Understanding the insulating phase in colossal magnetoresistance manganites: shortening of the Jahn-Teller long-bond across the phase diagram of La1-xCaxMnO3

Bridging Structural Inhomogeneity to Functionality: Pair Distribution Function Methods for Functional Materials Development

The correlation between structure and function lies at the heart of materials science and engineering. Especially, modern functional materials usually contain inhomogeneities at an atomic level, endowing them with interesting properties regarding electrons, phonons, and magnetic moments. Over the past few decades, many of the key developments in functional materials have been driven by the rapid advances in short-range crystallographic techniques. Among them, pair distribution function (PDF) technique, capable of utilizing the entire Bragg and diffuse scattering signals, stands out as a powerful tool for detecting local structure away from average. With the advent of synchrotron X-rays, spallation neutrons, and advanced computing power, the PDF can quantitatively encode a local structure and in turn guide atomic-scale engineering in the functional materials. Here, the PDF investigations in a range of functional materials are reviewed, including ferroelectrics/thermoelectrics, colossal magnetoresistance (CMR) magnets, high-temperature superconductors (HTSC), quantum dots (QDs), nano-catalysts, and energy storage materials, where the links between functions and structural inhomogeneities are prominent. For each application, a brief description of the structure-function coupling will be given, followed by selected cases of PDF investigations. Before that, an overview of the theory, methodology, and unique power of the PDF method will be also presented.

Polaronic effect in the x-ray absorption spectra of La1-x Ca x MnO3 manganites

X-ray absorption spectroscopy (XAS) is performed to study changes in the electronic structures of colossal magnetoresistance (CMR) and charged ordered (CO) La_1-x Ca _x MnO₃ manganites with respect to temperature. The pre-edge features in O and Mn K-edge XAS spectra, which are highly sensitive to the local distortion of MnO₆ octahedral, exhibit contrasting temperature dependence between CMR and CO samples. The seemingly counter-intuitive XAS temperature dependence can be reconciled in the context of polarons. These results help identify the most relevant orbital states associated with polarons and highlight the crucial role played by polarons in understanding the electronic structures of manganites.

Local Orthorhombicity in the Magnetic C_{4} Phase of the Hole-Doped Iron-Arsenide Superconductor Sr_{1-x}Na_{x}Fe_{2}As_{2}

We report on temperature-dependent pair distribution function measurements of Sr_{1-x}Na_{x}Fe_{2}As_{2}, an iron-based superconductor system that contains a magnetic phase with reentrant tetragonal symmetry, known as the magnetic C_{4} phase. Quantitative refinements indicate that the instantaneous local structure in the C_{4} phase comprises fluctuating orthorhombic regions with a length scale of ∼2  nm, despite the tetragonal symmetry of the average static structure. Additionally, local orthorhombic fluctuations exist on a similar length scale at temperatures well into the paramagnetic tetragonal phase. These results highlight the exceptionally large nematic susceptibility of iron-based superconductors and have significant implications for the magnetic C_{4} phase and the neighboring C_{2} and superconducting phases.

Effect of Tb3+ doping in mixed-valence manganites and cobaltites

The magnetic ordering of four Tb³⁺-doped manganites and cobaltites, La_0.7Tb_0.1Sr_0.2MnO₃, La_0.7Tb_0.1Ca_0.2MnO₃, La_0.7Tb_0.1Sr_0.2CoO₃ and La_0.7Tb_0.1Ca_0.2CoO₃, have been studied by means of neutron diffraction and SQUID magnetometry. All the samples were prepared by sintering of sol-gel precursors and their orthorhombic or rhombohedral perovskite structures at room and low temperatures were refined. A long-range ferromagnetic (FM) order was detected at the Mn and Co sites. In addition, a small but significant ordered moment was observed at A sites of studied cobaltites, which was attributed to local Tb³⁺ moments, aligned by exchange interactions due to FM ordered Co sublattice. No or minor Tb³⁺ contribution was detected in studied manganites.

Representational analysis of extended disorder in atomistic ensembles derived from total scattering data

Representational analysis is used to characterize correlated short-range order in large atomistic ensembles. This method, analogous to tight-binding methods, enables the extraction of relevant structural parameters in an orthogonal and local basis that permits robust statistical analysis of crystalline disorder.

With the increased availability of high-intensity time-of-flight neutron and synchrotron X-ray scattering sources that can access wide ranges of momentum transfer, the pair distribution function method has become a standard analysis technique for studying disorder of local coordination spheres and at intermediate atomic separations. In some cases, rational modeling of the total scattering data (Bragg and diffuse) becomes intractable with least-squares approaches, necessitating reverse Monte Carlo simulations using large atomistic ensembles. However, the extraction of meaningful information from the resulting atomistic ensembles is challenging, especially at intermediate length scales. Representational analysis is used here to describe the displacements of atoms in reverse Monte Carlo ensembles from an ideal crystallographic structure in an approach analogous to tight-binding methods. Rewriting the displacements in terms of a local basis that is descriptive of the ideal crystallographic symmetry provides a robust approach to characterizing medium-range order (and disorder) and symmetry breaking in complex and disordered crystalline materials. This method enables the extraction of statistically relevant displacement modes (orientation, amplitude and distribution) of the crystalline disorder and provides directly meaningful information in a locally symmetry-adapted basis set that is most descriptive of the crystal chemistry and physics.

Cu(Ir₁ - xCrx)₂S₄: a model system for studying nanoscale phase coexistence at the metal-insulator transition

Increasingly, nanoscale phase coexistence and hidden broken symmetry states are being found in the vicinity of metal-insulator transitions (MIT), for example, in high temperature superconductors, heavy fermion and colossal magnetoresistive materials, but their importance and possible role in the MIT and related emergent behaviors is not understood. Despite their ubiquity, they are hard to study because they produce weak diffuse signals in most measurements. Here we propose Cu(Ir_{1 − x}Cr_x)₂S₄ as a model system, where robust local structural signals lead to key new insights. We demonstrate a hitherto unobserved coexistence of an Ir⁴⁺ charge-localized dimer phase and Cr-ferromagnetism. The resulting phase diagram that takes into account the short range dimer order is highly reminiscent of a generic MIT phase diagram similar to the cuprates. We suggest that the presence of quenched strain from dopant ions acts as an arbiter deciding between the competing ground states.

Structure of methylammonium lead iodide within mesoporous titanium dioxide: active material in high-performance perovskite solar cells

We report the structure of methylammonium lead(II) iodide perovskite in mesoporous TiO2, as used in high-performance solar cells. Pair distribution function analysis of X-ray scattering reveals a two component nanostructure: one component with medium range crystalline order (30 atom %) and another with only local structural coherence (70 atom %). The nanostructuring correlates with a blueshift of the absorption onset and increases the photoluminescence. Our findings underscore the importance of fully characterizing and controlling the structure for improved solar cell efficiency.

Jahn-Teller distortion relaxation across the LaMnO3+Δ phase diagram

The evolution of the local Jahn-Teller distortion across the LaMnO3+Δ phase diagram was obtained using the perturbed angular correlation local probe technique. We found that upon doping, the local distortion decreases continuously with increasing doping and that no fully Jahn-Teller distorted Mn(3+)O6 octahedra are observed within the orthorhombic insulating phase. A local single-phase scenario is established for the orbital disordered orthorhombic crystallographic structure. We also show that the continuous weakening of the Jahn-Teller distortions is not limited to a single-phase environment and occurs in a similar manner within an undistorted rhombohedric matrix upon lowering the temperature.

Structural and thermal properties of LaMnO3 from neutron diffraction and first principles studies

Neutron diffraction experiments have been performed on powder samples of LaMnO(3) below and above the Jahn-Teller transition temperature of 750 K. Experimental investigations are assisted by density functional theory calculations. Theoretical studies are carried out for the orbitally ordered state of LaMnO(3) which allows one to compare the behavior of the orbitally ordered and disordered structures as a function of temperature. The temperature dependences of the structural parameters characterizing the Jahn-Teller distortions are reported and discussed. A gradual departure of the experimental data from theoretical predictions is observed above 650 K. In this range of temperatures, anions surrounding the Jahn-Teller active cations perform more isotropic thermal motion. The onset of structural phase transition induces a reduction of the crystal volume by about 0.4% which follows from the structural transformations yielding more regular oxygen octahedra formed above the phase transformation. It is found that above the Jahn-Teller transition the distortions of the MnO(6) octahedra are not completely removed. The non-vanishing distortions are accompanied by the lifted degeneracy of the Mn e(g) states. Weak residual distortions can be assigned to the short-range orbital order that persists within a local scale but it seems quenched on average giving rise to a disappearance of the long-range order coherency of the Jahn-Teller effect.

Detailed mapping of the local Ir4+ dimers through the metal-insulator transitions of CuIr2S4 thiospinel by X-ray atomic pair distribution function measurements

The evolution of the short-range structural signature of the Ir4+ dimer state in CuIr2S4 thiospinel has been studied across the metal-insulator phase transitions as the metallic state is induced by temperature, Cr doping, and x-ray fluence. An atomic pair distribution function (PDF) approach reveals that there are no local dimers that survive into the metallic phase when this is invoked by temperature and doping. The PDF shows Ir4+ dimers when they exist, regardless of whether or not they are long-range ordered. At 100 K, exposure to a 98 keV x-ray beam melts the long-range dimer order within a few seconds, though the local dimers remain intact. This shows that the metallic state accessed on warming and doping is qualitatively different from the state obtained under x-ray irradiation.

Substitutional disorder and charge localization in manganites

In the manganites RE(1 - x)AE(x)MnO(3) (RE and AE being rare-earth and alkaline-earth elements, respectively) the random distribution of RE(3 + ) and AE(2 + ) induces random, but correlated, shifts of site energies of charge carriers in the Mn sites. We consider a realistic model of this diagonal disorder, in addition to the double-exchange hopping disorder, and investigate the metal-insulator transition as a function of temperature, across the paramagnetic-ferromagnetic line, and as a function of doping  x. Contrary to previous results, we find that values of parameters, estimated from the electronic structure of the manganites, are not incompatible with the possibility of a disorder-induced metal to insulator transition accompanying the ferromagnetic to paramagnetic transition at intermediate doping (x ∼ 0.2-0.4). These findings indicate clearly that substitutional disorder has to be considered as an important effect when addressing the colossal magnetoresistance properties of manganites.

The evolution of Griffiths-phase-like features and colossal magnetoresistance in La(1-x)Ca(x)MnO(3) (0.18 ≤ x ≤ 0.27) across the compositional metal-insulator boundary

Detailed measurements of the magnetic and transport properties of single crystals of La(1-x)Ca(x)MnO(3) (0.18 ≤ x ≤ 0.27) are summarized, and lead to the following conclusions. While temperature-dependent (magneto-) resistance measurements narrow the compositionally modulated metal-insulator (M-I) transition to lie between 0.19 ≤ x(c) ≤ 0.20 in the series studied, comparisons between the latter magnetic data provide the first unequivocal demonstration that (i) the presence of Griffiths-phase-like (GP) features do not guarantee colossal magnetoresistance (CMR), while confirming (ii) that neither are the appearance of such features a prerequisite for CMR. These data also reveal that (iii) whereas continuous magnetic transitions occur for 0.18 ≤ x ≤ 0.25, the universality class of these transitions belongs to that of a nearest-neighbour 3D Heisenberg model only for x≤0.20, beyond which complications due to GP-like behaviour occur. The implications of the variation (or lack thereof) in critical exponents and particularly critical amplitudes and temperatures across the compositionally mediated M-I transition support the assertion that the dominant mechanism underlying ferromagnetism across the M-I transition changes from ferromagnetic super-exchange (SE) stabilized by orbital ordering in the insulating phase to double-exchange (DE) in the orbitally disordered metallic regime. The variations in the acoustic spin-wave stiffness, D, and the coercive field, H(C), support this conclusion. These SE and DE interaction mechanisms are demonstrated to not only belong to the same universality class but are also characterized by comparable coupling strengths. Nevertheless, their percolation thresholds are manifestly different in this system.

Formation and temperature evolution of correlated polarons in colossal magnetoresistive manganites

We investigate the temperature dependence of charge ordered clusters in manganites. In terms of an approximate treatment of the half-filled spinless Holstein model incorporating the double exchange effect and nearest-neighbor Coulomb interactions, we find that charge ordering and polaronic states appear simultaneously which naturally defines a correlated polaron state. Without the double exchange, the temperature evolution of the charge (polaron) ordering parameter exhibits a broad peak structure only in the strongly correlated quasiadiabatic regime. Including the double exchange, the peak becomes sharper and is observed both in the quasiadiabatic and antiadiabatic regimes. The peak structure in the quasiadiabatic regime provides an explanation for the temperature dependence of the polaron correlation in nanoscale charge ordered polaron clusters observed in the manganites with intermediate to narrow bandwidths.

Local structure of La1-xSrxCoO3 determined from EXAFS and neutron pair distribution function studies

The combined local structure techniques, extended x-ray absorption fine structure and neutron pair distribution function analysis, have been used for temperatures 4< or =T< or =330 K to rule out a large Jahn-Teller (JT) distortion of the Co-O bond in La1-xSrxCoO3 for a significant fraction of Co sites (x< or =0.35), indicating few, if any, JT-active, singly occupied e_{g} Co sites exist.

Is a Griffiths phase a prerequisite for colossal magnetoresistance?

Detailed measurements of the magnetic and transport behavior of the two La(1-x)Ca(x)MnO(3) single crystals exhibiting colossal magnetoresistance are summarized. The x=0.21 sample exhibits unusual exponents (delta = 20+/-1, gamma = 1.71+/-0.1, beta = 0.09+/-0.01, T(C) = 182+/-1 K) and, more importantly, a Griffiths phase characterized by an exponent lambda = 0.70+/-0.2. By contrast, the x=0.20 specimen displays Heisenberg model behavior with no evidence of such a phase. Thus while a Griffiths phase accounts for the behavior of La(1-x)Ca(x)MnO(3) near optimal doping, it does not appear to be a prerequisite for colossal magnetoresistance in this system.

Quadrupolar ordering in LaMnO3 revealed from scattering data and geometric modeling

Many strongly correlated materials display quadrupolar (Jahn-Teller) distortion of the local octahedral structural units. It is common for these distortions to be observed by probes of local structure but absent in the crystallographic average structure. The ordering of these quadrupoles is important in determining the properties of manganites and cuprates, and the nature of the disorder in these structures has been an unsolved problem. We combine high resolution scattering data and novel geometrical modeling techniques to obtain a detailed picture of the local atomic structure, and also to extract the quadrupolar order parameter associated with the distorted octahedra. We show that in LaMnO3, quadrupoles undergo a strong first-order phase transition at 730 K, but with nonzero order parameter remaining in the high-temperature phase.