Study of competing order parameters and relaxation dynamics in La1/3Sr2/3FeO3 using first-principles

La1/3Sr2/3FeO3 is a strongly correlated material exhibiting the strong interplay between spin, charge, and lattice degrees of freedom. It is an antiferromagnetic Mott insulator at low temperature below 200K accompanying a charge ordering with the Fe-O bond disproportionation. The charge ordering driven by magnetism shows the Fe3+/Fe5+/Fe3+/Fe3+/Fe5+/Fe3+ structure along the [111] direction, and it disappears above 200K as the magnetic order is suppressed. Using first-principles calculations, we identify two charge ordering structures can occur in this material. With close energetics near the ground state and study electronic and structural orders along the energy path obtained using method of climbing image nudged elastic band. We then solve the time-dependent Landau equation along the Free energy path and study the non-equilibrium dynamics of those competing order parameters. Our results can provide an insightful explanation to the slow dynamics of this material observed in the recent ultra-fast experimental measurement.