Magnetic Exchange Couplings from Noncollinear Spin Density Functional Perturbation Theory

We propose a method for the evaluation of magnetic exchange couplings based on noncollinear spin-density functional calculations. The method employs the second derivative of the total Kohn-Sham energy of a single reference state, in contrast to approximations based on Kohn-Sham total energy differences. The advantage of our approach is twofold: It provides a physically motivated picture of the transition from a low-spin to a high-spin state, and it utilizes a perturbation scheme for the evaluation of magnetic exchange couplings. The latter simplifies the way these parameters are predicted using first-principles: It avoids the non-trivial search for different spin-states that needs to be carried out in energy difference methods and it opens the possibility of "black-boxifying" the extraction of exchange couplings from density functional theory calculations. We present proof of concept calculations of magnetic exchange couplings in the H--He--H model system and in an oxovanadium bimetallic complex where the results can be intuitively rationalized.