I added spin polarization for calculation of transition metal (TM) slab, and set an initial magnetic moment. but I have some questions about this：
1. How can I verify the magnetic moment of each atom? Is it to set different initial moment and find the one with the minimum energy, or compare with a theoretical value ($\mu_{TM}=\sqrt{n(n+2)}$)?
2. Whether a Hubbard U correction is needed when calculating a metallic slab? How to verify the U (and J) parameter?
Thanks in advance!
1) What do you mean with "verify" ? The size or the congifuration (AFM/FM/...) of the moments. You can get the self-consistent magnetic moments from a VASP calculation for each atom by setting the LORBIT tag to do the projections. However, when it concerns magnetic configurations, there are a lot of local minima. This meaning evaluating different starting configurations and comparing them can be needed.
2) "needed" is a strong word. If adding a U can improve the description of the solid (lattice param, bulk modulus, band gap - not applicable here) one can make the argument that it will improve the surface as well.
Your formula refers only to the spin moment of the atom without taking into account the orbital moment and applicable in some sense for the 3d metals, in which orbital angular momentum is fixed ("frozen"), and the atoms with the orbital moments of the electrons compensate each other. But in the General case, the magnetic moment is defined as the spin and orbital motion of electrons (for example, 4f transition elements). Therefore, generally speaking, it is necessary to consider the contributions of spin and orbital magnetism.
In addition, the theoretically calculated value of the magnetic moment of the ground state of the atom (and/or their ions) in the simple vector model for some metals (for example, Sm, Eu) differs from the experimental value, which is associated with mixing of states closely spaced excited energy levels (van Vleck’s paramagnetism).
The Hubbard correction is needed when the compound on which you work has localized d or f electrons.
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