  A description of non-collinear magnetism in the framework of spin-density
functional theory is presented for the exact exchange energy functional which
depends explicitly on two-component spinor orbitals. The equations for the
effective Kohn-Sham scalar potential and magnetic field are derived within the
optimized effective potential (OEP) framework. With the example of a
magnetically frustrated Cr monolayer it is shown that the resulting
magnetization density exhibits much more non-collinear structure than standard
calculations. Furthermore, a time-dependent generalization of the non-collinear
OEP method is well suited for an ab-initio description of spin dynamics. We
also show that the magnetic moments of solids Fe, Co and Ni are well
reproduced.
