Doping and Field-Induced Insulator-Metal Transitions in Half-Doped Manganites

We argue that many properties of the half-doped manganites may be understood in terms of a new two-($e_g$ electron)-fluid description, which is energetically favorable at intermediate Jahn-Teller (JT) coupling. This emerges from a competition between canting of the core spins of Mn promoting mobile carriers and polaronic trapping of carriers by JT defects, in the presence of magnetic (CE), orbital and charge order. Using it we explain features of the doping and magnetic-field-induced insulator-metal transitions such as the electron-hole asymmetry and the smallness of the transition fields.

Figure 1

Phase diagram of the 3D two-orbital model ($T=0$, $x=0.5$, $K/t=10$). FM (${\mathrm{FM}}_d$): ferromagnetic metallic phase with no distortions (small uniform distortions). FI-CO (FM-CO): charge-ordered ferromagnetic insulating (metallic) phase with distortions that favor occupancy of the $x^2-y^2$ orbitals. ${\mathrm{A}}_d$: ferromagnetic planes AFM aligned with uniform distortions. A-CO: A with charge order. CE-CO: Ferromagnetic zig-zag chains AFM ordered, orbital ordered ($3x^2-r^2/3y^2-r^2$), and charge-ordered. G-CO: Néel AFM phase with charge-order. Inc.: Possible incommensurate states that interpolate between CE and G. Dotted dashed lines come from analytical expressions derived in the strong-coupling limit. Solid (dashed) lines show first-order (second-order) phase transitions.

Figure 2

Energy change when a single JT defect is introduced in the FI-CO phase. $Q^{(0)}-Q_d$ is the JT distortion on a defect site; all the other occupied sites having the same distortion $Q^{(0)}$. The softening of the excitation with $Q_d\sim Q^{(0)}$ at $\mathsf{g}/t\sim 6.8$ signals a phase transition with proliferation of defects. Finite-size effects are small and shown for $\mathsf{g}/t=6.7$.

Figure 3

Phase diagram, $\mathsf{g}/t$ vs doping, $x$ ($J_{\mathrm{AFM}}{S}^2/t=0.15$). CE-M-C: canted CE state with distortions and charge-order (metallic). CE-T: CE phase with extra carriers trapped in JT distortions (insulating). FM: ferromagnetic metallic phase with no distortions. The upper curve is valid for $x$ close enough to 0.5. C is a critical point ending a first-order line between two canted states (with different canting angles).

Figure 4

Magnetization vs field ($\mathsf{g}/t=1-5$, $J_{\mathrm{AFM}}{S}^2/t=0.15$). The first-order transition to an undistorted highly canted (or fully FM) metallic phase is accompanied with a relaxation of the JT distortions.