Short-range ordered phase of the double-exchange model in infinite dimensions

Using the dynamical mean-field theory, we have evaluated the magnetic instabilities and $T=0$ phase diagram of the double-exchange model on a Bethe lattice in infinite dimensions. In addition to ferromagnetic (FM) and antiferromagnetic (AF) phases, we also study a class of disordered phases with magnetic short-range order (SRO). In the weak-coupling limit, a SRO phase has a higher transition temperature than the AF phase for all fillings $p$ below 1 and can even have a higher transition temperature than the FM phase. At $T=0$ and for small Hund’s coupling $J_{\mathrm{H}}$, a SRO state has lower energy than either the FM or AF phases for $0.26⩽p<1$. Phase separation is absent in the $J_{\mathrm{H}}\to 0$ limit but appears for any nonzero value of $J_{\mathrm{H}}$.

Figure 1

The correlation parameter $q$ (solid) and the associated maximum SRO transition temperature $T_{\mathrm{SRO}}^{\left(\max \right)}$ (dashed) vs filling $p$ for a SRO state in the weak-coupling limit. Also plotted in the thin short-dashed line are the weak-coupling limits of $T_{\mathrm{C}}$ for $q=0$ and $T_{\mathrm{N}}$ for $q=1$.

Figure 2

(Color) The (a) magnetic instabilities and (b) $T=0$ phase diagram of the DE model.

Figure 3

The interacting DOS $N(\omega ,q)$ (normalized by $1∕W$) vs $\omega ∕W$ for $J∕W=0.2$ in the FM or $q=0$ (solid), SRO phase with $q=1∕4$ (long dash), NM or $q=1∕2$ (dash), SRO phase with $q=3∕4$ (small dash), and AF or $q=1$ (dot dash) phases.