some questions about TB2J

[Berry2Smith]

Dear Xu He
I have read the manual of TB2J, and there are some questions about averaging multiple parameters, which you mention in the manual. After reading, I know the purpose to do this is that the z component of DMI and the 𝑥𝑧, 𝑦𝑧, 𝑧𝑧, 𝑧𝑥, 𝑧𝑦, components of the anisotropic exchanges are non-physical. I want to ask you where the wrong come from and why we do this average. At the same time, I have read the CrI3 example you provide in git hub. I find that there is large different between the exchange parameters TB2J calculating and total energy method. The CrI3 is out-of-plane ferromagnetism, but the result of TB2J show that the anisotropic exchange parameters are negative, which is different from the result of experiment and the 𝑥𝑧, 𝑦𝑧, 𝑧𝑧, 𝑧𝑥, 𝑧𝑦, components of the anisotropic exchanges are not vanish. Could you tell me the reason for this?
thank you!!!