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We review our recent x-ray scattering studies of charge and orbital order in doped manganites, with specific emphasis on the role of orbital correlations in Pr_1-xCa_xMnO_3. For x=0.25, we find an orbital structure indistinguishable from the undoped structure with long range orbital order at low temperatures. For dopings 0.3<x<0.5, we find scattering consistent with a charge and orbitally ordered CE-type structure. While in each case the charge order peaks are resolution limited, the orbital order exhibits only short range correlations. We report the doping dependence of the correlation length and discuss the connection between the orbital correlations and the finite magnetic correlation length observed on the Mn^3+ sublattice with neutron scattering techniques. The physical origin of these domains, which appear to be isotropic, remains unclear. We find that weak orbital correlations persist well above the phase transitions, with a correlation length of 1-2 lattice constants at high temperatures. Significantly, we observe similar correlations at high temperatures in La_0.7Ca_0.3MnO_3, which does not have an orbitally ordered ground state, and we conclude that such correlations are robust to variations in the relative strength of the electron-phonon coupling.
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We study an effective one-dimensional (1D) orbital t-J model derived for strongly correlated e_g electrons in doped manganites. The ferromagnetic spin order at half filling is supported by orbital superexchange prop. to J which stabilizes orbital order with alternating x^2-y^2 and 3z^2-r^2 orbitals. In a doped system it competes with the kinetic energy prop. to t. When a single hole is doped to a half-filled chain, its motion is hindered and a localized orbital polaron is formed. An increasing doping generates either separated polarons or phase separation into hole-rich and hole-poor regions, and eventually polarizes the orbitals and gives a it metallic phase with occupied 3z^2-r^2 orbitals. This crossover, investigated by exact diagonalization at zero temperature, is demonstrated both by the behavior of correlation functions and by spectral properties, showing that the orbital chain with Ising superexchange is more classical and thus radically different from the 1D spin t-J model. At finite temperature we derive and investigate an effective 1D orbital model using a combination of exact diagonalization with classical Monte-Carlo for spin correlations. A competition between the antiferromagnetic and ferromagnetic spin order was established at half filling, and localized polarons were found for antiferromagnetic interactions at low hole doping. Finally, we clarify that the Jahn-Teller alternating potential stabilizes the orbital order with staggered orbitals, inducing the ferromagnetic spin order and enhancing the localized features in the excitation spectra. Implications of these findings for colossal magnetoresistance manganites are discussed.
We investigate the interplay between spin and orbital correlations in monolayer and bilayer manganites using an effective spin-orbital t-J model which treats explicitly the e_g orbital degrees of freedom coupled to classical t_{2g} spins. Using finite clusters with periodic boundary conditions, the orbital many-body problem is solved by exact diagonalization, either by optimizing spin configuration at zero temperature, or by using classical Monte-Carlo for the spin subsystem at finite temperature. In undoped two-dimensional clusters, a complementary behavior of orbital and spin correlations is found - the ferromagnetic spin order coexists with alternating orbital order, while the antiferromagnetic spin order, triggered by t_{2g} spin superexchange, coexists with ferro-orbital order. With finite crystal field term, we introduce a realistic model for La_{1-x}Sr_{1+x}MnO_4, describing a gradual change from predominantly out-of-plane 3z^2-r^2 to in-plane x^2-y^2 orbital occupation under increasing doping. The present electronic model is sufficient to explain the stability of the CE phase in monolayer manganites at doping x=0.5, and also yields the C-type antiferromagnetic phase found in Nd_{1-x}Sr_{1+x}MnO_4 at high doping. Also in bilayer manganites magnetic phases and the accompanying orbital order change with increasing doping. Here the model predicts C-AF and G-AF phases at high doping x>0.75, as found experimentally in La_{2-2x}Sr_{1+2x}Mn_2O_7.
A central line of inquiry in condensed matter science has been to understand how the competition between different states of matter give rise to emergent physical properties. Perhaps some of the most studied systems in this respect are the hole-doped LaMnO$_3$ perovskites, with interest in the past three decades being stimulated on account of their colossal magnetoresistance (CMR). However, phase segregation between ferromagnetic (FM) metallic and antiferromagnetic (AFM) insulating states, which itself is believed to be responsible for the colossal change in resistance under applied magnetic field, has until now prevented a full atomistic level understanding of the orbital ordered (OO) state at the optimally doped level. Here, through the detailed crystallographic analysis of the hole-doped phase diagram of a prototype system, we show that the superposition of two distinct lattice modes gives rise to a striped structure of OO Jahn-Teller active Mn$^{3+}$ and charge disordered (CD) Mn$^{3.5+}$ layers in a 1:3 ratio. This superposition leads to an exact cancellation of the Jahn-Teller-like oxygen atom displacements in the CD layers only at the 3/8th doping level, coincident with the maximum CMR response of the manganties. Furthermore, the periodic striping of layers containing Mn$^{3.5+}$, separated by layers of fully ordered Mn$^{3+}$, provides a natural mechanism though which long range OO can melt, a prerequisite for the emergence of the FM conducting state. The competition between insulating and conducting states is seen to be a key feature in understanding the properties in highly correlated electron systems, many of which, such as the CMR and high temperature superconductivity, only emerge at or near specific doping values.
Recently, based on the refined crystal structure of Pr0.6Ca0.4MnO3 from neutron diffraction, Daoud-Aladine et al.[PRL89,97205(2002)] have proposed a new ground state structure for the half-doped manganites R0.5Ca0.5MnO3, where R is a trivalent ion like Bi,La,Pr,Sm or Y. Their proposal describes the CE magnetic structure attributed to these materials as an arrangement of dimers along the ferromagnetic Mn zig-zag chains that form it. However, the dimers proposal is in conflict with the Goodenough-Kanamori-Anderson rules, which give a coherent description of many transition metal insulating compounds and predict the coexistence of Mn3+ and Mn4+ ions in equal parts in the half-doped manganites. On the other hand, Rivadulla et al.[PRB 66, 174432 (2002)] have studied several single crystal samples of half-doped manganites and propose a phase diagram in terms of the tolerance factor which contains both types of structures. In the present work we have calculated the magnon dispersion relations for the CE magnetic structure, arising for each type of proposal: the charge ordered and the dimer phases, respectively. We consider a three-dimensional unit cell containing 16 spins, and compare the magnetic excitations along different paths in the first Brillouin zone. We conclude that measurement of the magnon dispersion relations should allow a clear distinction between the two proposals, predicting qualitative differences arising along specific directions of propagation in the first Brillouin zone.
We employ time-resolved resonant x-ray diffraction to study the melting of charge order and the associated insulator-metal transition in the doped manganite Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ after resonant excitation of a high-frequency infrared-active lattice mode. We find that the charge order reduces promptly and highly nonlinearly as function of excitation fluence. Density functional theory calculations suggest that direct anharmonic coupling between the excited lattice mode and the electronic structure drive these dynamics, highlighting a new avenue of nonlinear phonon control.
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