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I am doing spin-orbit coupling (SOC) calculations using VASP. I had done a magnetic anisotropy calculation, but I do not know how to check whether the SOC is weak or strong. Any help would be highly appreciated.

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In quantum mechanics, energies associated with coupling, just like energies in other settings, are assessed based on how they compare to other energies.

For example, inserting a spin-orbit coupling operator into a Hamiltonian, can cause a splitting of energy levels (this type of phenomenon would usually be familiar to anyone that has learned "perturbation theory" in a quantum mechanics class). We may often compare this splitting to a different type of energy splitting, such as a hyperfine splitting or a rotational splitting (just to provide two out of many possible examples). If the spin-orbit splitting is larger than, or similar in size to the other energy splitting, then it can be very significant if you're interested in things at that energy scale.

Likewise, you can compare spin-orbit splittings in one system to other systems of interest, in order to decide whether you want to call your spin-orbit coupling strong or weak. For example, the spin-orbit splitting of the potential energy curves near the dissociation asymptotes, for electronic states of Na2 are very small compared to those in Rb2, so if your benchmark is Rb2, then it's fair to say that Na2 has a relatively weak spin-orbit coupling (but it is still much stronger than in Li2.

Finally, you may want to consider whether or not the spin-orbit coupling causes a significant affect in your system. For example, people have proposed theories that say that hyperfine interactions are involved in bird navigation, and for that to work, the hyperfine interaction has to have a certain strength. In a similar molecular system, if the hyperfine interaction were to be, say 10x weaker, then the bird navigation might not even be possible because the required threshold would not be passed: In this case we could say "the hyperfine interaction is too weak in this system [for bird navigation to work]", or if the hyperfine interaction were to be so strong that something extraordinary is observed, we could say "this system has an extraordinarily strong hyperfine interaction".

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