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### Ferromagnetism (in short) Part 1

• 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 BE 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

BE=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 (Tc) is the temperature above which spontaneous magnetization vanishes.

• Tc separates disordered paramagnetic phase at temperature T > Tc from ordered ferromagnetic phase at temperature T < Tc.
• If Ba is the external magnetic field then the effective field acting on atom or ion is

B= Ba+ BE = Ba+ λM
• If χp is paramagnetic susceptibility then
M= χp( Ba+ BE)
χp=C/T from curie law for paramagnetic materials
this implies that MT=C(Ba+ 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 Ba.

• Curie-Weiss law is
χ=C/(T-Tc) or Tc=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.