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Monday, November 22, 2010

Ferromagnetism (in short) Part 2

Nature of Ferromagnetic carriers
  • Entire magnetization must be essentially associated with electron spin, and not at all with the orbital motion of electrons.
  • Argon core (1s22s22p63s23p6) of Fe , Co and Ni can be left out of account as a source of ferromagnetism.
  • 4s electrons are responsible for electrical conductivity and crystal binding.
  • Thus 3d electrons with unpaired spins are responsible for magnetization of these metals.
  • An effective number of magnetic moment carriers per atom should be non integral, despite that each atom has an integral number of electrons Fe - 4 electrons  :   Co - 3 electrons : Ni - 2 electrons and each electron contributes a magnetic moment of 1μB due to spin alone.
  • Above argument applies to free atom but here they are bound into solids where atomic levels are bounded into bands.
  • Non integral values 2.22μB, 1.72μB and 0.54μB for Fe, Co, and Ni  resp. of magnetic moment carriers which each atom supplies can be explained as follows : Wide 4s band of these metals overlaps with narrow 3d band. As a consequence , there is , on an average a certain fraction of total number of 3d plus 4s electrons in each band; the relative occupation of two bands being determined by fermi level EF
          for example in case of nickle 10 sd electrons are distributed in them in such a way that on the average 9.40 electrons are in 3d band and 0.6 in 4s band. In accordance with hund rule 5 electrons set their spins parallel to the field and remaining 4.40 set their spins anti parallel to the field. Thus net parallel spin of Ni atom would be 5-4.40 = 0.60 and hence magnetic moment is 0.60μB agrees fairly with the experimental value

Origin of exchange interaction

  • Explanation of large value of molecular field is based on non magnetic interaction that is exchange interaction.
  • Exchange interaction arises as a consequence of Pauli's Exclusion principle. Because of this principle we can not change the relative orientation of two spins without changing the spatial distribution of charge , clearly indicating that interaction exists between two atoms.
  • This interaction depends on relative orientation of electron spins not on the magnetic moments.
  • The energy of this interaction between atoms i , j bearing spins Si , Sj is of the form Eex=-2JeSi.Sj where Je is the exchange integral , its value is related to the overlap of the charge distribution of atoms i and j i.e., on their inter atomic separation.
  • Energy of parallel configuration is lower than that of anti parallel by amount 2Je this implies that former configuration is more stable favouring magnetization to occur.
  • Note that exchange interaction is positive only for iron group and negative for others.

Ferromagnetic domains
  • The fundamental problem of ferromagnetism is to explain why the elementary moments of a ferromagnetic material can be aligned so much more easily then those of paramagnetic materials.
  • Weiss suggested that these were forces of interaction between elementary magnetic moments tending to make each one parallel to their neighbours.
  • Such forces would cause all moments to be aligned in the same direction at absolute zero of temperature and this ordering of moments would continue when temperature is raised, though with increasing deviation from perfect alignment, until a critical temperature is reached , above which the moments are arranged in random, as in a paramagnetic material.
  • Weiss theory can thus account for the fact that ferromagnetic materials may be spontaneously magnetized even in the absence of external magnetic field ; it does not explain why the majority of ferromagnetic are not actually found in this spontaneously magnetized state , but are much more likely to have zero magnetization.
  • This difficulty can be met by introducing the hypothesis of domain theory.
  • Here supposed that the forces of interaction only maintained the parallel alignment of elementary moments over fairly small regions .
  • Actual specimen are composed of small regions called domains , within each of which the local magnetization is saturated.
  • The direction of magnetization of different domains need not be parallel.
  • The increase of gross magnetic moment of a ferromagnetic specimen in an applied magnetic field takes place by two independent processes : (1) In weak applied fields the volume of domains favorably oriented w.r.t. the field increases at the expense of unfavorably oriented domains         (2) In strong applied fields the domain magnetization rotates towards the direction of the field.

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