Magnetic phases of mass- and population-imbalanced ultracold fermionic mixtures in optical lattices

We study magnetic phases of two-component mixtures of ultracold fermions with repulsive interactions in optical lattices in the presence of both hopping and population imbalance by means of dynamical mean-field theory (DMFT). It is shown that these mixtures can have easy-axis antiferromagnetic, ferrimagnetic, charge-density wave, and canted-antiferromagnetic order or be unordered depending on parameters of the system. We study the resulting phase diagram in detail and investigate the stability of the different phases with respect to thermal fluctuations. We also perform a quantitative analysis for a gas confined in a harmonic trap, both within the local density approximation and using a full real-space generalization of DMFT.

Figure 1

(a) Critical temperature for Néel ordering in the half-filled Hubbard model (${\mu }_{\uparrow ,\downarrow }=U/2$) versus mass imbalance at different values of the interaction strength in a cubic lattice, obtained within DMFT. (b) Dependence of the minimal temperature that can be reached for a fixed entropy $s$ per particle by minimizing over the interaction strength $U/t$, as a function of the mass-imbalance parameter $\Delta t$.

Figure 2

Phase diagram for a population- and mass-imbalanced mixture at half filling and finite temperature, obtained within DMFT for a cubic lattice. Dashed and solid lines correspond to the first- and second-order phase transition lines, respectively. The CDW parameter is defined in terms of the double occupancy $D_i=\langle {\widehat{n}}_{i\uparrow }{\widehat{n}}_{i\downarrow }\rangle$, $c=(D_i-D_{i+1})/(D_i+D_{i+1})$; $m_{z,x}^{\mathrm{stag}}=\langle {\widehat{S}}_i^{Z,X}\rangle -\langle {\widehat{S}}_{i+1}^{Z,X}\rangle$.

Figure 3

Set of phase diagrams for a population- and mass-imbalanced mixture at half filling, $T=0.4t$, and different $\Delta \mu$, obtained within DMFT for a cubic lattice, including easy-axis antiferromagnetic (Z-AF), charge-density wave (CDW), ferrimagnetic, canted AF, unordered Mott insulator (PM-I), and unordered Fermi liquid (PM-FL) phases.

Figure 4

Dependence of critical polarization destroying AF order on the mass-imbalance parameter, obtained by DMFT.

Figure 5

Real-space density and magnetization distributions for a cubic lattice in a harmonic trap obtained by $\mathrm{LDA}+\mathrm{DMFT}$. Parameters used in (a)–(d): $U=12t$, $T=0.2t$, $\Delta t=0.2$, and $V_i=0.1t{(r_i/a)}^2$, where $a$ is the lattice constant.

Figure 6

Comparison of real-space magnetization profiles for a square lattice in a harmonic trap obtained by $\mathrm{LDA}+\mathrm{DMFT}$ (lines) and R-DMFT (dots). Shadowed areas correspond to the regions where LDA fails to reproduce the detailed structure and has problems with convergence. (Insets) Contour plots representing real-space distributions of magnetizations obtained by R-DMFT with the same parameters. Parameters used in (a) and (b) and insets: $U=12t$, $T=0.2t$, $\Delta t=0.2$, and $V_i=0.1t{(r_i/a)}^2$.