Dimensional crossover and the magnetic transition in electron-doped manganites

We introduce a microscopic model for electron doped manganites that explains the mechanism of the observed transition from $G$-type antiferromagnetic ($G$-AF) to $C$-type antiferromagnetic ($C$-AF) order under increasing doping by the double-exchange mechanism. The model unravels the crucial role played by $e_g$ orbital degrees of freedom and explains the observed metal-to-insulator transition by a dimensional crossover at the magnetic phase transition. The specific heat and the spin-canting angle found for the $G$-AF phase agree with experimental findings. As a surprising outcome of the theory we find that spin canting is suppressed in the $C$-AF phase, in agreement with experiment, due to the Fermi surface topology.

Figure 1

Band structure in the $G$-AF phase along the high symmetry directions. Spin majority (minority) bands are shown by solid (dashed) lines. Parameters: $t=0.4$ eV, $J_H=0.74$ eV, and $x=0$. The inset shows the Fermi surface at low doping (heavy lines along $\Gamma$-$X$, $R$-$M$, and equivalent directions) and the special points $\Gamma =(0,0,0)$, $X=(\pi ,0,0)$, $M=(\pi ,\pi ,0)$, $R=(\pi ,\pi ,\pi )$, and $Z=(0,0,\pi )$.

Figure 2

Band structure in the $C$-AF phase along the high symmetry directions. Spin majority (minority) bands are shown by solid (dashed) lines. Parameters: $t=0.4$ eV, $J_H=0.74$ eV, $g=3$ eV, and $x=0.05$. The special points are as in Fig. 1. The inset shows the Fermi surface pockets at low doping near the $X$ and $Y$ points.

Figure 3

Densities of states for $e_g$ electrons, $N_z\left(\omega \right)$ and $N_x\left(\omega \right)$, in the spin majority bands as obtained for (a) the $G$-AF phase [$N_z\left(\omega \right)$ and $N_x\left(\omega \right)$ are here degenerate] with a singularity arising from the AF order at $\omega =-1.11$ eV, and (b) the $C$-AF phase; here the densities of $z$ [$N_z\left(\omega \right)$] and $x$ [$N_x\left(\omega \right)$] electron states are shown by solid (red) and dashed (blue) lines, respectively. Parameters: $t=0.4$ eV and $J_H=0.74$ eV; for the $C$-AF phase shown in (b) in addition $g=3$ eV and $x=0.05$.

Figure 4

Total energies of the $G$-AF ($E_{G\text{AF}}$) and $C$-AF ($E_{C\text{AF}}$) phases as obtained for increasing electron doping $x$. Parameters: $t=0.4$ eV, $J_H=0.74$ eV, $g=3$ eV, $K=20$ eV, and $J=3.79$ meV. The inset shows the phase diagram in the $(t,x_c)$ plane obtained for $g=0$ (circles, dashed line), and $g=3$ eV (diamonds, solid line).