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May I know how the denominator value of 12 comes in this example ?

https://www.vasp.at/wiki/index.php/Esti ... c_coupling

J_2 = (E_FM - E_AFM) / 12

I understand that the 2nd nearest neighbor has coordination number of 6 in NiO.

• Reading a similar thread previously posted, I wonder how is the denominator value of 12 obtained from this model?

https://www.vasp.at/forum/viewtopic.php?f=4&t=16998

I hope someone could clarify more details on how to estimate J from VASP results in OUTCAR...

• What values should be chosen for S in the above model?

I suppose in general, the magnetization (x) values we have at the end of OUTCAR can be different when computing FM and AFM configurations.

For example, if we have AFM with magnetization per site is 0.5
while for FM configuration the magnetization per site is only 0.2,

how to use this formula to estimate J in such case?

Hi,

The factor 12 comes from Eq. (7) (see also Fig. 1) in
https://doi.org/10.1088/1361-648X/aa7b00
when J_1 is neglected as done in the VASP example.

Thank you for the reference paper.

is there any relevance on how large the magnetizations at the end of the OUTCAR file in this model?
In this NiO example, the Ni magnetization (x) for AFM configuration is 1.67 and for FM is 1.75 bohr magnetons. They are maybe close enough.

However, hypothetically if the FM magnetization is much weaker than AFM, e.g. 0.3 vs 1.67, is it still okay to use this formula?
J_2 = (E_FM - E_AFM) / 12

No, the magnitude of the magnetic moment is not needed to calculate the J_n (the s_i in Eq. (3) are just unit vectors). Roughly speaking, the magnitude of the MM is somehow included in the J_n.

Thank you.
By the way, I have a related but separate question from this example.
do you have advice on how to effectively change the INCAR parameters in order to obtain the FM state of a material which has AFM ground state?
Obviously we change the MAGMOM tags from AFM order to FM order (say MAGMOM 3 -3 to 3 3)

However, I found changing MAGMOM alone often resulted in much smaller magnetizations in the relaxed structure (or even close to zero).
Since the FM is not the ground state of this material, in general how should I change other parameters?

Do you know some methods that worked for you?
e.g. make the EDIFF large so it gets trapped in the higher-energy FM state instead of NM or AFM state?

As you mentioned, with MAGMOM you can start the calculation with a chosen magnetic configuration. But then, the magnitude of the magnetic moment obtained at the end of the calculation is detemined by the variational principle. If the magnetic moment is smaller than what you expected (e.g., experiment), then you can try another exchange-correlation functional. There is also M_CONSTR that may be helpful, but this is a less standard method and you have to know what you are doing. As a general comment, the way to proceed is of course first to read literature on the topic one is working on.