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

Nanoscale inhomogeneity of charge density waves dynamics in La2−xSrxNiO4

While stripe phases with broken rotational symmetry of charge density are known to emerge in doped strongly correlated perovskites, the dynamics and heterogeneity of spatial ordering remain elusive. Here we shed light on the temperature dependent lattice motion and the spatial nanoscale phase separation of charge density wave order in the archetypal striped phase in La2−xSrxNiO4+y (LSNO) perovskite using X-ray photon correlation spectroscopy (XPCS) joint with scanning micro X-ray diffraction (SµXRD). While it is known that the CDW in 1/8 doped cuprates shows a remarkable stability we report the CDW motion dynamics by XPCS in nickelates with an anomalous quantum glass regime at low temperature, T < 65 K, and the expected thermal melting at higher temperature 65 < T < 120 K. The nanoscale CDW puddles with a shorter correlation length are more mobile than CDW puddles with a longer correlation length. The direct imaging of nanoscale spatial inhomogeneity of CDW by scanning micro X-ray diffraction (SµXRD) shows a nanoscale landscape of percolating short range dynamic CDW puddles competing with large quasi-static CDW puddles giving rise to a novel form of nanoscale phase separation of the incommensurate stripes order landscape.

Real Space Imaging of Spin Stripe Domain Fluctuations in a Complex Oxide

Understanding the formation and dynamics of charge and spin-ordered states in low-dimensional transition metal oxide materials is crucial to understanding unconventional high-temperature superconductivity. La_{2-x}Sr_{x}NiO_{4+δ} (LSNO) has attracted much attention due to its interesting spin dynamics. Recent x-ray photon correlation spectroscopy studies have revealed slow dynamics of the spin order (SO) stripes in LSNO. Here, we applied resonant soft x-ray ptychography to map the spatial distribution of the SO stripe domain inhomogeneity in real space. The reconstructed images show the SO domains are spatially anisotropic, in agreement with previous diffraction studies. For the SO stripe domains, it is found that the correlation lengths along different directions are strongly coupled in space. Surprisingly, fluctuations were observed in the real space amplitude signal, rather than the phase or position. We attribute the observed slow dynamics of the stripe domains in LSNO to thermal fluctuations of the SO domain boundaries.

Nanoscale Phase Separation of Incommensurate and Quasi-Commensurate Spin Stripes in Low Temperature Spin Glass of La2−xSrxNiO4

While spin striped phases in La2−xSrxNiO4+y for 0.25 < x < 0.33 are the archetypal case of a 1D spin density wave (SDW) phase in doped antiferromagnetic strongly correlated perovskites, few information is available on the SDW spatial organization. In this context, we have measured the spatial variation of the wave vector of the SDW reflection profile by scanning micro X-ray diffractions with a coherent beam. We obtained evidence of a SDW order–disorder transition by lowering a high temperature phase (T > 50 K) to a low temperature phase (T < 50 K). We have identified quasi-commensurate spin stripe puddles in the ordered phase at 50 < T < 70 K, while the low temperature spin glassy phase presents a nanoscale phase separation of T = 30 K, with the coexistence of quasi-commensurate and incommensurate spin stripe puddles assigned to the interplay of quantum frustration and strong electronic correlations.

Measurement of Spin Dynamics in a Layered Nickelate Using X-Ray Photon Correlation Spectroscopy: Evidence for Intrinsic Destabilization of Incommensurate Stripes at Low Temperatures

We study the temporal stability of stripe-type spin order in a layered nickelate with x-ray photon correlation spectroscopy and observe fluctuations on timescales of tens of minutes over a wide temperature range. These fluctuations show an anomalous temperature dependence: they slow down at intermediate temperatures and speed up on both heating and cooling. This behavior appears to be directly connected with spatial correlations: stripes fluctuate slowly when stripe correlation lengths are large and become faster when spatial correlations decrease. A low-temperature decay of nickelate stripe correlations, reminiscent of what occurs in cuprates as a result of a competition between stripes and superconductivity, hence occurs via loss of both spatial and temporal correlations.

Charge Condensation and Lattice Coupling Drives Stripe Formation in Nickelates

Revealing the predominant driving force behind symmetry breaking in correlated materials is sometimes a formidable task due to the intertwined nature of different degrees of freedom. This is the case for La_{2-x}Sr_{x}NiO_{4+δ}, in which coupled incommensurate charge and spin stripes form at low temperatures. Here, we use resonant x-ray photon correlation spectroscopy to study the temporal stability and domain memory of the charge and spin stripes in La_{2-x}Sr_{x}NiO_{4+δ}. Although spin stripes are more spatially correlated, charge stripes maintain a better temporal stability against temperature change. More intriguingly, charge order shows robust domain memory with thermal cycling up to 250 K, far above the ordering temperature. These results demonstrate the pinning of charge stripes to the lattice and that charge condensation is the predominant factor in the formation of stripe orders in nickelates.

Charge disproportionation and nano phase separation in [Formula: see text]

We have successfully grown centimeter-sized layered [Formula: see text] single crystals under high oxygen pressures of 120-150 bar by the floating zone technique. This enabled us to perform neutron scattering experiments where we observe close to quarter-integer magnetic peaks below [Formula: see text] that are accompanied by steep upwards dispersing spin excitations. Within the high-frequency Ni-O bond stretching phonon dispersion, a softening at the propagation vector for a checkerboard modulation can be observed. We were able to simulate the magnetic excitation spectra using a model that includes two essential ingredients, namely checkerboard charge disproportionation and nano phase separation. The results thus suggest that charge disproportionation is preferred instead of a Jahn-Teller distortion even for this layered [Formula: see text] system.

Direct Visualization of Spatial Inhomogeneity of Spin Stripes Order in La1.72Sr0.28NiO4

In several strongly correlated electron systems, the short range ordering of defects, charge and local lattice distortions are found to show complex inhomogeneous spatial distributions. There is growing evidence that such inhomogeneity plays a fundamental role in unique functionality of quantum complex materials. La1.72Sr0.28NiO4 is a prototypical strongly correlated perovskite showing spin stripes order. In this work we present the spatial distribution of the spin order inhomogeneity by applying micro X-ray diffraction to La1.72Sr0.28NiO4, mapping the spin-density-wave order below the 120 K onset temperature. We find that the spin-density-wave order shows the formation of nanoscale puddles with large spatial fluctuations. The nano-puddle density changes on the microscopic scale forming a multiscale phase separation extending from nanoscale to micron scale with scale-free distribution. Indeed spin-density-wave striped puddles are disconnected by spatial regions with negligible spin-density-wave order. The present work highlights the complex spatial nanoscale phase separation of spin stripes in nickelate perovskites and opens new perspectives of local spin order control by strain.

Disentangled Cooperative Orderings in Artificial Rare-Earth Nickelates

Coupled transitions between distinct ordered phases are important aspects behind the rich phase complexity of correlated oxides that hinder our understanding of the underlying phenomena. For this reason, fundamental control over complex transitions has become a leading motivation of the designer approach to materials. We have devised a series of new superlattices by combining a Mott insulator and a correlated metal to form ultrashort period superlattices, which allow one to disentangle the simultaneous orderings in RENiO_{3}. Tailoring an incommensurate heterostructure period relative to the bulk charge ordering pattern suppresses the charge order transition while preserving metal-insulator and antiferromagnetic transitions. Such selective decoupling of the entangled phases resolves the long-standing puzzle about the driving force behind the metal-insulator transition and points to the site-selective Mott transition as the operative mechanism. This designer approach emphasizes the potential of heterointerfaces for selective control of simultaneous transitions in complex materials with entwined broken symmetries.

Dynamical Effects in Resonant X-Ray Diffraction

Using resonant magnetic diffraction at the Ni L_{2,3} edge in a LaNiO_{3} superlattice, we show that dynamical effects beyond the standard kinematic approximation can drastically modify the resonant scattering cross section. In particular, the combination of extinction and refraction convert maxima to minima in the azimuthal-angle dependence of the diffracted intensity, which is commonly used to determine orbital and magnetic structures by resonant x-ray diffraction. We provide a comprehensive theoretical description of these effects by numerically solving Maxwell's equations in three dimensions. The understanding and description of dynamical diffraction enhances the capabilities of resonant x-ray scattering as a probe of electronic ordering phenomena in solids.

Symmetry of charge order in cuprates

Charge-ordered ground states permeate the phenomenology of 3d-based transition metal oxides, and more generally represent a distinctive hallmark of strongly correlated states of matter. The recent discovery of charge order in various cuprate families has fuelled new interest into the role played by this incipient broken symmetry within the complex phase diagram of high-T(c) superconductors. Here, we use resonant X-ray scattering to resolve the main characteristics of the charge-modulated state in two cuprate families: Bi2Sr(2-x)La(x)CuO(6+δ) (Bi2201) and YBa2Cu3O(6+y) (YBCO). We detect no signatures of spatial modulations along the nodal direction in Bi2201, thus clarifying the inter-unit-cell momentum structure of charge order. We also resolve the intra-unit-cell symmetry of the charge-ordered state, which is revealed to be best represented by a bond order with modulated charges on the O-2p orbitals and a prominent d-wave character. These results provide insights into the origin and microscopic description of charge order in cuprates, and its interplay with superconductivity.

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.

Real-time manifestation of strongly coupled spin and charge order parameters in stripe-ordered La(1.75)Sr(0.25)NiO(4) nickelate crystals using time-resolved resonant x-ray diffraction

We investigate the order parameter dynamics of the stripe-ordered nickelate, La(1.75)Sr(0.25)NiO(4), using time-resolved resonant x-ray diffraction. In spite of distinct spin and charge energy scales, the two order parameters' amplitude dynamics are found to be linked together due to strong coupling. Additionally, the vector nature of the spin sector introduces a longer reorientation time scale which is absent in the charge sector. These findings demonstrate that the correlation linking the symmetry-broken states does not unbind during the nonequilibrium process, and the time scales are not necessarily associated with the characteristic energy scales of individual degrees of freedom.

Symmetry of orbital order in Fe3O4 studied by Fe L(2,3) resonant x-ray diffraction

We studied the symmetry of the Fe 3d wave function in magnetite below the Verwey temperature T(V) with resonant soft-x-ray diffraction. Although the lattice structure of the low-temperature phase of Fe(3)O(4) is well described by the pseudo-orthorhombic Pmca with a slight monoclinic P2/c distortion, we find that the 3d wave function does not reflect the Pmca symmetry, and its distortion toward monoclinic symmetry is by far larger than that of the lattice. The result supports a scenario in which the Verwey transition involves the ordering of t(2g) orbitals with complex-number coefficients.

Phase fluctuations and the absence of topological defects in a photo-excited charge-ordered nickelate

The dynamics of an order parameter's amplitude and phase determines the collective behaviour of novel states emerging in complex materials. Time- and momentum-resolved pump-probe spectroscopy, by virtue of measuring material properties at atomic and electronic time scales out of equilibrium, can decouple entangled degrees of freedom by visualizing their corresponding dynamics in the time domain. Here we combine time-resolved femotosecond optical and resonant X-ray diffraction measurements on charge ordered La(1.75)Sr(0.25)NiO(4) to reveal unforeseen photoinduced phase fluctuations of the charge order parameter. Such fluctuations preserve long-range order without creating topological defects, distinct from thermal phase fluctuations near the critical temperature in equilibrium. Importantly, relaxation of the phase fluctuations is found to be an order of magnitude slower than that of the order parameter's amplitude fluctuations, and thus limits charge order recovery. This new aspect of phase fluctuations provides a more holistic view of the phase's importance in ordering phenomena of quantum matter.

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.

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.

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.

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.

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.

Direct observation of t2g orbital ordering in magnetite

Using soft-x-ray diffraction at the site-specific resonances in the Fe L2,3 edge, we find clear evidence for orbital and charge ordering in magnetite below the Verwey transition. The spectra show directly that the (001/2) diffraction peak (in cubic notation) is caused by t2g orbital ordering at octahedral Fe2+ sites and the (001) by a spatial modulation of the t2g occupation.

Quantum melting of the hole crystal in the spin ladder of Sr(14-x)CaxCu24O41

We have used resonant soft x-ray scattering to study the effects of discommensuration on the hole Wigner crystal (HC) in the spin ladder Sr(14-x)CaxCu24O41 (SCCO). As the hole density is varied the HC forms only with the commensurate wave vectors L(L) = 1/5 and L(L) = 1/3; for incommensurate values it "melts." A simple scaling between L(L) and temperature is observed, tau1/3/tau1/5 = 5/3, indicating an inverse relationship between the interaction strength and wavelength. Our results suggest that SCCO contains hole pairs that are crystallized through an interplay between lattice commensuration and Coulomb repulsion, reminiscent of the "pair density wave" scenario.