- A ferromagnetic material has a spontaneous magnetic moment- magnetic moment even in zero applied magnetic field this means that electron spins and magnetic moments are arranged in regular manner.

- Consider a paramagnet with a concentration of N ions of spin S. Given an internal interaction tending to line up the magnetic moments parallel to each other , we shall have a ferromagnet.

- This internal interaction is called exchange field.

- Orienting effect of exchange field is opposed by thermal agitation.

- At elevated temperatures the spin order is destroyed.

- Exchange field can be treated as equivalent to BE (magnetic field) also assume that the exchange field B
_{E}is proportional to the magnetization M.

- Magnetization M is defined as the magnetic moment per unit volume.

- In mean field approximation each magnetic atom experiences a field proportional to the magnetization

B_{E}=λM (1)

Where λ a is constant independent of temperature.

- Each spin sees average magnetization of all the other spins and more precisely of the neighboring spins.

- Curie Temperature (T
_{c}) is the temperature above which spontaneous magnetization vanishes.

- T
_{c}separates disordered paramagnetic phase at temperature T > T_{c}from ordered ferromagnetic phase at temperature T < T_{c}.

- If B
_{a}is the external magnetic field then the effective field acting on atom or ion is

B= B_{a}+ B_{E}= B_{a}+ λM

- If χ
_{p}is paramagnetic susceptibility then

M= χ_{p}( B_{a}+ B_{E})

χ_{p}=C/T from curie law for paramagnetic materials

this implies that MT=C(B_{a}+ λM)

- Susceptibility has singularity at T=Cλ.

- At this temperature and below there exists a spontaneous magnetization , because if χ is infinite, we can have a finite M for zero B
_{a}.

- Curie-Weiss law is

χ=C/(T-T_{c}) or T_{c}=Cλ

- This spontaneous magnetization decreases very slowly as the temperature is first raised above absolute zero and drops more steeply at higher temperatures until finally falls to zero at curie temperature.

## Friday, November 19, 2010

### Ferromagnetism (in short) Part 1

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