Direct observation of orbital ordering in La0.5Sr1.5MnO4 using soft x-ray diffraction

Spontaneous orbital polarization in the nematic phase of FeSe

The origin of nematicity in FeSe remains a critical outstanding question towards understanding unconventional superconductivity in proximity to nematic order. To understand what drives the nematicity, it is essential to determine which electronic degree of freedom admits a spontaneous order parameter independent from the structural distortion. Here we use X-ray linear dichroism at the Fe K pre-edge to measure the anisotropy of the 3d orbital occupation as a function of in situ applied stress and temperature across the nematic transition. Along with using X-ray diffraction to precisely quantify the strain state, we reveal a lattice-independent, spontaneously ordered orbital polarization within the nematic phase, as well as an orbital polarizability that diverges as the transition is approached from above. These results provide strong evidence that spontaneous orbital polarization serves as the primary order parameter of the nematic phase.

Symmetry Origin of the Dzyaloshinskii-Moriya Interaction and Magnetization Reversal in YVO3

We have investigated magneto-structural phase transitions in polycrystalline YVO₃ using high-resolution neutron powder diffraction toward understanding the phenomenon of magnetization reversal. Contrary to earlier reports, our study reveals that both C-type and G-type antiferromagnetic ordering, corresponding to G-type and C-type orbital ordered phases, respectively, occur at the same temperature (T_N = 115 K) with the G-type antiferromagnetic phase growing at the expense of the C-type one on cooling. These processes cease at T_S ∼ 77 K; however, a minor (∼4%) untransformed C-type phase remains unchanged down to 1.7 K. The symmetry analysis indicates different symmetry origins of the Dzyaloshinskii-Moriya interaction in each phase, which can explain the magnetization reversal observed between T_N and T_S. We discuss that magnetic phase separation and associated weak ferromagnetism may be the common mechanism underlying the magnetization reversal phenomenon observed in other RVO₃ systems (R = rare earth).

Orbital ordering and magnetism in layered Perovskite Ruthenate Sr2RuO4

Local density approximation plus on-site Coulomb interaction U electronic structure calculations reveal that layered perovskite oxide Sr₂RuO₄ exhibits the ferromagnetic (FM) half-metallic ground state, which is nearly degenerate with the antiferromagnetic (AFM) phase with a slightly higher total energy. The nearly degenerate FM/AFM total energies provide a reasonable explanation for the experimentally observed spin-fluctuation. In addition, a dumbbell-shape 4d − t_2g recombined d_xz − d_yz orbital ordering on the Ru sublattice is obtained owing to the on-site Coulomb interaction U associated with the elongated RuO₆ octahedron local structure. The discovered orbital ordering is robust against the spin-orbit interaction as well as the surface terminations. Our findings unravel the on-site Coulomb correlation as the driving force of the Ru-4d orbital ordering as well as the inherent magnetic degeneracy.

X-ray magnetic diffraction under high pressure

Advances in both non-resonant and resonant X-ray magnetic diffraction since the 1980s have provided researchers with a powerful tool for exploring the spin, orbital and ion degrees of freedom in magnetic solids, as well as parsing their interplay. Here, we discuss key issues for performing X-ray magnetic diffraction on single-crystal samples under high pressure (above 40 GPa) and at cryogenic temperatures (4 K). We present case studies of both non-resonant and resonant X-ray magnetic diffraction under pressure for a spin-flip transition in an incommensurate spin-density-wave material and a continuous quantum phase transition of a commensurate all-in-all-out antiferromagnet. Both cases use diamond-anvil-cell technologies at third-generation synchrotron radiation sources. In addition to the exploration of the athermal emergence and evolution of antiferromagnetism discussed here, these techniques can be applied to the study of the pressure evolution of weak charge order such as charge-density waves, antiferro-type orbital order, the charge anisotropic tensor susceptibility and charge superlattices associated with either primary spin order or softened phonons.

A soft x-ray-ultraviolet (SUV) beamline and diffractometer for resonant elastic scattering and ultraviolet-vacuum ultraviolet reflectance at the Singapore synchrotron light source

A new beamline and a six-circle UHV diffractometer have been constructed at the Singapore Synchrotron Light Source with a broad energy coverage from 3.5 to 1500 eV. The beamline is optimized for ultraviolet-vacuum-ultraviolet optical reflectivity and resonant soft X-ray scattering with medium energy resolution over a broad energy range, achieved by using a self-focusing monochromator consisting of a plane mirror and three variable line spacing gratings. The unique character of the diffractometer comprises 4-circles in the vertical plane and 2-circles in the horizontal plane. Thirteen motions are available inside the UHV chamber with a base pressure of 1 × 10^-9 mbar. Two sample holders working independently over a temperature range of 37 K-400 K are controlled by a closed-cycle cryostat, while the bottom holder inside a high field compact pulsed magnet is available for measurements requiring a magnetic field.

Site- and phase-selective x-ray absorption spectroscopy based on phase-retrieval calculation

Understanding the chemical state of a particular element with multiple crystallographic sites and/or phases is essential to unlocking the origin of material properties. To this end, resonant x-ray diffraction spectroscopy (RXDS) achieved through a combination of x-ray diffraction (XRD) and x-ray absorption spectroscopy (XAS) techniques can allow for the measurement of diffraction anomalous fine structure (DAFS). This is expected to provide a peerless tool for electronic/local structural analyses of materials with complicated structures thanks to its capability to extract spectroscopic information about a given element at each crystallographic site and/or phase. At present, one of the major challenges for the practical application of RXDS is the rigorous determination of resonant terms from observed DAFS, as this requires somehow determining the phase change in the elastic scattering around the absorption edge from the scattering intensity. This is widely known in the field of XRD as the phase problem. The present review describes the basics of this problem, including the relevant background and theory for DAFS and a guide to a newly-developed phase-retrieval method based on the logarithmic dispersion relation that makes it possible to analyze DAFS without suffering from the intrinsic ambiguities of conventional iterative-fitting. Several matters relating to data collection and correction of RXDS are also covered, with a final emphasis on the great potential of powder-sample-based RXDS (P-RXDS) to be used in various applications relevant to practical materials, including antisite-defect-type electrode materials for lithium-ion batteries.

Non-equilibrium control of complex solids by nonlinear phononics

We review some recent advances in the use of optical fields at terahertz frequencies to drive the lattice of complex materials. We will focus on the control of low energy collective properties of solids, which emerge on average when a high frequency vibration is driven and a new crystal structure induced. We first discuss the fundamentals of these lattice rearrangements, based on how anharmonic mode coupling transforms an oscillatory motion into a quasi-static deformation of the crystal structure. We then discuss experiments, in which selectively changing a bond angle turns an insulator into a metal, accompanied by changes in charge, orbital and magnetic order. We then address the case of light induced non-equilibrium superconductivity, a mysterious phenomenon observed in some cuprates and molecular materials when certain lattice vibrations are driven. Finally, we show that the dynamics of electronic and magnetic phase transitions in complex-oxide heterostructures follow distinctly new physical pathways in case of the resonant excitation of a substrate vibrational mode.

The contribution of Diamond Light Source to the study of strongly correlated electron systems and complex magnetic structures

We review some of the significant contributions to the field of strongly correlated materials and complex magnets, arising from experiments performed at the Diamond Light Source (Harwell Science and Innovation Campus, Didcot, UK) during the first few years of operation (2007-2014). We provide a comprehensive overview of Diamond research on topological insulators, multiferroics, complex oxides and magnetic nanostructures. Several experiments on ultrafast dynamics, magnetic imaging, photoemission electron microscopy, soft X-ray holography and resonant magnetic hard and soft X-ray scattering are described.

Form factor dispersion at La M5,4 edges and average density of resonant atoms

Resonant soft x-ray scattering on complex oxide superlattices shows very large variations in the superlattice reflection position and intensity near La M5,4 edges. Resonant dispersion of the La x-ray form factor describes the observations well. We determine the average density of resonant La atoms and the thickness of superlattice layers.

Resonant elastic soft x-ray scattering

Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site and valence specific probe to study spatial modulations of charge, spin and orbital degrees of freedom in solids on the nanoscopic length scale. It is not only used to investigate single-crystalline materials. This method also enables one to examine electronic ordering phenomena in thin films and to zoom into electronic properties emerging at buried interfaces in artificial heterostructures. During the last 20 years, this technique, which combines x-ray scattering with x-ray absorption spectroscopy, has developed into a powerful probe to study electronic ordering phenomena in complex materials and furthermore delivers important information on the electronic structure of condensed matter. This review provides an introduction to the technique, covers the progress in experimental equipment, and gives a survey on recent RSXS studies of ordering in correlated electron systems and at interfaces.

Microscopic theory of resonant soft-x-ray scattering in materials with charge order: the example of charge stripes in high-temperature cuprate superconductors

We present a microscopic theory of resonant soft-x-ray scattering that accounts for the delocalized character of valence electrons. Unlike past approaches based on local form factors, our functional determinant method treats realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. We show that the two-peak structure observed near the O K edge of stripe-ordered La1.875Ba0.125CuO4 is due to dynamical nesting within the canonical cuprate band structure. Our results provide evidence for reasonably well-defined, high-energy quasiparticles in cuprates and establish resonant soft-x-ray scattering as a bulk-sensitive probe of the electron quasiparticles.

Ground state in a half-doped manganite distinguished by neutron spectroscopy

We have measured the spin-wave spectrum of the half-doped bilayer manganite Pr(Ca,Sr)(2)Mn(2)O(7) in its spin, charge, and orbital ordered phase. The measurements, which extend throughout the Brillouin zone and cover the entire one-magnon spectrum, are compared critically with spin-wave calculations for different models of the electronic ground state. The data are described very well by the Goodenough model, which has weakly interacting ferromagnetic zig-zag chains in the CE-type arrangement. A model that allows ferromagnetic dimers to form within the zigzags is inconsistent with the data. The analysis conclusively rules out the strongly bound dimer (Zener polaron) model.

Resonant soft x-ray scattering from stepped surfaces of SrTiO3

We studied the resonant diffraction signal from stepped surfaces of SrTiO(3) at the Ti 2p → 3d (L(2,3)) resonance in comparison with x-ray absorption (XAS) and specular reflectivity data. The steps on the surface form an artificial superstructure suitable as a model system for resonant soft x-ray diffraction. A small step density on the surface is sufficient to produce a well defined diffraction peak. We determined the optical parameters of the sample across the resonance and found that the differences between the energy dependence of the x-ray absorption signal, the specular reflectivity and the step-related peak reflect the different quantities probed in these signals. When recorded at low incidence or detection angles, XAS and specular reflectivity spectra are strongly distorted by the changes of the angle of total reflection with energy. The resonant diffraction spectrum is less affected and can be used as a spectroscopic probe even in less favorable geometries.

Fragile magnetic ground state in half-doped LaSr2Mn2O7

We investigated the orbital and antiferromagnetic ordering behaviors of the half-doped bilayer manganite La(2-2x)Sr(1+2x)Mn2O7 (x ≃ 0.5) by using Mn L(2,3)-edge resonant soft x-ray scattering. Resonant soft x-ray scattering reveals the CE-type orbital order below T(oo) ≃ 220  K, which shows partial melting behavior below T(m) ≃ 165  K. We also found coexistence CE- and A-type antiferromagnetic orders. Both orders involve the CE-type orbital order with nearly the same orbital character and are coupled with each other. These results manifest that the ground state with the CE-type antiferromagnetic order is easily susceptible to destabilization into the A-type one even with a small fluctuation of the doping level, as suggested by the extremely narrow magnetic phase boundaries at x ≃ 0.5±0.005.

Development of a compact fast CCD camera and resonant soft x-ray scattering endstation for time-resolved pump-probe experiments

The designs of a compact, fast CCD (cFCCD) camera, together with a resonant soft x-ray scattering endstation, are presented. The cFCCD camera consists of a highly parallel, custom, thick, high-resistivity CCD, readout by a custom 16-channel application specific integrated circuit to reach the maximum readout rate of 200 frames per second. The camera is mounted on a virtual-axis flip stage inside the RSXS chamber. When this flip stage is coupled to a differentially pumped rotary seal, the detector assembly can rotate about 100°/360° in the vertical/horizontal scattering planes. With a six-degrees-of-freedom cryogenic sample goniometer, this endstation has the capability to detect the superlattice reflections from the electronic orderings showing up in the lower hemisphere. The complete system has been tested at the Advanced Light Source, Lawrence Berkeley National Laboratory, and has been used in multiple experiments at the Linac Coherent Light Source, SLAC National Accelerator Laboratory.

An in-vacuum diffractometer for resonant elastic soft x-ray scattering

We describe the design, construction, and performance of a 4-circle in-vacuum diffractometer for resonant elastic soft x-ray scattering. The diffractometer, installed on the resonant elastic and inelastic x-ray scattering beamline at the Canadian Light Source, includes 9 in-vacuum motions driven by in-vacuum stepper motors and operates in ultra-high vacuum at base pressure of 2 × 10(-10) Torr. Cooling to a base temperature of 18 K is provided with a closed-cycle cryostat. The diffractometer includes a choice of 3 photon detectors: a photodiode, a channeltron, and a 2D sensitive channelplate detector. Along with variable slit and filter options, these detectors are suitable for studying a wide range of phenomena having both weak and strong diffraction signals. Example measurements of diffraction and reflectivity in Nd-doped (La,Sr)(2)CuO(4) and thin film (Ga,Mn)As are shown.

Photoinduced melting of antiferromagnetic order in La(0.5)Sr(1.5)MnO4 measured using ultrafast resonant soft x-ray diffraction

We used ultrafast resonant soft x-ray diffraction to probe the picosecond dynamics of spin and orbital order in La(0.5)Sr(1.5)MnO(4) after photoexcitation with a femtosecond pulse of 1.5 eV radiation. Complete melting of antiferromagnetic spin order is evidenced by the disappearance of a (1/4,1/4,1/2) diffraction peak. On the other hand, the (1/4,1/4,0) diffraction peak, reflecting orbital order, is only partially reduced. We interpret the results as evidence of destabilization in the short-range exchange pattern with no significant relaxation of the long-range Jahn-Teller distortions. Cluster calculations are used to analyze different possible magnetically ordered states in the long-lived metastable phase. Nonthermal coupling between light and magnetism emerges as a primary aspect of photoinduced phase transitions in manganites.

Ferromagnetic enhancement of CE-type spin ordering in (Pr,Ca)MnO3

We present resonant soft x-ray scattering results from small bandwidth manganites (Pr,Ca)MnO(3), which show that the CE-type spin ordering (SO) at the phase boundary is stabilized only below the canted antiferromagnetic transition temperature and enhanced by ferromagnetism in the macroscopically insulating state (FM-I). Our results reveal the fragility of the CE-type ordering that underpins the colossal magnetoresistance effect in this system, as well as an unexpected cooperative interplay between FM-I and CE-type SO which is in contrast to the competitive interplay between the ferromagnetic metallic state and CE-type ordering.

Orbital reflectometry of oxide heterostructures

The occupation of d orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition-metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could not thus far be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft-X-ray reflectivity data, without resorting to model calculations. We demonstrate that the method is sensitive enough to resolve differences of ~3% in the occupation of Ni e(g) orbitals in adjacent atomic layers of a LaNiO(3)-LaAlO(3) superlattice, in good agreement with ab initio electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up many new perspectives for orbital physics in transition-metal oxides.

Jahn-Teller distortions and the magnetic order in the perovskite manganites

We introduce an effective model for e(g) electrons to describe three-dimensional perovskite (La(1 - x)Sr(x)MnO(3) and La(1 - x)Ca(x)MnO(3)) manganites and study the magnetic and orbital order on a 4 × 4 × 4 cluster using correlated wavefunctions. The model includes the kinetic energy, and on-site Coulomb interactions for e(g) electrons, antiferromagnetic superexchange interaction between S = 3/2 core spins, and the coupling between e(g) electrons and Jahn-Teller modes. The model reproduces the experimentally observed magnetic order: (i) an A-type antiferromagnetic phase in the undoped insulator LaMnO(3), with alternating e(g) orbitals and with small Jahn-Teller distortions, changing to a conducting phase at 32 GPa pressure, and (ii) ferromagnetic order in one-eighth-doped La(7/8)Sr(1/8)MnO(3) and in quarter-doped La(3/4)Sr(1/4)MnO(3) compounds. For half-doped La(1/2)Ca(1/2)MnO(3) one finds a competition between a ferromagnetic conductor and the CE insulating phase; the latter is stabilized by the Jahn-Teller coupling being two times larger than for the strontium-doped compound. Altogether, there is a subtle balance between all Hamiltonian parameters and the phase diagram is quite sensitive to the precise values they take.

KO2: realization of orbital ordering in a p-orbital system

KO2 is a molecular solid consisting of oxygen dimers. K present in the lattice donates an electron which goes on to occupy the O p levels. As the basic electronic structure is similar to that of an oxygen molecule, except for broadening due to solid state effects, KO2 represents the realization of the doping of oxygen molecules arranged in a lattice. These considerations alone result in magnetism with high ordering temperatures as our calculations reveal. However, we find that the high temperature structure is unstable to an orbital ordering (OO) transition. The microscopic considerations driving the OO transition, however, are electrostatic interactions instead of the often encountered superexchange driven ordering within the Kugel-Khomskii model often used to describe the OO. This OO transition is also found to preclude any possibility of high magnetic ordering temperatures, which otherwise seemed possible.

RASOR: an advanced instrument for soft x-ray reflectivity and diffraction

We report the design and construction of a novel soft x-ray diffractometer installed at Diamond Light Source. The beamline endstation RASOR is constructed for general users and designed primarily for the study of single crystal diffraction and thin film reflectivity. The instrument is comprised of a limited three circle (theta, 2theta, and chi) diffractometer with an additional removable rotation (phi) stage. It is equipped with a liquid helium cryostat, and post-scatter polarization analysis. Motorized motions are provided for the precise positioning of the sample onto the diffractometer center of rotation, and for positioning the center of rotation onto the x-ray beam. The functions of the instrument have been tested at Diamond Light Source, and initial test measurements are provided, demonstrating the potential of the instrument.

Nature of the magnetic order and origin of induced ferroelectricity in TbMnO3

The magnetic structures which endow TbMnO(3) with its multiferroic properties have been reassessed on the basis of a comprehensive soft x-ray resonant scattering (XRS) study. The selectivity of XRS facilitated separation of the various contributions (Mn L(2) edge, Mn 3d moments; Tb M(4) edge, Tb 4f moments), while its variation with azimuth provided information on the moment direction of distinct Fourier components. When the data are combined with a detailed group theory analysis, a new picture emerges of the ferroelectric transition at 28 K. Instead of being driven by the transition from a collinear to a noncollinear magnetic structure, as has previously been supposed, it is shown to occur between two noncollinear structures.

An ultrahigh-vacuum apparatus for resonant diffraction experiments using soft x rays (hnu=300-2000 eV)

We have developed an ultrahigh-vacuum instrument for resonant diffraction experiments using polarized soft x rays in the energy range of hnu=300-2000 eV at beamline BL17SU of SPring-8. The diffractometer consists of modified differentially pumped rotary feedthroughs for theta-2theta stages, a sample manipulator with motor-controlled x-y-z-, tilt (chi)-, and azimuth (phi)-axes, and a liquid helium flow-type cryostat for temperature dependent measurements between 30 and 300 K. Test results indicate that the diffractometer exhibits high reproducibility (better than 0.001 degrees ) for a Bragg reflection of alpha-quartz 100 at a photon energy of hnu=1950 eV. Typical off- and on-resonance Bragg reflections in the energy range of 530-1950 eV could be measured using the apparatus. The results show that x-ray diffraction experiments with energy-, azimuth-, and incident photon polarization-dependence can be reliably measured using soft x rays in the energy range of approximately 300-2000 eV. The facility can be used for resonant diffraction experiments across the L-edge of transition metals, M-edge of lanthanides, and up to the Si K-edge of materials.

Effects of layered structural features on charge/orbital ordering in (La, Sr)(n+1)Mn(n)O(3n+1) (n = 1 and 2)

The charge/orbital ordering (COO) of the layered mixed-valence manganites (La,Sr)(n+1)Mn(n)O(3n+1) (n = 1 and 2) is examined by first-principles calculations and discussed in comparison with the La(0.5)Ca(0.5)MnO(3) perovskite phase ([Formula: see text]). The results demonstrated that the layered structural features could yield not only visibly weak coupling between Mn-O layers but also various features in the orbital ordering associated with different types of local structural distortions. In both La(0.5)Sr(1.5)MnO(4) (n = 1) and LaSr(2)Mn(2)O(7) (n = 2) phases, the orbital ordering can be chiefly assigned to the d(x(2)-y(2)) orbital, in contrast with the zigzag-type d(z(2)) orbital ordering in the [Formula: see text] perovskite phase. Our theoretical analysis shows that a variety of essential factors, including the local structural distortions of the MnO(6) octahedra, the on-site Coulomb interaction, and magnetic interaction, have to be properly considered in order to achieve acceptable COO ground states for the layered variants in (La,Sr)(n+1)Mn(n)O(3n+1).

Interplay between the orbital and magnetic order in monolayer La(1-x)Sr(1+x)MnO(4) manganites

A two-dimensional model which describes e(g) electrons in a monolayer of an undoped and half doped manganite La(1-x)Sr(1+x)MnO(4) is studied using correlated wavefunctions. The effective Hamiltonian takes into account the kinetic energy, the crystal field splitting between x(2)-y(2) and 3z(2)-r(2) orbitals, and on-site Coulomb interactions for e(g) electrons. They interact with S = 3/2 spins due to t(2g) electrons, which are treated as frozen core spins. Furthermore, the model includes antiferromagnetic superexchange interaction between core spins, and the coupling between e(g) electrons and Jahn-Teller modes. The model reproduces the antiferromagnetic order in the undoped LaSrMnO(4) compound, with occupied 3z(2)-r(2) orbitals and elongated MnO(6) octahedra along the direction perpendicular to the Mn-O plane. In half doped La(0.5)Sr(1.5)MnO(4) manganite one finds robust chequerboard-like charge order using realistic parameters. However, the experimentally observed CE phase is more difficult to stabilize, and we discuss the necessary conditions to obtain it within the present model. Altogether, we conclude that the Jahn-Teller effect plays a crucial role in the entire regime of doping.

Determination of the antiferroquadrupolar order parameters in UPd(3)

By combining accurate heat capacity and x-ray resonant scattering results we have resolved the long standing question regarding the nature of the quadrupolar ordered phases in UPd(3). The order parameter of the highest temperature quadrupolar phase has been uniquely determined to be antiphase Q{zx} in contrast to the previous conjecture of Q{x{2}-y{2}}. The azimuthal dependence of the x-ray scattering intensity from the quadrupolar superlattice reflections indicates that the lower temperature phases are described by a superposition of order parameters. The heat capacity features associated with each of the phase transitions characterize their order, which imposes restrictions on the matrix elements of the quadrupolar operators.

Orbital ordering and Jahn-Teller distortion in Perovskite ruthenate SrRuO3

Local density approximation plus on-site Coulomb interaction U band structure calculations reveal that SrRuO3 exhibits a half-metallic ground state with an integer spin moment of 2.0 microB/SrRuO3. An associated tilting 4dt2g orbital ordering on a Ru sublattice is observed under the on-site Coulomb interaction U in the presence of lattice distortion. This finding unravels the on-site Coulomb correlation as the driving force of the 4d orbital ordering and Jahn-Teller distortion as well as of the half-metallic ground state.

Resonant x-ray diffraction studies on the charge ordering in magnetite

Here we show that the low temperature phase of magnetite is associated with an effective, although fractional, ordering of the charge. Evidence and a quantitative evaluation of the atomic charges are achieved by using resonant x-ray diffraction (RXD) experiments whose results are further analyzed with the help of ab initio calculations of the scattering factors involved. By confirming the results obtained from x-ray crystallography we have shown that RXD is able to probe quantitatively the electronic structure in very complex oxides, whose importance covers a wide domain of applications.

Spin-wave dispersion in orbitally ordered La1/2Sr3/2MnO4

The magnon dispersion in the charge, orbital, and spin ordered phase in La1/2Sr3/2MnO4 has been studied by means of inelastic neutron scattering. We find excellent agreement with a magnetic interaction model based on the CE-type superstructure. The magnetic excitations are dominated by ferromagnetic exchange parameters revealing a nearly one-dimensional character at high energies. The strong ferromagnetic interaction in the charge or orbital ordered phase appears to be essential for the capability of manganites to switch between metallic and insulating phases.

Charge-orbital ordering and Verwey transition in magnetite measured by resonant soft X-ray scattering

We report experimental evidence for the charge-orbital ordering in magnetite below the Verwey transition temperature T(V). Measurements of O K-edge resonant x-ray scattering on magnetite reveal that the O 2p states in the vicinity of the Fermi level exhibit a charge-orbital ordering along the c axis with a spatial periodicity of the doubled lattice parameter of the undistorted cubic phase. Such a charge-orbital ordering vanishes abruptly above T(V) and exhibits a thermal hysteresis, correlating closely with the Verwey transition in magnetite.

Spectroscopy of stripe order in La1.8Sr0.2NiO4 using resonant soft x-ray diffraction

Strong resonant enhancements of the charge-order and spin-order superstructure-diffraction intensities in La1.8Sr0.2NiO4 are observed when x-ray energies in the vicinity of the Ni L2,3 absorption edges are used. The pronounced photon-energy and polarization dependences of these diffraction intensities allow for a critical determination of the local symmetry of the ordered spin and charge carriers. We found that not only the antiferromagnetic order but also the charge-order superstructure resides within the NiO2 layers; the holes are mainly located on in-plane oxygens surrounding a Ni2+ site with the spins coupled antiparallel in close analogy to Zhang-Rice singlets in the cuprates.

Direct Investigation of Orbital Ordering in a Colossal Magnetoresistance Manganite by Means of X-ray Linear Dichroism at the Mn L Edge

We have investigated for the first time the orbital ordering in a three-dimensional colossal magnetoresistance manganite, namely La(7/8)Sr(1/8)MnO3, by applying soft X-ray linear dichroism (XLD) to the Mn L edge. We found that the cooperative Jahn-Teller distorted orthorhombic phase, which is present at a temperature of 240 K, is probably accompanied by a predominantly cross type (x2 - z2)/(y2 - z2) orbital ordering. This result is discussed in the light of different exchange interaction models.

Soft x-ray resonant diffraction study of magnetic and orbital correlations in a manganite near half doping

We have utilized resonant x-ray diffraction at the Mn L(II,III) edges in order to directly compare magnetic and orbital correlations in Pr0.6Ca0.4MnO3. Comparing the widths of the magnetic and orbital diffraction peaks, we find that the magnetic correlation length exceeds that of the orbital order by nearly a factor of 2. Furthermore, we observe a large (approximately 3 eV) spectral weight shift between the magnetic and orbital resonant line shapes, which cannot be explained within the classic Goodenough picture of a charge-ordered ground state. To explain the shift, we calculate the orbital and magnetic resonant diffraction line shapes based on a relaxed charge-ordered model.

Two-dimensional charge order in layered 2-1-4 perovskite oxides

Monte Carlo simulations are performed on the three-dimensional (3D) Ising model with the 2-1-4 layered perovskite structure as a minimal model for checkerboard charge ordering phenomena in layered perovskite oxides. Because of the interlayer frustration, only 2D long-range order emerges with a finite correlation length along the c axis. Critical exponents of the transition change continuously as a function of the interlayer coupling constant. The interlayer long-range Coulomb interaction decays exponentially and is negligible even between the second-neighbor layers. Instead, monoclinic distortion of a tetragonal unit cell lifts the macroscopic degeneracy to induce a 3D charge ordering. The dimensionality of the charge order in La0.5Sr1.5MnO4 is discussed from this viewpoint.