Now , I understand the origins of the tetragonal and the orthorombic
distortions for the cubic structure of Chromium Cr.

I know how to add the spin-orbit coupling in the wien2k code to get the
tertragonal structure , but I don't know how to take  the spin-density wave
 in account .

Would you explain to me how to do that

We did that long ago:

J. Phys.: Condens. Matter 14 (2002) 3275–3283

It boils down to preparing a supercell in which one period of the spin density wave fits (in this case a 1x1x21 supercell), and preparing in case.inst antiferromagnetic moments with a cosine profile as starting situation.

In those calculations, the lattice parameters were constrained to (multiples of) the cubic values, as the effect of the spin-density wave on the energy was much larger then the effect of the induced tetragonal symmetry.

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