Firefly Algorithm Applied to Noncollinear Magnetic Phase Materials Prediction

In most noncollinear crystal magnets, the number of metastable states is quite large and any calculation that tries to predict the ground state can fall into one of the possible metastable phases. In this work, we generalize the population based meta-heuristic firefly algorithm to the problem of the noncollinear magnetic phase ground state prediction within density functional theory (DFT). We extend the different steps in the firefly algorithm to this specific problem by using polarized constrained DFT calculations, whereby using Lagrange multipliers the directions of the atom magnetic moments remain fixed. By locking the directions of the magnetic moments at each search iteration, the method allows one to explore the entire Born-Oppenheimer energy surface of existing and physically plausible noncollinear configurations present in a crystal. We demonstrate that the number of minima can be large, which restrains the use of exhaustive searches.