(NiO example) need help with the J2 calculation

[taishan@mit.edu]

Dear all,

Can anyone help and explain to me with more details on why the J2 is calculated by the formula given in the following example please?
wiki/index.php/Estimation_of_J_magnetic_coupling

My understanding is:
E_FM = E0 - 12 J1 - 6 J2
E_AFM = E0 + 6 J2

also, why is this different from this paper? https://journals.aps.org/prb/pdf/10.110 ... .84.115114
where
E_FM = E0 - 6 J1 - 3 J2
E_AFM = E0 + 3 J2

Thank you very much,

Best,
Tai

[martin.schlipf]

If you use your equations and set J1 = 0 (neglecting it), you get the equation as given in the tutorial. Of course, you can include further magnetic structures to determine more J parameters.

When comparing to literature results, you need to be extra careful, because a lot of different definitions are used. First, you need to discuss what length your spin has (1 or 1/2 or 5/2). Depending on which one you choose, you get different values for your J's. Secondly, when you use those J's to approximate transition temperatures, you need to decide whether to use classical or quantum mechanical spins (S^2 or S*(S+1)).

[taishan@mit.edu]

Dear Martin,

Thanks very much for your reply. I guess my question then is: i) how valid is it to neglect J1 but retain J2? J1 is the nearest-neighbor exchange coupling, J2 is the next-nearest.
2) If I use the formula given in the tutorial, I have an extra minus sign: -(E_{FM}-E_{AFM})/12.
3) Could you kindly give me more details how to control spin length in vasp, and how to estimate the transition temperature please?

Thank you so much.

Best,
Tai

If you use your equations and set J1 = 0 (neglecting it), you get the equation as given in the tutorial. Of course, you can include further magnetic structures to determine more J parameters.

When comparing to literature results, you need to be extra careful, because a lot of different definitions are used. First, you need to discuss what length your spin has (1 or 1/2 or 5/2). Depending on which one you choose, you get different values for your J's. Secondly, when you use those J's to approximate transition temperatures, you need to decide whether to use classical or quantum mechanical spins (S^2 or S*(S+1)).

[martin.schlipf]

how valid is it to neglect J1 but retain J2? J1 is the nearest-neighbor exchange coupling, J2 is the next-nearest.

There is no general rule when you can neglect J1. The proper way is to include more and more Js by calculating more magnetic structures until your Js do no longer change.

If I use the formula given in the tutorial, I have an extra minus sign: -(E_{FM}-E_{AFM})/12.

The equation that you get depends on the definition of the Hamiltonian that you use. The Js are only well defined up to a prefactor. I alluded to this in the last post that the Js change depending on the length of the spin. But as soon as you evaluate quantities from the Js (like the mean field transition temperature), you will get consistent results.

Could you kindly give me more details how to control spin length in vasp, and how to estimate the transition temperature please?

I'm not sure what you mean by controlling the spin length. If you mean in the equation, then that is just a definition. You can define your spin to have length 1 or 1/2 or ... . If you are talking about the initial magnetic moment, these are set by MAGMOM.
Vasp does not give access to the transition temperature directly, but you can simulate the model Hamiltonian. The mean-field theory is even explained on wikipedia, but more advanced simulations are possible. I did a RPA and a MC simulation in these two papers a long time ago (PRB, 84, 125142, PRB, 88 094433). You can find the necessary references within.

[taishan@mit.edu]

Dear Martin,

Thank you very much for the detailed explanation and suggested papers.

Best,
Tai