HRTEM lattice images and diffraction results of the Zener polaron charge and orbital ordered state at room temperature. (A) Lattice fringes of a (b,c) plane. (B) Typical example of structural and electronic phase separation between a Zener polaron type charge and orbital ordered (P2₁nm) and a disordered (Pbnm) structure, as observed in a wide temperature 80 ≤ T ≤ 300 K and doping 0.3 ≤ x ≤ 0.5 regime. The fringes correspond to the superlattice modulation with a doubled lattice parameter in b direction. (C and D) Diffraction patterns of the ordered state along the [010] and [100] zone axis, respectively. C shows extinction of the h0l reflections for h + l = 2n + 1; this confirms the space group P2₁nm for the ordered state with the Zener polaron type of ordering. (D) Nearly extinction of 0kl for k = 4n + 2 confirms the preservation of local b glide planes for subgroups of atoms and therefore gives constraints to the symmetry of the cooperative JT distortions.

Electron optic evidence for ferroelectric domain structure in PCMO with x = 0.32. (A) Fresnel (out-of-focus) image of a thin area of the sample surrounded by vacuum; the peculiar Fresnel diffraction fringes are clearly visible when the defocus is large enough (we estimate a defocus value of ≈200–300 μm for this picture). (B) Reconstructed phase shift from the electron hologram (not shown) recorded in-focus over the same area as in A. (C) Experimental line scan (dashed line in B) taken across four domains. From the line scan, we can estimate the domain size, o, the order of 25 nm (with relatively large variations), the phase gradient (slope), o, the order of 16 mrad/nm, and the total phase shift associated to each domain, ≈0.4 rad. (D) Simple model describing the ferroelectric polarization P₀ and phase shift across the domains. Full agreement with the profile in C is obtained for a value of 1.2 mC/m² for the quantity P₀/ε_r, where ε_r denotes the static dielectric permittivity.

In situ TEM study of the local colossal resistance (CER) effect at two different PCMO grains induced by a Pt/Ir tip. (A–C) Low-magnification images of the first grain (slightly defocused) visualizing electric domain patterns and the disorder transition at applied current. (A) PCMO grain with a high volume ratio of the ordered phase and some ferroelectric domains at zero current I = 0 μA. (B) Same area with I = 6 μA and bias U = 1 V. The electric domain structure has been strongly modified and the order–disorder transition sets in. (C) I = 10 μA, where the major grain area is involved in the order–disorder transition. (D–F) HRTEM images and SAED patterns (Inset) of a second grain far away from the tip with a defect as a marker. (D) Ordered area with a 2b₀ superlattice immediately before the disorder transition at I = 200 μA. (E) Snapshot of a moving domain boundary (DB) between an ordered and disordered domain 5 s after increase of the current to I = 210 μA (SI Movie 1). (F) Same as E with a second ordered domain moving into the image area, ≈8 s after increasing I to 210 μA. All diffraction patterns are acquired at the [1̄01] zone axis. (G) U–I and R–I curves that are recorded during the experiment at grain 2. Note that a sign reversal of the current is required to obtain a full recovery of the high-resistance ordered state in most of the grain area.

Structure projection along the [001] direction. Projected structure of the charge and orbital disordered (A) and the Zener polaron ordered (B) states with a schematic representation of the e_g orbitals for half doping x = 0.5. The displacement of Mn and O sites due to ordering is indicated in yellow. Increasing MnOMn bond angles (color index) result in an enhancement of the ferromagnetic double exchange and orbital occupation by the e_g electrons. The in-plane electric dipole moments p of the MnOMn dimers determined from the noncentrosymmetric atomic displacements are indicated by red arrows. Their canted structure results in a net-polarization P_a along the crystallographic a direction, whereas P_b sums up to zero. The directions of the perpendicular magnetic moments of the Mn atoms m below T_N as expected from CE-type antiferromagnetic ordering are indicated with black arrowheads. (C) Symmetry elements and displacements of the ordered phase. Sites related by the P2₁nm space group are indicated by same colors. Additional pairing in the displacements is due to the local b glide plane of O_II,1 and O_II,2, O_II,3, and O_II,4, respectively. This symmetry element is preserved along the b and c directions.

Colossal electroresistance effect (CER) as a polaron order–disorder transition between the polaron-solid and liquid phases. (A) Temperature dependence of the resistivity ρ(T) for different constant electric currents in a c-axis-oriented epitaxial Pr_0.5Ca_0.5MnO₃ film. At the percolation temperature T_p, a step-like resistivity drop is observed. (B) Frequency dependence of the relative permittivity ε_r(ω) at 70 K as a function of the applied bias. The drop in this excess low-frequency ε_r(ω) is related to a suppression of the static ferroelectric order of the Zener polaron ordered phase.