Density functional for noncollinear magnetic systems

Neither local-spin-density nor generalized-gradient approximation (GGA) calculations of {γ}-Fe have produced the experimental wave vector of its spiral-spin-density-wave ground state. This we attribute to the fact that these approximations for exchange and correlation are oblivious to the noncollinear nature of the magnetization. We derive the form of an additional term in the density functional which eliminates this shortcoming of the local-spin-density approximation and the GGA.