Semi-Classical Treatment of Spin Waves in Antiferromagnetic Systems

[thoughtgaze]

Hey,

can anyone point me to some useful reading material on the semi-classical treatment of spin waves for the antiferromagnetic case? Thanks.

 

[DrDu]

P W Anderson, Concepts in solids, World Scientific, Singapore, 1997

 

[sokrates]

P W Anderson, Concepts in solids, World Scientific, Singapore, 1997

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.

 

[genneth]

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.)

 

[sokrates]

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.

 

[genneth]

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.

 

[DrDu]

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.

 

[sokrates]

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.

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?

 

[sokrates]

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.

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.