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Friday, November 19, 2010

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.

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