Correlated electron phases

A prominent class of correlated electron materials are transition-metal oxides (TMO), based on the perovskite crystal structure, with transition-metal ions in octahedral environments. Figure V.2 indicates, using the example of Mn3+ and Mn4+, the splitting of the 3d-electron energy levels caused by the octahedral crystal-field and the Jahn-Teller distortion (see also Chapters I and II). Note that a large correlation energy causes both ions to be in the Hund’s rule “high-spin” state.

Fig. V.2. a) The undistorted ABO3 perovskite structure, showing the green transition-metal ions (B) at the center of O2- octahedra. b) Energy splitting of the 3d-electron states in an octahedral crystal field (Mn4+) and due to the Jahn-Teller effect (Mn3+). Fig. V.3. The unit cells in the MnO2 planes of the layered material La0.5Sr1.5MnO4 [3]. The small dots are O2-, and the large black and blue dots represent Mn3+ and Mn4+ ions, respectively. One distinguishes the I4/mmm crystallographic (dots), the charge (small dashes), the orbital (solid) and the magnetic (large dashes) unit cells.
TMO materials show ordered phases of the charge, spin and orbital degrees of freedom; Figure V.3 indicates the different unit cells which occur in the MnO2 planes of the manganite La0.5Sr1.5MnO4 [3].

Fig. V.4. a) The phase diagram of La1-xCaxMnO3, as a function of the electron doping x [4]. The antiferromagnetic insulator (AFI) and the ferromagnetic insulator (FMI) and metal (FMM) phases show magnetic order. Charge and orbital order occur in the FMM and CE phases, while orbital order is also found near x = 0 above 140 K. Disordered polarons of the CE-type occur above the magnetic ordering temperatures, with spatial correlations on the nanometer scale. b) In the “dynamic” region, inelastic neutron scattering shows the polarons to be fluctuating on the ps time-scale, as evidenced by the inelastic shoulder at the right of the E = 0 elastic scattering peak.
An example of the variety of phases which arise in TMOs is that of the manganite La1-xCaxMnO3 (LCMO) (see Fig. V.4 a) [4]. As the electron concentration is increased by Ca doping, the stable low-temperature phase changes from antiferromagnetic insulator (AFI), to ferromagnetic insulator (FMI), to ferromagnetic metal (FMM) and ­finally to a charge-orbitally ordered state (CE). In the FMM phase of LCMO, colossal magnetoresistivity is associated with the formation of nanoscale polarons that develop at elevated temperature, which, around x ≈ 0.3, show correlations with a wave-vector ≈ (¼, ¼, 0) [3]. These correlations develop into long-range order at x ≈ 0.5, where equal numbers of Mn3+ and Mn4+ form a charge- and orbitally-ordered structure known as “CE”. Above the magnetic ordering temperature, a correlated polaron glass phase is formed, with a weakly temperature-dependent correlation length in the nanometer range. At still higher temperature, these static polarons become purely dynamic in character, as evidenced by inelastic neutron scattering (see Fig. V.4 b).

Fig. V.4. a) The phase diagram of La1-xCaxMnO3, as a function of the electron doping x [4]. The antiferromagnetic insulator (AFI) and the ferromagnetic insulator (FMI) and metal (FMM) phases show magnetic order. Charge and orbital order occur in the FMM and CE phases, while orbital order is also found near x = 0 above 140 K. Disordered polarons of the CE-type occur above the magnetic ordering temperatures, with spatial correlations on the nanometer scale. b) In the “dynamic” region, inelastic neutron scattering shows the polarons to be fluctuating on the ps time-scale, as evidenced by the inelastic shoulder at the right of the E = 0 elastic scattering peak.
Another famous example of correlated-electron TMOs are the cuprates showing high-temperature superconductivity. The crystal structure and (schematic) phase diagram for YBa2Cu3O7-x, a hole-doped superconductor, are shown in Figure V.5. CuO2 planes in the layered, oxygen-deficient perovskite structure are responsible for superconductivity. Besides the superconducting phase (SC), of particular interest in the “underdoped” regime, are the spin-glass (SG) and pseudo-gap regions. Here there is evidence that static and dynamic “stripes” occur, with characteristic arrangements of Cu-ion charge and spin on the nanometer scale [5].