As we are aware that there is optical mode in the phonon. Is there optical mode in the spin waves? Can spins make out-of-phase movements to lead to optical mode? If there is, how to understand its physical picture and origin? In my understandings, the antisymmetric oscillations of the spins may lead to the optical mode.
If there is optical mode of spin waves in a system where strong spin-lattice coupling exists, how do we distinguish that this is purely a spin excitation or spin/lattice coupling induced excitation?
Can anybody advise me? Thanks in advance and Merry Christmas for everybody!
Optical modes appear when there is more than one atom in the unit cell. More than one magnetic atom in the unit cell for spin waves.
Dear Quiang,
The optical spin wave does not exist, opposite of what happens with the phonons, because spreading a discrete disturbance in the spin lattice over a long wavelength makes no sense when spins have only two possible orientations. This the condition for having optical modes which move in opposite phases. This is also the reason that there are not spin waves in an Ising model.
In fact, if we have spin waves is because we assume a precession of the spins collectively allowed in an infinite number of degenerate ground states, as it happens when there is a breaking of symmetry in ferromagnetic phase. The spin waves in antiferromagnetism are much more complex to explain but the basic reason is the same.
I hope that this can help you.
Thank Igor and Daniel very much for your advice! I am very sorry for my late response since I need some time to do more research on this issue.
Daniel, it does help a lot. Thank you. I understand that for an Ising model, there is no optical mode. What about complex magnetic system? In alpha-Fe2O3 (J.Phys.C:Solid State Phys,5, 1226,(1972)) and Mn2O3 (PRB, 77, 54412(2008)), the authors claimed there is optical magnon. I attached these two papers for your reference. Could you please comment if they are correct on this issue? Thanks again for your advice.
Dear Qiang,
My answer was for "free spins" and ferromagnetic order where the magnons are usually well defined thanks to have a breaking of symmetry of the paramagnetic phase. The things are much more complex if you use antiferromagnetic order because the vacuum is degenerate and there much more possibilities. And if you include more structural conditions then the interactions have more enable modes. Thus let me try to read more carefully the papers that you have attached previously to give you my opinion.
Dear Qiang,
I have been reading the two papers and they are quite interesting, over all the first one of O Nagai et al. They obtain in formula 12 one equivalent to a dispersion law where the energy is two solutions + and - one interesting term. The sign + corresponds to the acoustic magnons and - corresponds to the optic ones. This is comprehensible but the oscillation of these quasiparticles is far to be clear, at least for me. Thus I am afraid that it would be necessary to define clearly these basic conditions if a comparison with other solutions are going to be in agreement, e.g. acoustic and optic photons, where the modes of oscillations in the lattice must be clear.
In any case, thank you very much for these references and have a good luck with the subject.
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