Efficient method for magnetic structure exploration based on first-principles calculations: application to MnO and hexagonal ferrites SrFe$_{12}$O$_{19}$

We propose an approach for exploring magnetic structures by using Liechtenstein's method for exchange couplings from the results of first-principles calculations. Our method enables efficient and accurate exploration of stable magnetic structures by greatly reducing the number of firstprinciples calculations required. We apply our method to the magnetic structures of MnO and hexagonal ferrite SrFe12O19. Our method correctly identifies the ground-state magnetic structure with a small number of first-principles calculations in these systems.