According to what your are saying , the real magnetic structures for
Chromide is tetragonal and orthorhombic and not cubic as it's mentionned
in the userguide.
I think the cubic magnetic structure fo Cr is given just to simply the
calculation for the beginners of the antiferromagnetic calculation.
The deviation from cubic symmetry is very, very small, and for most
purposes it is perfectly fine to treat Cr as cubic.
Moreover, spin-orbit coupling is needed to allow the magnetic moments to
break the cubic symmetry to tetragonal. Spin-orbit coupling is a very
small effect for a light element as Cr. And in order to get the
reduction to orthorhombic symmetry, the spin-density wave in Cr is must
be taken into account (its wave vector is transversal to the magnetic
moments between 123 K and 311 K, whence the orthorhombic symmetry -- it
is parallel to the magnetic moments between 0 K and 123 K, that's why a
tetragonal symmetry is possible).
When Cr is approximated as an antiferromagnetic crystal without
spin-density wave and without spin-orbit coupling, its ground state is
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