- 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
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.
Ferromagnetism (in short) Part 1
at 7:22:00 AM
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