magnetic domain theory was developed by Weiss who suggested their existence 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, namely easy axes. Weiss still had to explain the reason for the alignment of atomic moments within a ferromagnetic and he came up with the so called Weiss mean field. This was essentially an interatomic interaction that caused neighbouring moments to align parallel since it was more energetically favourable.

In the original Weiss theory the mean field was proportional to the bulk magnetisation M, so that

$H_e = alpha M$

where $alpha$ is the mean field constant. However this is not applicable to ferromagnets due to the variation of magnetisation from domain to domain. In this case, the interaction field is

$H_e = alpha M_s$

Where $M_s$ is the saturation magnetisation at 0K.

Energy Considerations

The existence of magnetic domains is a result of energy minimisation.Landau and Lifshitz [1] proposed theoretical domain structures based on a minimum energy concept, which forms the basis for modern domain theory. The primary reason for the existence of domains within a crystal is that their formation reduces the magnetic free energy. In the simplest case for such a crystal, the energy, E, is the sum of several free energy terms:

E = (Eex+Ek)+Eλ+ED+EH (3) where Eex is the exchange energy, Ek is the magnetocrystalline anisotropy energy, Eλ is the magnetoelastic energy, ED is the magneto-static energy, and EH is the energy of the domains in the presence of an applied field. There is also a wall energy Ew which is examined in detail in section 1.5.4. However, since Ew comprises Eex and Ek, it is not necessary to include Ew as a separate term in equation 3.

1. Cited in Carey R., Isaac E.D., Magnetic domains and techniques for their observation, The English University Press Ltd, London, (1966).

Magnetostatic Energy

This is essentially the energy associated with sources of internal or external fields.

Magnetostrictive Energy

This energy is based on the effect of magnetostriction. The magnet establishes a preferred axis when pressed in order to decrease the pressure.

Anisotropy Energy

The favourability for moments to align along certain axes.

Zeeman Energy

Energy resulting from an externally applied field.

Domain Observation

There are many ways to observe magnetic domains. Each method has a different application because not all domains are the same. In condensed matter, domains can be circular, square, irregular, elongated, and striped, all of which have varied sizes and dimensions. Large domains, within the range of 25-100 micrometers can be easily seen by Kerr microscopy, which applies a physical phenomenon called the magneto-optic Kerr effect. Other domains, such as domains within the range of a few nanometers can be documented by the use of magnetic force microscopy.

ee also

*Weiss domains
*Magnetostatic energy

References

*cite book |author=Jiles, David |title=Introduction to magnetism and magnetic materials |publisher=Chapman & Hall |location=London |year=1998 |isbn=0-412-79860-3

* [http://www.magnet.fsu.edu/education/tutorials/java/domains/index.html Interactive Java tutorial on magnetic domains] National High Magnetic Field Laboratory
* [http://schulzeundschultze.anphy.uni-duesseldorf.de/veroff/Diplome/Volker.Solinus/node3.phtml Magnetismus und Magnetooptik] a German text about magnetism and magneto-optics

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