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-metal-like atoms in optical lattices that can be effectively described by the two-band spin-$1/2$ Hubbard model including 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 ongoing and future experiments aiming at approaching and studying long-range ordered states in optical lattices.

Figure 1

Magnetic susceptibility $\chi$ and residual magnetization $M_0$ as functions of temperature $T$ for fixed $\mu =2.5, V=22, V_{ex}=21$ and two different values $U, U=6$ (left) and $U=12$ (right).

Figure 2

Curie temperature as a function of (a) exchange interaction (Ising-type Hund's coupling) at $U=12$ and $V=22$ and (b) intraorbital interactions at $V=22$ and $V_{ex}=21$. A fixed chemical potential $\mu =2.5$ is chosen to yield $n\approx 1.5$ in the PM phase.

Figure 3

$T-n$ phase diagram at $U=12, V=22$, and $V_{ex}=21$ including magnetically ordered states that are schematically illustrated in the lower part: paramagnetic (PM), ferromagnetic (FM), and antiferromagnetic (AFM). PS denotes the region of phase separation. Inset: $T-\mu$ phase diagram.

Figure 4

$T-n$ phase diagram at $U=12, V=22$, and different values of the exchange interaction (left) and $V=22, V_{ex}=21$, and different values of intraorbital interactions (right). The AFM instability is indicated here only schematically around half filling.

Figure 5

$T-U$ phase diagram at $V=22, V_{ex}=21$, and different values of lattice filling $n$ obtained by DMFT.

Figure 6

Isentropic lines at different values of filling: $n=0.85, n=1.2, n=1.6$, and $n=1.8$. The interband interactions are kept fixed, $V=22$ and $V_{ex}=21$.