Domain theory of ferromagnetism

Domain theory of ferromagnetism explains^[1] two significant observations of materials such as iron:

1. The material may become strongly magnetized by application of a weak external magnetizing field.
2. The same specimen may return to the demagnetized state when the external field is removed.

For example, when a refrigerator magnet is applied to a refrigerator door, the iron under the magnet becomes magnetized, causing the magnet to be attracted to the door. When the magnet is removed, the spot on the door loses its magnetization.

According to domain theory, quantum mechanical exchange forces make magnetic moments of nearby atoms tend to point in the same direction. Collections of nearby atoms pointing in the same direction are called magnetic domains. Over longer distances, domains point in random directions, canceling each other, and leaving the material unmagnetized. When an external magnetic field is applied, the domains line up in the direction of the field, and add to the external field. Although an external field would have little influence on individual atoms, it has a stronger effect the on atoms in a domain, because they all point the same way. This explains why a weak external field, can cause a ferromagnetic material to become strongly magnetized.

Below a certain temperature called the Curie temperature, quantum mechanical exchange forces overcome thermal energy, which would otherwise randomize the magnetic moments of individual atoms. The existence of sufficient exchange forces in some materials makes them ferromagnetic. Each ferromagnetic material has a unique Curie temperature. Above the Curie temperature thermal energy dominates, and the material becomes paramagnetic. Domain theory also explains other magnetic properties, such as the existence of permanent magnets.

Energy minimization

A system is more stable, when it contains less energy^[2]. A magnetic field contains energy. When magnetic fields cancel each other, they contain less energy.

This is easy to demonstrate. When two bar magnets are lined up next to each other, with their north poles pointing in the same direction, they will tend to spin around with the north pole of one magnet next to the south pole of the other magnet. The energy to spin the magnets around, came from magnetic fields. After spinning around, the system contains less energy, and is more stable.

As ferromagnetic domains become smaller, the material has less magnetic energy, however, the exchange energy increases, because atoms on opposite sides of the domain boundaries are not pointing in the same direction. The magnetic energy goes down as the number of domains increases, but the energy at the boundaries goes up in proportion to the surface area of the boundaries.

There are several types of energies the influence the size, shape, and orientation of domains:

Exchange energy

The interaction of energy which makes adjacent dipoles line up in the same direction is called exchange energy.

Anisotropy energy

In ferromagnetic crystals the magnetization energy depends upon the direction of magnetization. This direction dependency is called Magnetic anisotropy, and the directions are called easy and hard:

1. Easy direction, a weak magnetic field has to be applied.
2. Hard direction, a strong magnetic field has to be applied.

For example, iron atoms are arranged in a cubic latice, and the easy direction is along the <100> edges of the cube, with the hard directions along the face diagonals <110>.^{[citation needed]} Nickel is also cubic, but the easy direction is along the body <111> diagonals of the cube, with the hard direction along the <100> edges.

Domain wall energy

Domain wall is a transition layer which separates the adjacent domains magnetised in different directions. Domain wall energy is due to both exchange energy and anisotropy energy.

Magnetostrictive energy

When domain walls are magnetized in different directions, they will either expand or shrink. This results in deformation. This effect is called magnetostriction and energy produced is called magnetostriction energy.

Magnetostatic energy

• The self-energy of a permanent magnet acting on its own field.
• The energy of interaction of a permanent magnet acting an external field.

History

Domain theory of ferromagnetism was developed by Pierre Weiss. It is understandable from the thermodynamic principle.

See also

• Bohr–van Leeuwen theorem proves classical physics cannot account for ferromagnetism
• ferromagnetism
• Magnetic domain
• Bloch wall
• Domain wall
• Weiss domain
• Weiss magneton
• Bohr magneton
• Barkhausen effect
• Coercivity

References

1. ^ Kittel, Charles (1949), Physical Theory of Ferromagnetic Domains, American Physical Society, http://rmp.aps.org/pdf/RMP/v21/i4/p541_1, retrieved 2011-09-14 
2. ^ Kittel, Charles (1986). Introduction to Solid State Physics (6th ed.). John Wiley & Sons. pp. pp. 351-352. ISBN 0-471-87474-4.