The many-electron ground-state determines uniquely the potential in Spin-Density-Functional Theory for non-collinear magnetism

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 non-collinear magnetic fields and systems with more than one electron. We then discuss the non-collinear exchange and correlation energy functional and suggest improvements.