From the Wien2k UG, chapter 7.1 on lapw0, I take it that Wien2k
calculates the potential, and from that the EFG, from the TOTAL electron
density. For lapw0 explicitely including interstitials, for the
decomposition in lapw2 (chapter 7.7) explicitely only the electron
density in the atomic sphere. So as a reminder to Muhammad there may
appear (minor) differences within Wien2k between the two methods.

Exactly. This is the difference between the :EFGxxx (total) and :VZZxxx (in sphere) labels.

But in my understanding both calculations in Wien2k always include core,
semi-core, and valence electrons (within the atomic sphere)?

Yes, that's what I think too.

The difference to VASP can then occure because that code only considers core
states for the EFG?

The opposite. VASP uses only valence states for the EFG (I think). If there would be a sizeable 3p contribution for Co, then VASP would miss it. We observed such sizeable 5p core contributions to the EFG in lanthanides, where the core anisotropy was induced by the 4f anisotropy (http://dx.doi.org/10.1103/PhysRevB.77.155101, Table II). No idea whether a related mechanism could be at work for Co in this crystal (I doubt), but if all obvious other explanations fail it is worth trying (@Muhammad : there is not much more to explain, take the pdf quoted before, understand the example on page 9, and apply it to your own case).

Stefaan
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