# 29.10: Summary


This TLP has covered the basic points of ferromagnetism:

1. In a magnetic atom there are two contributions to the magnetic dipole moment; firstly the spin of the electrons themselves and secondly that of electrons orbiting the nucleus.
2. Ferromagnetism occurs in materials where all the magnetic dipole moments align parallel below the Curie temperature.
3. Ferromagnetic ordering was explained by Weiss via a hypothetical average field which acts to cause the parallel alignment. However, the microscopic explanation for this can be found by looking at the Pauli Exclusion Principle; it is energetically more favourable for electrons be placed in different orbitals as this reduces the Coulomb repulsion energy and allows for the alignment of the electron spins.
4. The magnitude of the magnetisation is dependent on temperature and modelled by the Curie-Weiss law:
$\chi = \frac{C}{T-T_c} = \frac{M}{H}$
1. The formation of domains is driven by the minimisation of energy, with the main driving force often being that of the magnetostatic energy.
2. Magnetic hysteresis is seen, due to the defects found in crystals, as these hinder the movement of domain walls.
3. Hard magnets have a large coercive field, whereas soft magnets are easily demagnetised and so has a small coercive field.
4. Both magnetocrystalline anisotropy and shape anisotropy give directions in a material along which it is easier to magnetise a sample.

## Going further

### Books and Papers

1. Magnetic Materials : Fundamentals and Device Applications by N.A. Spaldin, Cambridge University Press (2003)
A good overall explanation of ferromagnetism which also covers other types of magnetism and some applications.
2. The Feynman Lectures on Physics by R.P. Feynman, R.B. Leighton and M. Sands, Addison-Wesley Publishing Company (1970)
Provides a complete explanation of magnetism including the mathematics and qualitative explanations.
3. P.A.M. Dirac, The quantum theory of the electron, Proc. R. Soc. London A 117 610-612 (1928)
4. P.A.M. Dirac, The quantum theory of the electron Part II, Proc. R. Soc. London A 118 351-361 (1928)

These are the original papers by Dirac in which the spin of the electron was derived.

### Websites

• Get Perpendicular: Hitachi Global Storage Technologies
This website gives a fun summary of one of the latest developments in magnetic memory.

This page titled 29.10: Summary is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Dissemination of IT for the Promotion of Materials Science (DoITPoMS).