Resonant soft x-ray scattering from stepped surfaces of SrTiO3
J. Schlappa, C. Schüßler-Langeheine, C. F. Chang, Z. Hu, E. Schierle, H. Ott, E. Weschke, G. Kaindl, M. Huijben, G. Rijnders, D. H. A. Blank, L. H. Tjeng
We studied the resonant diffraction signal from stepped surfaces of SrTiO3 at the Ti 2p -> 3d (L2,3) resonance in comparison with x-ray absorption (XAS) and specular reflectivity data. The steps on the surface form an artificial superstructure suited 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, showing the high sensitivity of the method. At larger incidence angles, the resonant diffraction spectrum from the steps on the surface resembles the spectrum for specular reflectivity. Both deviate from the XAS data in the relative peak intensities and positions of the peak maxima. We determined the optical parameters of the sample across the resonance and found that the differences between the XAS and scattering spectra reflect the different quantities probed in the different signals. When recorded at low incidence or detection angles, XAS and specular reflectivity spectra are distorted by the changes of the angle of total reflection with energy. Also the step peak spectra, though less affected, show an energy shift of the peak maxima in grazing incidence geometry.
Magnetite, Fe$_3$O$_4$, displays a highly complex low temperature crystal structure that may be charge and orbitally ordered. Many of the recent experimental claims of such ordering rely on resonant soft x-ray diffraction at the oxygen K and iron L edges. We have re-examined this system and undertaken soft x-ray diffraction experiments on a high-quality single crystal. Contrary to previous claims in the literature, we show that the intensity observed at the Bragg forbidden (001/2)$_c$ reflection can be explained purely in terms of the low-temperature structural displacements around the resonan…
Soft X-ray resonant powder diffraction has been performed at the Mn L2,3 edges of A-site ordered SmBaMn2O6. The energy and polarization dependence of the (1/2 1/2 0) reflection provide direct evidence for a (x2-z2)/(y2-z2) type orbital ordering in contrast to the single layer manganite. The temperature dependence of the reflection indicates an orbital reorientation transition at 210 K, below which the charge and orbital ordered MnO2 sheets show AAAA type of stacking. The concurring reduction of the ferromagnetic super exchange correlations leads to further charge localization.
We use resonant soft X-ray diffraction to track the photo-induced dynamics of the antiferromagnetic structure in a NdNiO$_{3}$ thin film. Femtosecond laser pulses with a photon energy of 0.61 eV, resonant with electron transfer between long-bond and short-bond nickel sites, are used to excite the material and drive an ultrafast insulator-metal transition. Polarization sensitive soft X-ray diffraction, resonant to the nickel L$_{3}$-edge, then probes the evolution of the underlying magnetic spiral as a function of time delay with 80 picosecond time resolution. By modelling the azimuthal depende…
The evolution of electron correlation in Sr$_{x}$Ca$_{1-x}$VO$_3$ has been studied using a combination of bulk-sensitive resonant soft x-ray emission spectroscopy (RXES), surface-sensitive photoemission spectroscopy (PES), and ab initio band structure calculations. We show that the effect of electron correlation is enhanced at the surface. Strong incoherent Hubbard subbands are found to lie ~ 20% closer in energy to the coherent quasiparticle features in surface-sensitive PES measurements compared with those from bulk-sensitive RXES, and a ~ 10% narrowing of the overall bandwidth at the surfac…
Resonant soft X-ray scattering was used to determine the presence of more subtle orderings not detected in standard structural analyses. By tuning to specific Co absorption edges, arrangements particular to the electronic states of those elements are enhanced. We have discovered an ordering commensurate to the lattice at the ($\frac{1}{4}~\frac{1}{4}~\frac{1}{4}$) position. Incommensurate peaks near this position were also observed. The intensity of these peaks depends on the oxygen concentration of the sample, and can be suppressed at temperatures above 320 K. Regular orderings of charge dens…
The utility of resonant scattering spectroscopies for identifying electronic symmetries and density distributions changes dramatically as a function of photon energy. In the hard X-ray regime, strong core hole monopole potentials tend to produce X-ray absorption features with well defined electron number on the scattering site. By contrast, in the vacuum ultraviolet (VUV), resonant scattering from Mott insulators tends to reveal spectra that are characteristic of only the nominal valence, and are insensitive to deviations from nominal valence brought on by metal-ligand hybridization. Here, ato…
We studied the stripe phase of La1.8Sr0.2NiO4 using neutron diffraction, resonant soft x-ray diffraction (RSXD) at the Ni L2,3 edges, and resonant x-ray diffraction (RXD) at the Ni K threshold. Differences in the q-space resolution of the different techniques have to be taken into account for a proper evaluation of diffraction intensities associated with the spin and charge order superstructures. We find that in the RSXD experiment the spin and charge order peaks show the same temperature dependence. In the neutron experiment by contrast, the spin and charge signals follow quite different temp…
The hexaferrites are known to exhibit a wide range of magnetic structures, some of which are connected to important technological applications and display magnetoelectric properties. We present data on the low field magnetic structures stabilised in a Y-type hexaferrite as observed by resonant soft X-ray diffraction. The helical spin block arrangement that is present in zero applied magnetic field becomes fan-like as a field is applied in plane. The propagation vectors associated with each fan structure are studied as a function of field, and a new magnetic phase is reported. Mean field calcul…
Resonant soft x-ray Bragg diffraction at the Dy M4,5 edges has been exploited to study Dy multipole motifs in DyB2C2. Our results are explained introducing the intra-atomic quadrupolar interaction between the core 3d and valence 4f shell. This allows us to determine for the first time higher order multipole moments of dysprosium $4f$ electrons and to draw their precise charge density. The Dy hexadecapole and hexacontatetrapole moment have been estimated at -20% and +30% of the quadrupolar moment, respectively. No evidence for the lock-in of the orbitals at T_N has been observed, in contrast to…
Polarization-controlled synchrotron radiation was used to map the electronic structure of buried conducting interfaces of LaAlO$_3$/SrTiO$_3$ in a resonant angle-resolved photoemission experiment. A strong dependence on the light polarization of the Fermi surface and band dispersions is demonstrated, highlighting the distinct Ti 3d orbitals involved in 2D conduction. Samples with different 2D doping levels were prepared and measured by photoemission, revealing different band occupancies and Fermi surface shapes. A direct comparison between the photoemission measurements and advanced first-prin…
We have utilized the resonant x-ray diffraction technique at the Mn L-edge in order to directly compare magnetic and orbital correlations in the Mn sub-lattice of Pr0.6Ca0.4MnO3. The resonant line shape is measured below T_OO ~ 240 K at the orbital ordering wave vector (0,1/2,0), and below T_N ~ 175 K at the antiferromagnetic wave vector (1/2,0,0). Comparing the width of the super-lattice peaks at the two wavevectors, we find that the correlation length of the magnetism exceeds that of the orbital order by nearly a factor of two. Furthermore, we observe a large (~ 3 eV) shift in spectral weigh…
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 wi…
Soft X-ray resonant scattering (XRS) has been used to observe directly, for the first time, the ordering of localized electronic states on both the Mn and Tb sites in multiferroic TbMnO$_3$. Large resonant enhancement of the X-ray scattering cross-section were observed when the incident photon energy was tuned to either the Mn $L$ or Tb $M$ edges which provide information on the Mn 3d and Tb $4f$ electronic states, respectively. The temperature dependence of the XRS signal establishes, in a model independent way, that in the high-temperature phase (28 K $\leq$ T $\leq$ 42 K) the Mn 3d sublatti…
Photo-excitation in complex oxides1 transfers charge across semicovalent bonds, drastically perturbing spin and orbital orders2. Light may then be used in compounds like magnetoresistive manganites to control magnetism on nanometre lengthscales and ultrafast timescales. Here, we show how ultrafast resonant soft x-ray diffraction can separately probe the photo-induced dynamics of spin and orbital orders in La0.5Sr1.5MnO4. Ultrafast melting of CE 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) peak, reflecting …
Soft X-ray resonant scattering studies at the Mn $L_{\texttt{II, III}}$- and the La $M_{\texttt{IV, V}}$- edges of single-crystal LaSr$_2$Mn$_2$O$_7$ are reported. At low temperatures, below $T_\texttt{N} \approx 160$ K, energy scans with a fixed momentum transfer at the \emph{A}-type antiferromagnetic (0 0 1) reflection around the Mn $L_{\texttt{II, III}}$-edges with incident linear $σ$ and $π$ polarizations show strong resonant enhancements. The splitting of the energy spectra around the Mn $L_{\texttt{II, III}}$-edges may indicate the presence of a mixed valence state, e.g., Mn$^{3+}$/Mn$^{…
Soft x-ray resonant scattering has been used to examine the charge and magnetic interactions in the cycloidal antiferromagnetic compound \dyfeal. By tuning to the Dy $M_4$ and $M_5$ absorption edges and the Fe L(2) and L(3) absorption edges we can directly observe the behavior of the Dy 4f and Fe 3d electron shells. Magnetic satellites surrounding the (110) Bragg peak were observed below 60 K. The diffraction peaks display a complex spectra at the Dy M(5) edge, indicative of a split 4f electron band. This is in contrast to a simple resonance observed at the Fe L(3) absorption edge, which probe…
We report resonant x-ray scattering data of the orbital and magnetic ordering at low temperatures at the Mn $L_{\rm 2,3}$ edges in \lsmo. The orderings display complex energy features close to the Mn absorption edges. Systematic modeling with atomic multiplet crystal field calculations was used to extract meaningful information regarding the interplay of spin, orbital and Jahn-Teller order. These calculations provide a good general agreement with the observed energy dependence of the scattered intensity {for a} dominant orbital ordering of the $ d_{x^2 - z^2} / d_{y^2 - z^2} $ type. In additio…
We compare for Ho metal the x-ray absorption spectrum and the resonant soft x-ray diffraction spectra obtained at the $3d_{5/2} \to 4f$ ($M_5$) resonance for the magnetic 1st and 2nd order diffraction peaks $(0,0,τ)$ and $(0,0,2τ)$ with the result of an atomic multiplet calculation. We find a good agreement between experiment and simulation giving evidence that this kind of simulation is well suited to quantitatively analyze resonant soft x-ray diffraction data from correlated electron systems.
We describe a strategy for using resonant soft x-ray scattering (RSXS) to study the electronic structure of transition metal oxide quantum wires. Using electron beam lithography and ion milling, we have produced periodic, patterned arrays of colossal magnetoresistance (CMR) phase La(1-x)Sr(x)MnO(3) consisting of ~ 5000 wires, each of which is 80 nm in width. The scattered intensity exhibits a series of peaks that can be interpreted as Bragg reflections from the periodic structure or, equivalently, diffraction orders from the grating-like structure. RSXS measurements at the Mn L(2,3) edge, whic…
We have performed a photoemission spectroscopy (PES) study of CeM2Al10 (M = Fe, Ru, and Os) to directly observe the electronic structure involved in the unusual magnetic ordering. Soft X-ray resonant (SXR) PES provides spectroscopic evidence of the hybridization between conduction and Ce 4f electrons (c-f hybridization) and the order of the hybridization strength (Ru < Os < Fe). High-resolution (HR) PES of CeRu2Al10 and CeOs2Al10, as compared with that of CeFe2Al10, identifies two structures that can be ascribed to structures induced by the c-f hybridization and the antiferromagnetic ordering,…
The magnetic properties of rare earth compounds are usually well captured by assuming a fully localized f shell and only considering the Hund's rule ground state multiplet split by a crystal electrical field (CEF). Currently, the standard technique for probing CEF excitations in lanthanides is inelastic neutron scattering. Here we show that with the recent leap in energy resolution, resonant inelastic soft X-ray scattering has become a serious alternative for looking at CEF excitations with some distinct advantages compared to INS. As an example we study the CEF scheme in CeRh2Si2, a system th…
Angle-resolved photoelectron spectroscopy in the Ce 3d-4f excitation region was measured for the paramagnetic state of CeRu2Si2, CeRu2(Si0.82Ge0.18)2, and LaRu2Si2 to investigate the changes of the 4$f$ electron Fermi surfaces around the quantum critical point. While the difference of the Fermi surfaces between CeRu2Si2 and LaRu2Si2 was experimentally confirmed, a strong 4f-electron character was observed in the band structures and the Fermi surfaces of CeRu2Si2 and CeRu2(Si0.82Ge0.18)2, consequently indicating a delocalized nature of the 4$f$ electrons in both compounds. The absence of Fermi …
Soft resonant x-ray Bragg diffraction (SRXD) at the Ho M$_{4,5}$ edges has been used to study Ho $4f$ multipoles in the combined magnetic and orbitally ordered phase of HoB$_2$C$_2$. A full description of the energy dependence for both $σ$ and $π$ incident x-rays at two different azimuthal angles, as well as the ratio $I_σ/I_π$ as a function of azimuthal angle for a selection of energies, allows a determination of the higher order multipole moments of rank 1 (dipole) to 6 (hexacontatetrapole). The Ho 4f multipole moments have been estimated, indicating a dominant hexadecapole (rank 4) order wi…
We use resonant soft x-ray scattering (RSXS) to quantify the hole distribution in a superlattice of insulating La2CuO4 (LCO) and overdoped La_{2-x}Sr_{x}CuO4 (LSCO). Despite its non-superconducting constituents, this structure is superconducting with T_{c}=38 K. We found that the conducting holes redistribute electronically from LSCO to the LCO layers. The LCO layers were found to be optimally doped, suggesting they are the main drivers of superconductivity. Our results demonstrate the utility of RSXS for separating electronic from structural effects at oxide interfaces.
Magnetic spiral structures can exhibit ferroelectric moments as recently demonstrated in various multiferroic materials. In such cases the helicity of the magnetic spiral is directly correlated with the direction of the ferroelectric moment and measurement of the helicity of magnetic structures is of current interest. Soft x-ray resonant diffraction is particularly advantageous because it combines element selectivity with a large magnetic cross-section. We calculate the polarization dependence of the resonant magnetic x-ray cross-section (electric dipole transition) for the basal plane magneti…
Samarium hexaboride (SmB$_6$), a Kondo insulator with mixed valence, has recently attracted much attention as a possible host for correlated topological surface states. Here, we use a combination of x-ray absorption and reflectometry techniques, backed up with a theoretical model for the resonant $M_{4,5}$ absorption edge of Sm and photoemission data, to establish laterally averaged chemical and valence depth profiles at the surface of SmB$_6$. We show that upon cleaving, the highly polar (001) surface of SmB$_6$ undergoes substantial chemical and valence reconstruction, resulting in boron ter…
We present a microscopic theory of resonant soft x-ray scattering (RSXS) that accounts for the delocalized character of valence electrons. Unlike past approaches defined in terms of form factors for atoms or clusters, we develop a functional determinant method that allows us to treat realistic band structures. This method builds upon earlier theoretical work in mesoscopic physics and accounts for both excitonic effects as well as the orthogonality catastrophe arising from interaction between the core hole and the valence band electrons. Comparing to RSXS measurements from stripe-ordered LBCO, …
We investigated the electronic structure of the SrTiO$_3$/LaAlO$_3$ superlattice (SL) by resonant soft x-ray scattering. The (003) peak, which is forbidden for our "ideal" SL structure, was observed at all photon energies, indicating reconstruction at the interface. From the peak position analyses taking into account the effects of refraction, we obtained evidence for electronic reconstruction of Ti 3d and O $2p$ states at the interface. From reflectivity analyses, we concluded that the AlO$_2$/LaO/TiO$_2$/SrO and the TiO$_2$/SrO/AlO$_2$/LaO interfaces are quite different, leading to highly as…
We review the current state of efforts to use resonant soft x-ray scattering (RSXS), which is an elastic, momentum-resolved, valence band probe of strongly correlated electron systems, to study stripe-like phenomena in copper-oxide superconductors and related materials. We review the historical progress including RSXS studies of Wigner crystallization in spin ladder materials, stripe order in 214-phase nickelates, 214-phase cuprates, and other systems. One of the major outstanding issues in RSXS concerns its relationship to more established valence band probes, namely angle-resolved photoemiss…
Resonant soft X-ray Raman scattering measurements on NiO have been made at photon energies across the Ni 2p absorption edges. The details of the spectral features are identified as Raman scattering due to d-d and charge-transfer excitations. The spectra are interpreted within the single impurity Anderson model, including multiplets, crystal-field and charge-transfer effects. At threshold excitation, the spectral features consists of triplet-triplet and triplet-singlet transitions of the 3d8 configuration. For excitation energies corresponding to the charge-transfer region in the Ni 2p X-ray ab…
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 cannot only be used to investigate single crystalline materials. This method also enables 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 in…
Multiple intriguing phenomena have recently been discovered in tetragonal Heusler compounds, where $D_{2d}$ symmetry sets a unique interplay between Dzyaloshinskii-Moriya (DM) and magnetic dipolar interactions. In the prototype $D_{2d}$ compound Mn$_{1.4}$PtSn, this has allowed the stabilization of exotic spin textures such as first-reported anti-skyrmions or elliptic Bloch-type skyrmions. While less attention has so far been given to the low-field spiral state, this remains extremely interesting as a simplest phase scenario on which to investigate the complex hierarchy of magnetic interaction…
The frustrated magnet has been regarded as a system that could be a promising host material for the quantum spin liquid (QSL). However, it is difficult to determine the spin configuration and the corresponding mechanism in this system, because of its geometrical frustration (i.e., crystal structure and symmetry). Herein, we systematically investigate one of the geometrically frustrated magnets, the TbB$_{4}$ compound. Using resonant soft x-ray scattering (RSXS), we explored its spin configuration, as well as Tb's quadrupole. Comprehensive evaluations of the temperature and photon energy / pola…
We report the study of magnetic and orbital order in Pr$_{0.5}$Ca$_{0.5}$MnO$_3$ epitaxial thin films grown on (LaAlO$_3$)$_{0.3}$-(SrAl$_{0.5}$Ta$_{0.5}$O$_3$)$_{0.7}$ (LSAT) (011)$_c$. In a new experimental approach, the polarization and energy dependence of resonant soft x-ray scattering are used to reveal significant modifications of the magnetic order in the film as compared to the bulk, namely (i) a different magnetic ordering wave vector, (ii) a different magnetic easy axis and (iii) an additional magnetic reordering transition at low temperatures. These observations indicate a strong i…
Identifying what broken symmetries are present in the cuprates has become a major area of research. Many authors have reported evidence for so-called "$Q \sim 0$" order that involves broken inversion, mirror, chiral, or time-reversal symmetry that is uniform in space. Not all these observations are well understood and new experimental probes are needed. Here we use resonant soft x-ray scattering (RSXS) to search for $Q \sim 0$ order in Bi$_{2.1}$Sr$_{1.9}$CaCu$_2$O$_{8+x}$ (Bi-2212) by measuring the region of a forbidden Bragg peak, $(0,0,3)$, which is normally extinguished by symmetry but may…
Resonant soft X-ray scattering with photon energies near the O K and the Cu L3 edges was used to study charge ordering in the system La_{1.8-x}Eu_{0.2}Sr_xCuO_4 as a function of temperature for x = 0.125 and 0.15. From the superstructure diffraction intensities a charge ordering with a doping dependent wave vector is derived which is in this system well below the transition temperature of the low-temperature tetragonal phase but well above the onset of spin ordering. This indicates that charge ordering is the primary driving force for the formation of stripe-like phases in two-dimensional dope…
The spin transition in LaCoO3 is investigated by temperature-dependent resonant soft X-ray emission spectroscopy near the Co 2p absorption edges. This element-specific technique is more bulk sensitive with respect to the temperature induced spin-state of the Co3+ ions in LaCoO3 than other high-energy spectroscopic methods. The spin transition is interpreted and discussed with ab-initio density-functional theory within the fixed-spin moment method, which is found to yield consistent spectral functions to the experimental data. The spectral changes for LaCoO3 as a function of temperature suggest…
We describe the design, construction and performance of a 4-circle in-vacuum diffractometer for resonant elastic soft x-ray scattering and reflectivity. The diffractometer, installed on the REIXS 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 x10^-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 s…
We report the direct observation of slow fluctuations of helical antiferromagnetic domains in an ultra-thin holmium film using coherent resonant magnetic x-ray scattering. We observe a gradual increase of the fluctuations in the speckle pattern with increasing temperature, while at the same time a static contribution to the speckle pattern remains. This finding indicates that domain-wall fluctuations occur over a large range of time scales. We ascribe this non-ergodic behavior to the strong dependence of the fluctuation rate on the local thickness of the film.
The relationship between the magnetic interaction and photoinduced dynamics in antiferromagnetic perovskites is investigated in this study. In La${}_{1/3}$Sr${}_{2/3}$FeO${}_{3}$ thin films, commensurate spin ordering is accompanied by charge disproportionation, whereas SrFeO${}_{3}$ thin films show incommensurate helical antiferromagnetic spin ordering due to increased ferromagnetic coupling compared to La${}_{1/3}$Sr${}_{2/3}$FeO${}_{3}$. To understand the photoinduced spin dynamics in these materials, we investigate the spin ordering through time-resolved resonant soft X-ray scattering. In …
We report the first direct resonant soft x-ray scattering observations of orbital ordering. We have studied the low temperature phase of La$_{0.5}$Sr$_{1.5}$MnO$_4$, a compound that displays charge and orbital ordering. Previous claims of orbital ordering in such materials have relied on observations at the Manganese $K$ edge. These claims have been questioned in several theoretical studies. Instead we have employed resonant soft x-ray scattering at the manganese $L_{III}$ and $L_{II}$ edges which probes the orbital ordering directly. Energy scans at constant wavevector are compared to theoret…
Resonant elastic X-ray scattering has been widely employed for exploring complex electronic ordering phenomena, like charge, spin, and orbital order, in particular in strongly correlated electronic systems. In addition, recent developments of pump-probe X-ray scattering allow us to expand the investigation of the temporal dynamics of such orders. Here, we introduce a new time-resolved Resonant Soft X-ray Scattering (tr-RSXS) endstation developed at the Pohang Accelerator Laboratory X-ray Free Electron Laser (PAL-XFEL). This endstation has an optical laser (wavelength of 800 nm plus harmonics) …
Static charge-density wave (CDW) and spin-density wave (SDW) order has been convincingly observed in La-based cuprates for some time. However, more recently it has been suggested by quantum oscillation, transport and thermodynamic measurements that density wave order is generic to underdoped cuprates and plays a significant role in YBa_2Cu_3O_{6+delta} (YBCO). We use resonant soft x-ray scattering at the Cu L and O K edges to search for evidence of density wave order in Ortho-II and Ortho-VIII oxygen-ordered YBCO. We report a null result -- no evidence for static CDW order -- in both Ortho-II …
Resonant Inelastic X-ray Scattering (RIXS) in the soft x-ray range is an element-specific energy-loss spectroscopy used to probe the electronic and magnetic excitations in strongly correlated solids. In the recent years, RIXS has been progressing very quickly in terms of energy resolution and understanding of the experimental results, but the interpretation of spectra could further improve, sometimes decisively, from a full knowledge of the polarization of incident and scattered photons. Here we present the first implementation, in a high resolution RIXS spectrometer used to analyze the scatte…
Resonant Bragg diffraction of soft, circularly polarized x-rays has been used to observe directly the temperature dependence of chiral-order melting in a motif of Mn ions in terbium manganate. The underlying mechanism uses the b-axis component of a cycloid, which vanishes outside the polar phase. Melting is witnessed by the first and second harmonics of a cycloid, and we explain why the observed temperature dependence is different in the two harmonics. Our direct observation of melting is supported by a solid foundation of evidence, derived from extensive studies of the azimuthal-angle depende…
Resonant soft x-ray scattering (RSXS) is a leading probe of valence band order in materials best known for detecting charge density wave order in the copper-oxide superconductors. One of the biggest limitations on the RSXS technique is the presence of a severe fluorescence background which, like the RSXS cross section itself, is enhanced under resonant conditions. This background prevents the study of weak signals such as diffuse scattering from glassy or fluctuating order that is spread widely over momentum space. Recent advances in superconducting transition edge sensor (TES) detectors have …
We report a high-resolution resonant inelastic soft x-ray scattering study of the quantum magnetic spin-chain materials Li2CuO2 and CuGeO3. By tuning the incoming photon energy to the oxygen K-edge, a strong excitation around 3.5 eV energy loss is clearly resolved for both materials. Comparing the experimental data to many-body calculations, we identify this excitation as a Zhang-Rice singlet exciton on neighboring CuO4-plaquettes. We demonstrate that the strong temperature dependence of the inelastic scattering related to this high-energy exciton enables to probe short-range spin correlations…
The dependence with energy of the resonant soft x-ray Bragg diffraction intensity in DyB$_2$C$_2$ for the $(00{1/2})$ reflection at the Dy M$_{4,5}$ edges have been calculated by using an atomic multiplet hamiltonian including the effect of crystal field and introducing an intra-atomic quadrupolar interaction between the 3d core and 4f valence shell. These calculations are compared with the experimental results (Mulders et al., J. Phys.: Condens. Matter 18 (2006) 11195) in the antiferroquadrupolar and antiferromagnetic phases of DyB$_2$C$_2$. We reproduce all the features appearing $(00{1/2})$…
We performed resonant soft X-ray diffraction on known charge density wave (CDW) compounds, rare earth tri-tellurides. Near the $M_5$ (3d - 4f) absorption edge of rare earth ions, an intense diffraction peak is detected at a wavevector identical to that of CDW state hosted on Te$_2$ planes, indicating a CDW-induced modulation on the rare earth ions. Surprisingly, the temperature dependence of the diffraction peak intensity demonstrates an exponential increase at low temperatures, vastly different than that of the CDW order parameter. Assuming 4f multiplet splitting due to the CDW states,we pres…
Resonant elastic x-ray scattering (REXS) is an exquisite element-sensitive tool for the study of subtle charge, orbital, and spin superlattice orders driven by the valence electrons, which therefore escape detection in conventional x-ray diffraction (XRD). Although the power of REXS has been demonstrated by numerous studies of complex oxides performed in the soft x-ray regime, the cross section and photon wavelength of the material-specific elemental absorption edges ultimately set the limit to the smallest superlattice amplitude and periodicity one can probe. Here we show -- with simulations …
We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $π$, whereas the two-spin correlator is peaked around $π/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping…
Using resonant soft X-ray techniques we follow the magnetic behavior of a strained epitaxial film of CoCr2O4, a type-II multiferroic. The film is [110]-oriented, such that both the ferroelectric and ferromagnetic moments can coexist in plane. X-ray magnetic circular dichroism (XMCD) is used in scattering and in transmission modes to probe the magnetization of Co and Cr separately. The transmission measurements utilized X-ray excited optical luminescence from the substrate. Resonant soft X-ray diffraction (RSXD) was used to study the magnetic order of the low temperature phase. The XMCD signals…
Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the indirect resonant inelastic x-ray scattering (RIXS) response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the RIXS response changes qualitatively at two well-separated temperature scales, $T_L$ and $T_H$, which correspond to the characteristic energies of the two kinds of fractionalized excitations, $\mathbb{Z}_2$ gauge fluxes and Majorana fermions, respectively. While thermally excited $\mathbb{Z}_2$ gauge fl…
Angle-resolved soft x-ray measurements made at the boron K-edge in single crystal MgB2 provide new insights into the B-2p local partial density of both unoccupied and occupied band states. The strong variation of absorption with incident angle of exciting x-rays permits the clear separation of contributions from σstates in the boron plane and πstates normal to the plane. A careful comparison with theory accurately determines the energy of selected critical $k$ points in the conduction band. Resonant inelastic x-ray emission at an incident angle of 15 degrees shows a large enhancement of the em…
We report an Fe $L$-edge resonant inelastic x-ray scattering (RIXS) study of the unusual superconductor $β$-FeSe. The high energy resolution of this RIXS experiment ($\approx\,$55$\,$meV FWHM) made it possible to resolve low-energy excitations of the Fe $3d$ manifold. These include a broad peak which shows dispersive trends between 100-200$\,$meV along the $(π,0)$ and $(π,π)$ directions of the one-Fe square reciprocal lattice, and which can be attributed to paramagnon excitations. The multi-band valence state of FeSe is among the most metallic in which such excitations have been discerned by s…
A nematic order in stripe-ordered cuprates was recently identified with (001) reflection at resonant energies associated with the in-plane states. However, whether this resonant reflection is ubiquitous among all 214 cuprates is still unknown. Here we report a Resonant soft X-ray Scattering (RXS) measurement on two La$_{2-x}$Sr$_x$CuO$_{4+y}$ crystals. Charge order was found in La$_2$CuO$_{4+y}$ with a total hole concentration near 0.125/Cu but no measurable (001) peak at any resonance, while in a La$_{1.94}$Sr$_{0.06}$CuO$_{4+y}$ sample near 0.16/Cu a (001) peak resonant was identified to be …
X-ray absorption spectroscopy and resonant soft x-ray reflectivity show a non-uniform distribution of oxygen holes in a La2NiO4 - La2CuO4 (LNO-LCO) superlattice, with excess holes concentrated in the LNO layers. Weak ferromagnetism with Tc = 160 K suggests a coordinated tilting of NiO6 octahedra, similar to that of bulk LNO. Ni d3z2-r2 orbitals within the LNO layers have a spatially variable occupation. This variation of the Ni valence near LNO-LCO interfaces is observed with resonant soft x-ray reflectivity at the Ni L edge, at a reflection suppressed by the symmetry of the structure, and is …
