Charge ordering, charge fluctuations and lattice effects in strongly correlated electron systems

Charge fluctuation and charge-ordering phenomena in compounds based on the 3d electrons of transition-metal ions and 4f electrons of rare-earth ions are reviewed with particular emphasis on the mutual coupling of charge and lattice degrees of freedom. For the description of charge ordering in inhomogeneously mixed-valence compounds of localized 3d or 4f-electron systems, we employ Landau's phenomenological theory for second-order phase transitions. By use of the group-theoretical method, the charge fluctuation mode corresponding to the active representation for the second-order transition is determined. The localization of 3d and 4f electrons makes the valence for the specific ions an integer number of charge units e in the ordered phases at low temperatures. The elastic soft mode observed by the ultrasonic method is often a useful indication for the charge fluctuation mode that is frozen below the charge-ordering point T-C. The transverse c(44) mode exhibiting a considerable softening in the rare-earth compound Yb4As3 couples to the 5 triplet of the charge fluctuation mode, giving rise to a linear chain of magnetic Yb3+ ions along [111] below T-C=292 K. Magnetite Fe3O4 and the substitution system Fe3-xZnxO4 exhibit softening of the c(44) mode that couples to the charge fluctuation mode, which freezes below the Verwey transition temperature T-V=124 K. The soft c(66) mode of the transition-metal compound NaV2O5 gives evidence for a zigzag structure of V4+ ions in the a-b plane below T-C=34 K and is the precursor for the orthorhombic monoclinic phase transition. The charge glass compounds of Sm3X4 (X=Se or Te) show ultrasonic dispersion due to thermal hopping of 4f electrons between Sm2+ and Sm3+ ions. The ln T decrease in elastic constants of Sm3X4 is described in terms of a two-level system of the 4f-electron tunnelling in the random potential. The characteristic ultrasonic dispersion for the copper oxide compound Sr12Ca2Cu24O41 is also presented. The elastic anomaly associated with the charge ordering in the hole-doped Mn compounds La1-xSrxMnO3 and Pr1-xCaxMnO3 with colossal magnetoresistance is discussed. In short, the temperature dependence of some symmetry elastic constants and the frequency dependence of ultrasonic attenuation coefficients help to characterize the charge-ordering transitions. They can predict the symmetry of charge orderings of the second-order transition, or they describe the thermal hopping processes of charge or they can identify a charge glass.