INDEX

Sr.No.                    Title                                                          Page no.

1.             INTRODUCTION TO DOMAIN                              1

2.             REVIEW OF LITERATURE                                     2

3.             DEVELOPMENT OF DOMAIN THEORY              3

4.             FORMATION OF DOMAIN                                  4-6

5.             DOMAIN WALL                                                    7-8

6.             ENERGY CONSIDERATION                                   9

7.             APPLICATION-MAGNETIC DOMAIN IN      10-11

FERROMAGNET

8.              BIBLIOGRAPHY                                                    12

INTRODUCTION

DOMAIN THEORY OF MAGNETISM

Magnetic domains

Domain theory states that inside a magnet there are small regions in which the magnetic alignments of all the atoms are aligned in the same directions. A magnetic domain within a material has uniform magnetization and seperated by other domain by domain walls of thickness between about 5 to 200 nanometer depending upon the material. In the next domain it may be in a completely different direction.  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. On average over the many domains in the magnet there is no preferential direction for the magnetic force. However, using a magnet the direction of the magnetic direction in each domain can be made to point in the same direction. In this way the magnetic field can be increased.

REVIEW OF LITERATURE

• Weiss discovered in 1907 that the magnetic moment of atoms (”elementary magnets”) of ferromagnetic materials become oriented, even without an external magnetic field. The size of these oriented domains is in the range of 10^-3 to 10^-5 mm including a volume of about 10⁶ to 10⁹ atoms. The orientation is related to the crystal structure of the material.
• Carey R., Isaac E.D.,in 1966 at the English University Press Ltd, London worked on  Magnetic domains and techniques for their observation,
• Jiles, David (1998). Introduction to magnetism and magnetic materials

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

Where 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

Where M_s is the saturation magnetisation at 0K.

FORMATION OF DOMAINS

Consider a bar magnet which has been magnetised such that the entire magnet forms a single magnetic domain. Surface charges will appear at either end of the crystal. Associated with the surface charges is a secondary magnetic field called the demagnetising field which acts to reduce the magnetic field. The energy of the surface charges is called the magnetostatic energy.

Domain Formation in a Magnet

The magnetostatic energy can be reduced if the crystal forms a second domain, magnetised in the opposite direction. In this way, the separation of positive and negative surface charges are reduced decreasing the spatial extent of the demagnetising field. The reason being that energy is required to produce and maintain the region of transition from one domain to another, the domain wall.

Equilibrium will be reached when the magnetostatic energy is equal to the energy required to maintain the domain walls. However, domains are much larger than the individual molecules within the magnet.

There are only 4 ferromagnetic elements at room temperature. Of these, iron (Fe), nickel (Ni), and cobalt (Co). The fourth is gadolinium (Gd).

The formation made visible with the use of magnetic colloidal suspensions which concentrate along the domain boundaries. The domain boundaries can be imaged by polarized light, and also with the use of electron diffraction. Observation of domain boundary movement under the influence of applied magnetic fields has aided in the development of theoretical treatments. It has been demonstrated that the formation of domains minimizes the magnetic contribution to the free energy.

if a magnetic field is applied to the crystal, the domains that align with the

magnetic field will grow as the expense of the domains that are pointing in other

directions.

DOMAIN WALL

Domain wall (B) with gradual re-orientation of the magnetic moments between two 180-degree domains (A) and (C)

In magnetism, a domain wall is an interface separating magnetic domains. It is a transition between different magnetic moments and usually undergoes an angular displacement of 90° or 180°. Domain wall is a gradual reorientation of individual moments across a finite distance. The domain wall thickness depends on the anisotropy of the material, but on average spans across around 100-150 atoms.

The energy of a domain wall is simply the difference between the magnetic moments before and after the domain wall was created. This value is usually expressed as energy per unit wall area.

The width of the domain wall varies due to the two opposing energies that create it: the Magnetocrystalline anisotropy energy and the exchange energy (J_ex), both of which want to be as low as possible so as to be in a more favorable energetic state. The anisotropy energy is lowest when the individual magnetic moments are aligned with the crystal lattice axes thus reducing the width of the domain wall. Whereas the exchange energy is reduced when the magnetic moments are aligned parallel to each other and thus makes the wall thicker, due to the repulsion between them. (Where anti-parallel alignment would bring them closer – working to reduce the wall thickness.) In the end an equilibrium is reached between the two and the domain wall’s width is set as such.

An ideal domain wall would be fully independent of position, however, they are not ideal and so get stuck on inclusion sites within the medium, also known as Crystallographic defects. These include missing or different (foreign) atoms, oxides, insulators and even stresses within the crystal. This prevents the formation of domain walls and also inhibits their propagation through the medium. Thus a greater applied magnetic field is required to overcome these sites.

The magnetic domain walls are exact solutions to classical nonlinear equations of magnets .

Energy Considerations

Rotation of orientation and inrease in size of magnetic domains due to an externally applied field (compare Zeeman energy).

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.

APPLICATION -

Magnetic Domains IN FERROMAGNETS:

Ferromagnetic materials get their magnetic properties not only because their atoms carry a magnetic moment but also because the material is made up of small regions known as magnetic domains. In each domain, all of the atomic dipoles are coupled together in a preferential direction. This alignment develops as the material develops its crystalline structure during solidification from the molten state. Magnetic domains can be detected using Magnetic Force Microscopy (MFM) and images of the domains like the one shown below can be constructed.

During solidification, a trillion or more atom moments are aligned parallel so that the magnetic force within the domain is strong in one direction. Ferromagnetic materials are said to be characterized by “spontaneous magnetization” since they obtain saturation magnetization in each of the domains without an external magnetic field being applied. Even though the domains are magnetically saturated, the bulk material may not show any signs of magnetism because the domains develop themselves and are randomly oriented relative to each other.

Ferromagnetic materials become magnetized when the magnetic domains within the material are aligned. This can be done by placing the material in a strong external magnetic field or by passing electrical current through the material. Some or all of the domains can become aligned. The more domains that are aligned, the stronger the magnetic field in the material. When all of the domains are aligned, the material is said to be magnetically saturated. When a material is magnetically saturated, no additional amount of external magnetization force will cause an increase in its internal level of magnetization.

BIBLIOGRAPHY

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• www.wikipedia.com
• www.answer.com
• www.goiit.com
• MAGNETIC DOMAINS BOOK IS ALSO REFERRED