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Antiferromagnetic spin waves

  1. Apr 11, 2010 #1

    can anyone point me to some useful reading material on the semi-classical treatment of spin waves for the antiferromagnetic case? Thanks.
  2. jcsd
  3. Apr 12, 2010 #2


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    P W Anderson, Concepts in solids, World Scientific, Singapore, 1997
  4. Apr 18, 2010 #3

    great book...

    though not quite sure whether it treats spin waves semi-classically..

    edit: in fact I just checked it and the treatment is completely quantum-mechanical.
  5. Apr 18, 2010 #4
    Can you treat spin-waves in AF semi-classically? I seem to think that you don't get a reasonable limit as the spin S -> infinity --- it oscillates in behaviour on S being a half-integer and S being integer. (And that's ignoring possible lattice frustration.)
  6. Apr 18, 2010 #5
    Yes, you can.

    Just like you can semi-classically treat, phonons, electrons, etc..

    you can treat "magnons" semi-clasically too.

    Semi-classical,in this context, means an input from quantum mechanics (like dispersion relations, density of states, or effective mass which more or less give equivalent information) accompanied with classical dynamics equations.
  7. Apr 19, 2010 #6
    No, I mean does it make for a good approximation (of course you *can* always just postulate a classical particle + corrections). Certainly in 1D spin-1/2 AF do not have spin waves as an elementary particle, since the spinon and holons are deconfined; in this case, I would say that a semi-classical treatment of spin-waves is not appropriate. Usually, in the ferromagnetic case, things are justified because S->infinity is a well defined limit in which we really do get spin waves, and we can argue for a 1/S expansion, in which case the leading order corrections can be seen as interactions. In the AF case, this can not be done analogously.
  8. Apr 19, 2010 #7


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    sokrates, I had a look at my copy again. Methinks that Anderson uses in the last chapter "anti-ferromagnetism and broken symmetry" basically a semi-classical approximation, especially the decoupling of the equation of motion, where he replaces the cross product of spin operators by their mean values, neglecting quantum fluctuations is a semi-classical argumentation.
  9. Apr 19, 2010 #8
    Maybe semi-classical is used in a different context, here. I don't know what the OP needed. I am familiar with the usage I said above.

    Just wondering, is Anderson, himself, saying it's a semi-classical treatment?
  10. Apr 19, 2010 #9
    I could not follow your argument. But "we can treat de-localized Bloch electrons as semi-classical particles using a band diagram coupled with Boltzmann equation" is what I really meant.
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