Hermit = false is wrong?

[tombadmanship]

Hi,
I've emailed about this several times. In the manual, it says that the dispersions provided by Hermit = 0/false are wrong. Setting hermit = 0 is the only way I can generate results for my system. Can you please explain to me in what way it is wrong, and if the results could be considered correct or approximate in any context?
thanks.

[mducle]

@tombadmanship SpinW development has mostly moved to https://github.com/spinw/spinw - Sandor has moved on from physics and doesn't really have time to develop SpinW any more. I've also copied this question and answer to that repository.

To answer your question - a non-hermitian Hamiltonian matrix can give imaginary eigenvalues (imaginary magnon energies) which cannot be correct. This comes about basically because the exchange interaction and the magnetic structure inputted are inconsistent in some way (e.g. an extreme case would be giving a ferromagnetic nearest neighbour exchange interaction in an antiferromagnetic structure; but it could also be something like an incommensurate structure with slight wrong k or the spins not agreeing with the SIA).

Now, it could be just a numerical issue and you can solve this by optimising the magnetic structure using optmagsteep - you can then plot the magnetic structure and see whether the program has changed too much or not. This is analogous to "relaxing" the crystal structure in a DFT calculation: the calculation is only an approximation to the reality and using real world structures often yields inconsistent calculations - instead of forcing the calculation to use the experimental structure you should use a consistent "theoretical" structure (as long as that structure is not totally different from the experiments). If the relaxation is producing completely different structures then you've likely got incorrect exchange parameters and should change them.

Another aspect is that SpinW doesn't consider every interaction which may be present in your material - it could be that some other interaction is stabilising a particular magnetic structure in the real material which would not be stable with purely magnetic interactions. So, if you are only getting very small imaginary energies (<0.1meV say) I would say that this is probably ok - you'd have to judge based on other information whether you should adjust your magnetic structure or exchange parameters.