Incommensurate stripe order in La2-xSrxNiO4 with x=0.225

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.

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.

Evidence for a Nematic Phase in La_{1.75}Sr_{0.25}NiO_{4}

Determining the nature of electronic states in doped Mott insulators remains a challenging task. In the case of tetragonal La_{2-x}Sr_{x}NiO_{4}, the occurrence of diagonal charge and spin stripe order in the ground state is now well established. In contrast, the nature of the high-temperature "disordered" state from which the stripe order develops has long been a subject of controversy, with considerable speculation regarding a polaronic liquid. Following the recent detection of dynamic charge stripes, we use neutron scattering measurements on an x=0.25 crystal to demonstrate that the dispersion of the charge-stripe excitations is anisotropic. This observation provides compelling evidence for the presence of electronic nematic order.

Stacked charge stripes in the quasi-2D trilayer nickelate La4Ni3O8

The quasi-2D nickelate La4Ni3O8 (La-438), consisting of trilayer networks of square planar Ni ions, is a member of the so-called T' family, which is derived from the Ruddlesden-Popper (R-P) parent compound La4Ni3O10-x by removing two oxygen atoms and rearranging the rock salt layers to fluorite-type layers. Although previous studies on polycrystalline samples have identified a 105-K phase transition with a pronounced electronic and magnetic response but weak lattice character, no consensus on the origin of this transition has been reached. Here, we show using synchrotron X-ray diffraction on high-pO2 floating zone-grown single crystals that this transition is associated with a real space ordering of charge into a quasi-2D charge stripe ground state. The charge stripe superlattice propagation vector, q = (2/3, 0, 1), corresponds with that found in the related 1/3-hole doped single-layer R-P nickelate, La5/3Sr1/3NiO4 (LSNO-1/3; Ni(2.33+)), with orientation at 45° to the Ni-O bonds. The charge stripes in La-438 are weakly correlated along c to form a staggered ABAB stacking that reduces the Coulomb repulsion among the stripes. Surprisingly, however, we find that the charge stripes within each trilayer of La-438 are stacked in phase from one layer to the next, at odds with any simple Coulomb repulsion argument.

Solitary Magnons in the S=5/2 Antiferromagnet CaFe_{2}O_{4}

CaFe_{2}O_{4} is a S=5/2 anisotropic antiferromagnet based upon zig-zag chains having two competing magnetic structures, denoted as the A (↑↑↓↓) and B (↑↓↑↓) phases, which differ by the c-axis stacking of ferromagnetic stripes. We apply neutron scattering to demonstrate that the competing A and B phase order parameters result in magnetic antiphase boundaries along c which freeze on the time scale of ∼1  ns at the onset of magnetic order at 200 K. Using high resolution neutron spectroscopy, we find quantized spin wave levels and measure 9 such excitations localized in regions ∼1-2 c-axis lattice constants in size. We discuss these in the context of solitary magnons predicted to exist in anisotropic systems. The magnetic anisotropy affords both competing A+B orders as well as localization of spin excitations in a classical magnet.

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.

Direct observation of dynamic charge stripes in La2-xSrxNiO4

The insulator-to-metal transition continues to be a challenging subject, especially when electronic correlations are strong. In layered compounds, such as La2-xSrxNiO4 and La2-xBaxCuO4, the doped charge carriers can segregate into periodically spaced charge stripes separating narrow domains of antiferromagnetic order. Although there have been theoretical proposals of dynamically fluctuating stripes, direct spectroscopic evidence of charge-stripe fluctuations has been lacking. Here we report the detection of critical lattice fluctuations, driven by charge-stripe correlations, in La2-xSrxNiO4 using inelastic neutron scattering. This scattering is detected at large momentum transfers where the magnetic form factor suppresses the spin fluctuation signal. The lattice fluctuations associated with the dynamic charge stripes are narrow in q and broad in energy. They are strongest near the charge-stripe melting temperature. Our results open the way towards the quantitative theory of dynamic stripes and for directly detecting dynamical charge stripes in other strongly correlated systems, including high-temperature superconductors such as La2-xSrxCuO4.

Ultrafast charge localization in a stripe-phase nickelate

Self-organized electronically ordered phases are a recurring feature in correlated materials, resulting in, for example, fluctuating charge stripes whose role in high-TC superconductivity is under debate. However, the relevant cause-effect relations between real-space charge correlations and low-energy excitations remain hidden in time-averaged studies. Here we reveal ultrafast charge localization and lattice vibrational coupling as dynamic precursors of stripe formation in the model compound La(1.75)Sr(0.25)NiO4, using ultrafast and equilibrium mid-infrared spectroscopy. The opening of a pseudogap at a crossover temperature T* far above long-range stripe formation establishes the onset of electronic localization, which is accompanied by an enhanced Fano asymmetry of Ni-O stretch vibrations. Ultrafast excitation triggers a sub-picosecond dynamics exposing the synchronous modulation of electron-phonon coupling and charge localization. These results illuminate the role of localization in forming the pseudogap in nickelates, opening a path to understanding this mysterious phase in a broad class of complex oxides.

Incommensurate sinusoidal oxygen modulations in layered manganites La(1-x)Sr(1+x)MnO4 (x≥0.5)

We have studied the incommensurate-ordered phase in overdoped La0.4Sr1.6MnO4 by resonant x-ray diffraction at the Mn K edge. Weak resonant superlattice (h±0.2 h±0.2 0) and (h±0.4 h±0.4 0) reflections of the tetragonal structure were found below ~240 K. The energy, azimuth angle, and polarization dependencies of the resonant scattering have revealed sinusoidal modulations of the oxygen motions that are transverse and longitudinal to the tetragonal [110] direction. This result discards (Mn(3+),Mn(4+))-like stripe-type order but point to a charge-density-modulation picture.

Hourglass dispersion in overdoped single-layered manganites

The incommensurate stripelike magnetic ordering in two single-layered manganites, Nd0.33Sr1.67MnO4 and Pr0.33Ca1.67MnO4, is found to exhibit an hourglasslike excitation spectrum very similar to that seen in various cuprates superconductors, but only for sufficiently short correlation lengths. Several characteristic features of an hourglass dispersion can be identified: enhancement of intensity at the merging of the incommensurate branches, rotation of the intensity maxima with higher energy transfer, and suppression of the outward-dispersing branches at low energy. The correlation length of the magnetic ordering and the large ratio of intra- to interstripe couplings are identified as the decisive parameters causing the hourglass shape of the spectrum.

Jahn-Teller mechanism of stripe formation in doped layered La(2-x)Sr(x)NiO4 nickelates

We introduce an effective model for e(g) electrons to describe quasi-two-dimensional layered La(2-x)Sr(x)NiO(4) nickelates and study it using correlated wavefunctions on 8 × 8 and 6 × 6 clusters. The effective Hamiltonian includes the kinetic energy, on-site Coulomb interactions for e(g) electrons (intraorbital U and Hund's exchange J(H)) and the coupling between e(g) electrons and Jahn-Teller distortions (static modes). The experimental ground state phases with inhomogeneous charge, spin and orbital order at the dopings x = 1/3 and 1/2 are reproduced very well by the model. Although the Jahn-Teller distortions are weak, we show that they play a crucial role and stabilize the observed cooperative charge, magnetic and orbital order in the form of a diagonal stripe phase at x = 1/3 doping and a chequerboard phase at x = 1/2 doping.

Evidence for charge orbital and spin stripe order in an overdoped manganite

Overdoped La0.42Sr1.58MnO4 exhibits a complex ordering of charges, orbitals, and spins. Neutron diffraction experiments reveal three incommensurate and one commensurate order parameters to be tightly coupled. The position and the shape of the distinct superstructure scattering as well as higher-order signals are inconsistent with a harmonic charge and spin-density-wave picture but point to a stripe arrangement in which ferromagnetic zigzag chains are disrupted by excess Mn(4+).

Pseudogap of metallic layered nickelate R(2-x)Sr(x)NiO4 (R = Nd, Eu) crystals measured using angle-resolved photoemission spectroscopy

We have investigated charge dynamics and electronic structures for single crystals of metallic layered nickelates, R(2-x)Sr(x)NiO4 (R = Nd, Eu), isostructural to La(2-x)Sr(x)CuO4. Angle-resolved photoemission spectroscopy on the barely metallic Eu(0.9)Sr(1.1)NiO4 (R = Eu, x = 1.1) has revealed a large hole surface of x2-y2 character with a high-energy pseudogap of the same symmetry and comparable magnitude with those of underdoped (x<0.1) cuprates, although the antiferromagnetic interactions are 1 order of magnitude smaller. This finding strongly indicates that the momentum-dependent pseudogap feature in the layered nickelate arises from the real-space charge correlation.

Charge excitations in the stripe-ordered La5/3Sr1/3NiO4 and La2-x(Ba,Sr)xCuO4 superconducting compounds

Charge excitations in stripe-ordered 214 compounds La_{5/3}Sr_{1/3}NiO_{4} and 1/8-doped La2-x(Ba or Sr)xCuO4 are studied using resonant inelastic x-ray scattering in the hard x-ray regime. We observe = or approximately 1 eV excitation with a momentum transfer corresponding to the charge stripe spatial period both for the diagonal (nickelate) and parallel (cuprates) stripes. They are interpreted as collective stripe excitations or anomalous softening of the charge excitonic modes of the in-gap states.

Magnetic correlations in La2-xSrxCoO4 studied by neutron scattering: possible evidence for stripe phases

Spin correlations in La2-xSrxCoO4 (0.3 < or = x < or = 0.6) have been studied by neutron scattering. The commensurate antiferromagnetic order of La2CoO4 persists in a very short range up to a Sr content of x = 0.3, whereas small amounts of Sr suppress commensurate antiferromagnetism in cuprates and in nickelates. La2-xSrxCoO4 with x > 0.3 exhibits incommensurate spin ordering with the modulation closely following the amount of doping. These incommensurate phases strongly resemble the stripe phases observed in cuprates and nickelates, but incommensurate magnetic ordering appears only at larger Sr content in the cobaltates due to a reduced charge mobility.

Commensurate-incommensurate crossover of charge stripe in La2-xSrxNiO4 (x approximately 1/3)

The temperature (T) dependence of the charge-stripe order in La2-xSrxNiO4 has been investigated in the vicinity of x approximately 1/3 by synchrotron radiation x-ray diffraction measurements. With decreasing T, a prominent commensurate-incommensurate (C-IC) crossover is observed in the x<1/3 region, while for the x>1/3 region the IC order is dominant over the whole T range. Such a C-IC crossover is interpreted as the entropy-driven self-doping of the charge stripes, and its x dependence indicates the clear electron-hole asymmetry with the x=1/3 compound as the Mott insulator.