Orbital magnetism of ultracold fermionic gases in a lattice: dynamical mean-field approach

We study finite-temperature properties of ultracold four-component mixtures of alkaline-earth-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including the Hund's exchange coupling term. Our main goal is to investigate the effect of exchange interactions on finite-temperature magnetic phases for a wide range of lattice fillings. We use the dynamical mean-field theory approach and its real-space generalization to obtain finite-temperature phase diagrams including transitions to magnetically-ordered phases. It allows to determine optimal experimental regimes for approaching long-range ferromagnetic ordering in ultracold gases. We also calculate the entropy in the vicinity of magnetically-ordered phases, which provides quantitative predictions for on-going and future experiments aiming at approaching and studying long-range ordered states in optical lattices.