Potential in spin-density-functional theory of noncollinear magnetism determined by the many-electron ground state

Since spin-density-functional theory was first proposed, but also recently, examples were constructed to show that a spin potential may share its ground state with other spin potentials. In fact, for collinear magnetic fields and systems with fixed magnetization, the mapping between potentials and ground states is invertible, provided the magnetization is not saturated and that spin potentials are determined within a spin constant. We complete the proof that the mapping is invertible also for noncollinear magnetic fields and systems with more than one electron. We then discuss the noncollinear exchange and correlation energy functional in the local-spin-density approximation and suggest improvements.