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We present a tree tensor-network impurity solver suited for general multiorbital systems. The network is constructed to efficiently capture the entanglement structure and symmetry of an impurity problem. The solver works directly on the real-time/frequency axis and generates spectral functions with energy-independent resolution of the order of one percent of the correlated bandwidth. Combined with an optimized representation of the impurity bath, it efficiently solves self-consistent dynamical mean-field equations and calculates various dynamical correlation functions for systems with off-diagonal Green's functions. For the archetypal correlated Hund's metal Sr$_2$RuO$_4$, we show that both the low-energy quasiparticle spectra related to the van Hove singularity and the high-energy atomic multiplet excitations can be faithfully resolved. In particular, we show that while the spin-orbit coupling has only minor effects on the orbital-diagonal one-particle spectral functions, it has a more profound impact on the low-energy spin and orbital response functions., Comment: Updated results with SOC; as published

Herein we show that non-resonant inelastic x-ray scattering involving an $s$ core level is a powerful spectroscopic method to characterize the excited states of transition metal compounds. The spherical charge distribution of the $s$ core hole allows the orientational dependence of the intensities of the various spectral features to produce a spatial charge image of the associated multiplet states in a straightforward manner, thereby facilitating the identification of their orbital character. In addition, the $s$ core hole does not add an extra orbital angular momentum component to the multiplet structure so that the well-established Sugano-Tanabe-Kamimura diagrams can be used for the analysis of the spectra. For $\alpha$-MnS we observe the spherical charge density corresponding to its high spin $3d^5$ ($^6A_1$) ground state configuration and we were able to selectively image its excited states and identify them as $t_{2g}$ ($^5T_2$) and $e_g$ ($^5E$) with an energy splitting $10Dq$ of 0.78\,eV.

Determining the electron neutrino mass by electron capture in $^{163}$Ho relies on an accurate understanding of the differential electron capture nuclear decay rate as a function of the distribution of the total decay energy between the neutrino and electronic excitations. The resulting spectrum is dominated by resonances due to local atomic multiplet states with core holes. Coulomb scattering between electrons couple the discrete atomic states, via Auger-Meitner decay, to final states with free electrons. The atomic multiplets are above the auto-ionisation energy, such that the delta functions representing these discrete levels turn into a superposition of Lorentzian, Mahan- and Fano-like line-shapes. We present an \textit{ab initio} method to calculate nuclear decay modifications due to such processes. It includes states with multiple correlated holes in local atomic orbitals interacting with unbound Auger-Meitner electrons. A strong energy-dependent, asymmetric broadening of the resonances in good agreement with recent experiments is found. We present a detailed analysis of the mechanisms determining the final spectral line-shape and discuss both the Fano interference between different resonances, as well as the energy dependence of the Auger-Meitner Coulomb matrix elements. The latter mechanism is shown to be the dominant channel responsible for the asymmetric line-shape of the resonances in the electron capture spectrum of $^{163}$Ho.

We extend a previously proposed rotation and truncation scheme to optimize quantum Anderson impurity calculations with exact diagonalization [PRB 90, 085102 (2014)] to density-matrix renormalization group (DMRG) calculations. The method reduces the solution of a full impurity problem with virtually unlimited bath sites to that of a small subsystem based on a natural impurity orbital basis set. The later is solved by DMRG in combination with a restricted-active-space truncation scheme. The method allows one to compute Green's functions directly on the real frequency or time axis. We critically test the convergence of the truncation scheme using a one-band Hubbard model solved in the dynamical mean-field theory. The projection is exact in the limit of both infinitely large and small Coulomb interactions. For all parameter ranges the accuracy of the projected solution converges exponentially to the exact solution with increasing subsystem size., Comment: 10 pages and 6 figures; accepted in PRB

We report on our investigation on the magnetism of the iridate double perovskite Sr$_2$CoIrO$_6$, a nominally Ir$^{5+}$ Van Vleck $J_{eff}=0$ system. Using x-ray absorption (XAS) and x-ray magnetic circular dichroism (XMCD) spectroscopy at the Ir-$L_{2,3}$ edges, we found a nearly zero orbital contribution to the magnetic moment and thus an apparent breakdown of the $J_{eff}=0$ ground state. By carrying out also XAS and XMCD experiments at the Co-$L_{2,3}$ edges and by performing detailed full atomic multiplet calculations to simulate all spectra, we discovered that the compound consists of about 90% Ir$^{5+}$ ($J_{eff}=0$) and Co$^{3+}$ ($S=2$) and 10% Ir$^{6+}$ ($S=3/2$) and Co$^{2+}$ ($S=3/2$). The magnetic signal of this minority Ir$^{6+}$ component is almost equally strong as that of the main Ir$^{5+}$ component. We infer that there is a competition between the Ir$^{5+}$-Co$^{3+}$ and the Ir$^{6+}$-Co$^{2+}$ configurations in this stoichiometric compound.

We used high-resolution resonant inelastic x-ray scattering (RIXS) at the Ni $L_3$ edge to simultaneously investigate high-energy interband transitions characteristic of Ni-O bond ordering and low-energy collective excitations of the Ni spins in the rare-earth nickelates $R$NiO$_3$ ($R$ = Nd, Pr, La) with pseudocubic perovskite structure. With the support of calculations based on a double-cluster model we quantify bond order (BO) amplitudes for different thin films and heterostructures and discriminate short-range BO fluctuations from long-range static order. Moreover we investigate magnetic order and exchange interactions in spatially confined $R$NiO$_3$ slabs by probing dispersive magnon excitations. While our study of superlattices (SLs) grown in the (001) direction of the perovskite structure reveals a robust non-collinear spin spiral magnetic order with dispersive magnon excitations that are essentially unperturbed by BO modulations and spatial confinement, we find magnons with flat dispersions and strongly reduced energies in SLs grown in the $(111)_{\text{pc}}$ direction that exhibit collinear magnetic order. These results give insight into the interplay of different collective ordering phenomena in a prototypical 3$d$ transition metal oxide and establish RIXS as a powerful tool to quantitatively study several order parameters and the corresponding collective excitations within one experiment., Comment: 13 pages, 8 figures, accepted in Physical Review B

We present core level non-resonant inelastic x-ray scattering (NIXS) data of the heavy fermion compounds CeCoIn$_5$ and CeRhIn$_5$ measured at the Ce $N_{4,5}$-edges. The higher than dipole transitions in NIXS allow determining the orientation of the $\Gamma_7$ crystal-field ground-state orbital within the unit cell. The crystal-field parameters of the Ce$M$In$_5$ compounds and related substitution phase diagrams have been investigated in great detail in the past; however, whether the ground-state wavefunction is the $\Gamma_7^+$ ($x^2\,-\,y^2$) or $\Gamma_7^-$ ($xy$ orientation) remained undetermined. We show that the $\Gamma_7^-$ doublet with lobes along the (110) direction forms the ground state in CeCoIn$_5$ and CeRhIn$_5$. For CeCoIn$_5$, however, we find also some contribution of the first excited state crystal-field state in the ground state due to the stronger hybridization of 4$f$ and conduction electrons, suggesting a smaller $\alpha^2$ value than originally anticipated from x-ray absorption. A comparison is made to the results of existing density functional theory plus dynamical mean-field theory calculations., Comment: 6 pages, 4 figures

In this set of three papers, we present the results of a combined study by density-functional (LDA) band theory (NMTO) and angle-resolved photoemission spectroscopy (ARPES) of lithium purple bronze, 2(Li$_{1x}$Mo$_{6}$O$_{17}$). This material is particularly notable for its unusually robust quasi-one-dimensional (quasi-1D) behavior. The band structure, in a large energy window around the Fermi energy, is basically 2D and formed by three Mo $t_{2g}$-like extended Wannier orbitals (WOs) per cell, each one giving rise to a 1D band running at a 120$^{\circ }$ angle to the two others. A structural "dimerization" from $\mathbf{c}/2$ to $\mathbf{c}$ gaps the $xz$ and $yz$ bands while leaving the $xy$ bands metallic in the gap but resonantly coupled to the gap edges and, hence, to the two other directions. The resulting complex shape of the quasi-1D Fermi surface (FS), verified by our ARPES, thus depends strongly on the Fermi energy position in the gap, implying a great sensitivity to Li stoichiometry of properties dependent on the FS, such as FS nesting or superconductivity. The band structure, expressed as a six-band, analytical tight-binding (TB) Hamiltonian, is verified in detail by the recognition and application of an ARPES selection rule that enables, for the first time, the separation in ARPES spectra of the two barely split $xy$ bands and the observation of their complex split FS. The strong resonances prevent either a two-band TB model or a related real-space ladder picture from giving a valid description of the low-energy electronic structure. Down to a temperature of 6$\,$K we find no evidence for a theoretically expected downward renormalization of perpendicular single particle hopping due to LL fluctuations in the quasi-1D chains.

$Fe_3O_4$ is a mixed-valence strongly correlated transition metal oxide which displays the intriguing metal to insulator Verwey transition. Here we investigate the electronic and magnetic structure of $Fe_3O_4$ by a unique combination of high-resolution Fe 2p3d resonant inelastic scattering magnetic circular (RIXS-MCD) and magnetic linear (RIXS-MLD) dichroism. We show that by coupling the site selectivity of RIXS with the magnetic selectivity imposed by the incident polarization handedness, we can unambiguously identify spin-flip excitations and quantify the exchange interaction of the different sublattices. Furthermore, our RIXS-MLD measurements show spin-orbital excitations that exhibit strong polarization and magnetic field dependence. Guided by theoretical simulations, we reveal that the angular dependence arises from a strong interplay between trigonal crystal-field, magnetic exchange and spin-orbit interaction at the nominal $Fe^{2+}$ sites. Our results highlight the capabilities of RIXS magnetic dichroism studies to investigate the ground state of complex systems where in-equivalent sites and bonds are simultaneously present.

We have used high-resolution resonant inelastic x-ray scattering (RIXS) to study a thin film of NdNiO$_3$, a compound whose unusual spin- and bond-ordered electronic ground state has been of long-standing interest. Below the magnetic ordering temperature, we observe well-defined collective magnon excitations along different high-symmetry directions in momentum space. The magnetic spectra depend strongly on the incident photon energy, which we attribute to RIXS coupling to different local electronic configurations of the expanded and compressed NiO$_6$ octahedra in the bond-ordered state. Both the noncollinear magnetic ground state and the observed site-dependent magnon excitations are well described by a model that assumes strong competition between the antiferromagnetic superexchange and ferromagnetic double-exchange interactions. Our study provides direct insight into the magnetic dynamics and exchange interactions of the rare-earth nickelates, and demonstrates that RIXS can serve as a site-selective probe of magnetism in these and other materials., Comment: Phys. Rev. X, in press

We report a combined experimental and theoretical x-ray magnetic circular dichroism (XMCD) spectroscopy study at the Ir-$L_{2,3}$ edges on the Ir$^{5+}$ ions of the layered hybrid solid state oxide Sr$_2$Co$_{0.5}$Ir$_{0.5}$O$_4$ with the K$_2$NiF$_4$ structure. From theoretical simulation of the experimental Ir-$L_{2,3}$ XMCD spectrum, we found a deviation from a pure $J_{eff}=0$ ground state with an anisotropic orbital-to-spin moment ratio ($L_x/2S_x$ = 0.43 and $L_z/2S_z$ = 0.78). This deviation is mainly due to multiplet interactions being not small compared to the cubic crystal field and due to the presence of a large tetragonal crystal field associated with the crystal structure. Nevertheless, our calculations show that the energy gap between the singlet ground state and the triplet excited state is still large and that the magnetic properties of the Ir$^{5+}$ ions can be well described in terms of singlet Van Vleck paramagnetism.

The determination of the electron neutrino mass by electron capture in $^{163}$Ho relies on a precise understanding of the deexcitation of a core hole after an electron capture event. We here present an \textit{ab intio} calculation of the electron capture spectrum in $^{163}$Ho, including all intra-atomic decay channels into bound-states. We use theoretical methods developed for the calculation of core level spectroscopy on correlated electron compounds. Our comparison critically tests the reality of these theories. We find that relativistic interactions beyond the Dirac equation, i.e. quantum-electro dynamics, only lead to minor shifts of the spectral peaks. The electronic relaxation after an electron capture event due to the changed nuclear potential leads to a mixing of different edges, but due to conservation of angular momentum of each scattered electron, no additional structures emerge. Many-body Coulomb interactions lead to the formation of multiplets and to additional peaks with multiple core-holes due to Auger decay. Multiplets crucially change the appearance of the resonances on a Rydberg energy scale. The additional structures due to Auger decay are, although clearly visible, relatively weak compared to the one core hole states and accidentally far away from the end-point region of the spectrum. As the end-point of the spectrum is effected most by the neutrino mass these additional states do not influence the statistics for determining the neutrino mass directly. The multiplet broadening and Auger shake-up of the main core-level edges do change the apparent line-width and accompanying lifetime of these edges, thereby invalidating experimentally obtained lifetimes at the resonance for regions far away from the resonance.

We report on our investigation of the electronic structure of Ti$_2$O$_3$ using (hard) x-ray photoelectron and soft x-ray absorption spectroscopy. From the distinct satellite structures in the spectra we have been able to establish unambiguously that the Ti-Ti $c$-axis dimer in the corundum crystal structure is electronically present and forms an $a_{1g}a_{1g}$ molecular singlet in the low temperature insulating phase. Upon heating we observed a considerable spectral weight transfer to lower energies with orbital reconstruction. The insulator-metal transition may be viewed as a transition from a solid of isolated Ti-Ti molecules into a solid of electronically partially broken dimers where the Ti ions acquire additional hopping in the $a$-$b$ plane via the $e_g^{\pi}$ channel, the opening of which requires the consideration of the multiplet structure of the on-site Coulomb interaction., Comment: 7 pages, 4 figures

Engineering and enhancing inversion symmetry breaking in solids is a major goal in condensed matter physics and materials science, as a route to advancing new physics and applications ranging from improved ferroelectrics for memory devices to materials hosting Majorana zero modes for quantum computing. Here, we uncover a new mechanism for realising a much larger energy scale of inversion symmetry breaking at surfaces and interfaces than is typically achieved. The key ingredient is a pronounced asymmetry of surface hopping energies, i.e. a kinetic energy-driven inversion symmetry breaking, whose energy scale is pinned at a significant fraction of the bandwidth. We show, from spin- and angle-resolved photoemission, how this enables surface states of 3d and 4d-based transition-metal oxides to surprisingly develop some of the largest Rashba-like spin splittings that are known. Our findings open new possibilities to produce spin textured states in oxides which exploit the full potential of the bare atomic spin-orbit coupling, raising exciting prospects for oxide spintronics. More generally, the core structural building blocks which enable this are common to numerous materials, providing the prospect of enhanced inversion symmetry breaking at judiciously-chosen surfaces of a plethora of compounds, and suggesting routes to interfacial control of inversion symmetry breaking in designer heterostructures.

Spin excitations in the overdoped high temperature superconductors Tl$_2$Ba$_2$CuO$_{6+\delta}$ and (Bi,Pb)$_2$(Sr,La)$_{2}$CuO$_{6+\delta}$ were investigated by resonant inelastic x-ray scattering (RIXS) as functions of doping and detuning of the incoming photon energy above the Cu-$L_3$ absorption peak. The RIXS spectra at optimal doping are dominated by a paramagnon feature with peak energy independent of photon energy, similar to prior results on underdoped cuprates. Beyond optimal doping, the RIXS data indicate a sharp crossover to a regime with a strong contribution from incoherent particle/hole excitations whose maximum shows a fluorescence-like shift upon detuning. The spectra of both compound families are closely similar, and their salient features are reproduced by exact-diagonalization calculations of the single-band Hubbard model on a finite cluster. The results are discussed in the light of recent transport experiments indicating a quantum phase transition near optimal doping., Comment: 6 pages, 3 figures, accepted in Physical Review Letters

We have carried out bulk-sensitive hard x-ray photoelectron spectroscopy (HAXPES) measurements on in-situ cleaved and ex-situ polished SmB6 single crystals. Using the multiplet-structure in the Sm 3d core level spectra, we determined reliably that the valence of Sm in bulk SmB6 is close to 2.55 at ~5 K. Temperature dependent measurements revealed that the Sm valence gradually increases to 2.64 at 300 K. From a detailed line shape analysis we can clearly observe that not only the J=0 but also the J=1 state of the Sm 4f 6 configuration becomes occupied at elevated temperatures. Making use of the polarization dependence, we were able to identify and extract the Sm 4f spectral weight of the bulk material. Finally, we revealed that the oxidized or chemically damaged surface region of the ex-situ polished SmB6 single crystal is surprisingly thin, about 1 nm only., Comment: 11 pages, 8 figures

We have investigated the electronic structure of Sr2IrO4 using core level resonant inelastic x-ray scattering. The experimental spectra can be well reproduced using ab initio density functional theory based multiplet ligand field theory calculations, thereby validating these calculations. We found that the low-energy, effective Ir t2g orbitals are practically degenerate in energy. We uncovered that covalency in Sr2IrO4, and generally in iridates, is very large with substantial oxygen ligand hole character in the Ir t2g Wannier orbitals. This has far reaching consequences, as not only the onsite crystal-field energies are determined by the long range crystal-structure, but, more significantly, magnetic exchange interactions will have long range distance dependent anisotropies in the spin direction. These findings set constraints and show pathways for the design of d^5 materials that can host compass-like magnetic interactions.

We investigated the ground state symmetry of the cubic hidden order compound CeB$_6$ by means of core level non-resonant inelastic x-ray scattering (NIXS). The information is obtained from the directional dependence of the scattering function that arises from higher than dipole transitions. Our new method confirms that the ground state is well described using a localized crystal-field model assuming a $\Gamma_8$ quartet ground state., Comment: 5 pages, 4 figures

We present a combined study of Ni $K$-edge resonant x-ray scattering and density functional calculations to probe and distinguish electronically driven ordering and lattice distortions in nickelate heterostructures. We demonstrate that due to the low crystal symmetry, contributions from structural distortions can contribute significantly to the energy-dependent Bragg peak intensities of a bond-ordered NdNiO$_3$ reference film. For a LaNiO$_3$-LaAlO$_3$ superlattice that exhibits magnetic order, we establish a rigorous upper bound on the bond-order parameter. We thus conclusively confirm predictions of a dominant spin density wave order parameter in metallic nickelates with a quasi-two-dimensional electronic structure.

Soft x-ray linear and circular dichroism (XLD, XMCD) experiments at the Ce M$_{4,5}$ edges are being used to determine the energy scales characterizing the Ce $4f$ degrees of freedom in the ultrathin ordered surface intermetallic CeAg$_x$/Ag(111). We find that all relevant interactions, i. e. Kondo scattering, crystal field splitting and magnetic exchange coupling occur on small scales. Our study demonstrates the usefulness of combining x-ray absorption experiments probing linear and circular dichroism owing to their strong sensitivity for anisotropies in both charge distribution and paramagnetic response, respectively., Comment: 5 pages, 4 figures

Topological insulators form a novel state of matter that provides new opportunities to create unique quantum phenomena. While the materials used so far are based on semiconductors, recent theoretical studies predict that also strongly correlated systems can show non-trivial topological properties, thereby allowing even the emergence of surface phenomena that are not possible with topological band insulators. From a practical point of view, it is also expected that strong correlations will reduce the disturbing impact of defects or impurities, and at the same increase the Fermi velocities of the topological surface states. The challenge is now to discover such correlated materials. Here, using advanced x-ray spectroscopies in combination with band structure calculations, we infer that CeRu$_4$Sn$_6$ is a strongly correlated material with non-trivial topology., Comment: 10 pages, 6 figures, submitted to Scientific Reports

Using a recently developed impurity solver we exemplify how dynamical mean field theory captures band excitations, resonances, edge singularities and excitons in core level x-ray absorption (XAS) and core level photo electron spectroscopy (cPES) on metals, correlated metals and Mott insulators. Comparing XAS at different values of the core-valence interaction shows how the quasiparticle peak in the absence of core-valence interactions evolves into a resonance of similar shape, but different origin. Whereas XAS is rather insensitive to the metal insulator transition, cPES can be used, due to nonlocal screening, to measure the amount of local charge fluctuation.

The occupancy of the 4f^n contributions in the Kondo semiconductors CeM2Al10(M = Ru, Os and Fe) has been quantitatively determined by means of bulk-sensitive hard x-ray photoelectron spectroscopy (HAXPES) on the Ce 3d core levels. Combining a configuration interaction scheme with full multiplet calculations allowed to accurately describe the HAXPES data despite the presence of strong plasmon excitations in the spectra. The configuration interaction parameters obtained from this analysis -- in particular the hybridization strength V_eff and the effective f binding energy Delta_f -- indicate a slightly stronger exchange interaction in CeOs2Al10 compared to CeRu2Al10, and a significant increase in CeFe2Al10. This verifies the coexistence of a substantial amount of Kondo screening with magnetic order and places the entire CeM2Al10 family in the region of strong exchange interactions., Comment: 9 pages, 4 figures, submitted to Physical Review B

We here present how a self-consistent solution of the dynamical mean field theory equations can be obtained using exact diagonalization of an Anderson impurity model with accuracies comparable to those found using renormalization group or quantum Monte Carlo methods. We show how one can solve a correlated quantum impurity coupled to several hundred uncorrelated bath sites, using a restricted active basis set. The number of bath sites determines the resolution of the obtained spectral function, which consists of peaks roughly spaced by the band width divided by the number of bath sites. The self-consistency cycles are fully performed on the real frequency axis and expressed as numerical stable matrix operations. The same impurity solver has been used on Ligand Field and finite size cluster calculations and is capable of treating involved Hamiltonians including the full rotational invariant Coulomb interaction, spin-orbit coupling and low symmetry crystal-fields. The proposed method allows for the calculation of a variety of correlation functions at little extra cost.

We study the manipulation of the photoelectron spin-polarization in Bi$_2$Se$_3$ by spin- and angle-resolved photoemission spectroscopy. General rules are established that enable controlling the spin-polarization of photoemitted electrons via light polarization, sample orientation, and photon energy. We demonstrate the $\pm$100% reversal of a single component of the measured spin-polarization vector upon the rotation of light polarization, as well as a full three-dimensional manipulation by varying experimental configuration and photon energy. While a material-specific density-functional theory analysis is needed for the quantitative description, a minimal two-atomic-layer model qualitatively accounts for the spin response based on the interplay of optical selection rules, photoelectron interference, and topological surface-state complex structure. It follows that photoelectron spin-polarization control is generically achievable in systems with a layer-dependent, entangled spin-orbital texture., Comment: 5 pages, 4 figures. A high-resolution version with supplementary material can be found at: http://www.phas.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Articles/BiSe_spin_ARPES.pdf

A combined analysis of x-ray absorption and resonant reflectivity data was used to obtain the orbital polarization profiles of superlattices composed of four-unit-cell-thick layers of metallic LaNiO3 and layers of insulating RXO3 (R=La, Gd, Dy and X=Al, Ga, Sc), grown on substrates that impose either compressive or tensile strain. This superlattice geometry allowed us to partly separate the influence of epitaxial strain from interfacial effects controlled by the chemical composition of the insulating blocking layers. Our quantitative analysis reveal orbital polarizations up to 25%. We further show that strain is the most effective control parameter, whereas the influence of the chemical composition of the blocking layers is comparatively small., Comment: 9 pages, 8 figures

We report on the observation of orbital excitations in YVO3 by means of resonant inelastic x-ray scattering (RIXS) at energies across the vanadium L3 and oxygen K absorption edges. Due to the excellent experimental resolution we are able to resolve the intra-t2g excitations at 0.1-0.2 eV, 1.07 eV, and 1.28 eV, the lowest excitations from the t2g into the eg levels at 1.86 eV, and further excitations above 2.2 eV. For the intra-t2g excitations at 0.1-0.2 eV, the RIXS peaks show small shifts of the order of 10-40 meV as a function of temperature and of about 13-20 meV as a function of the transferred momentum q||a. We argue that the latter reflects a finite dispersion of the orbital excitations. For incident energies tuned to the oxygen K edge, RIXS is more sensitive to intersite excitations. We observe excitations across the Mott-Hubbard gap and find an additional feature at 0.4 eV which we attribute to two-orbiton scattering, i.e., an exchange of orbitals between adjacent sites. Altogether, these results indicate that both superexchange interactions and the coupling to the lattice are important for a quantitative understanding of the orbital excitations in YVO3., Comment: 14 pages, 10 figures

We have used resonant x-ray diffraction to develop a detailed description of antiferromagnetic ordering in epitaxial superlattices based on two-unit-cell thick layers of the strongly correlated metal LaNiO3. We also report reference experiments on thin films of PrNiO3 and NdNiO3. The resulting data indicate a spiral state whose polarization plane can be controlled by adjusting the Ni d-orbital occupation via two independent mechanisms: epitaxial strain and quantum confinement of the valence electrons. The data are discussed in the light of recent theoretical predictions., Comment: 5 pages, 3 figures

Spin-orbit coupling has been conjectured to play a key role in the low-energy electronic structure of Sr2RuO4. Using circularly polarized light combined with spin- and angle-resolved photoemission spectroscopy, we directly measure the value of the effective spin-orbit coupling to be 130 +/- 30 meV. This is even larger than theoretically predicted and comparable to the energy splitting of the dxy and dxz,yz orbitals around the Fermi surface, resulting in a strongly momentum-dependent entanglement of spin and orbital character. As demonstrated by the spin expectation value obtained for a pair of electrons with zero total momentum, the classification of the Cooper pairs in terms of pure singlets or triplets fundamentally breaks down, necessitating a description of the unconventional superconducting state of Sr2RuO4 in terms of these newly found spin-orbital entangled eigenstates., Comment: Accepted for publication in PRL. A high-resolution version with supplementary material can be found at http://www.phas.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Articles/SpinOrbitInSr214.pdf

We study Bi2Se3 by polarization-dependent angle-resolved photoemission spectroscopy (ARPES) and density-functional theory slab calculations. We find that the surface state Dirac fermions are characterized by a layer-dependent entangled spin-orbital texture, which becomes apparent through quantum interference effects. This explains the discrepancy between the spin polarization from spin-resovled ARPES - ranging from 20 to 85% - and the 100% value assumed in phenomenological models. It also suggests a way to probe the intrinsic spin texture of topological insulators, and to continuously manipulate the spin polarization of photoelectrons and photocurrents all the way from 0 to +/-100% by an appropriate choice of photon energy, linear polarization, and angle of incidence., Comment: 5 pages, 4 figures. A high-resolution version with supplementary material can be found at: http://www.phas.ubc.ca/~quantmat/ARPES/PUBLICATIONS/Articles/BiSe_P.pdf

We have succeeded in establishing the crystal-field ground state of CeRu2Al10, an orthorhombic intermetallic compound recently identified as a Kondo insulator. Using polarization dependent soft x-ray absorption spectroscopy at the Ce M4,5 edges, together with input from inelastic neutron and magnetic susceptibility experiments, we were able to determine unambiguously the orbital occupation of the 4f shell and to explain quantitatively both the measured magnetic moment along the easy a axis and the small ordered moment along the c-axis. The results provide not only a platform for a realistic modeling of the spin and charge gap of CeRu2Al10, but demonstrate also the potential of soft x-ray absorption spectroscopy to obtain information not easily accessible by neutron techniques for the study of Kondo insulators in general., Comment: submitted to Physical Review B Rapid Communications

We present a temperature-dependent x-ray absorption (XAS) and resonant elastic x-ray scattering (REXS) study of the metal-insulator transition (MIT) in Sr3(Ru1-xMnx)2O7. The XAS results reveal that the MIT drives the onset of local antiferromagnetic correlations around the Mn impurities, a precursor of the long-range antiferromagnetism detected by REXS at T_order

As an elementary particle the electron carries spin \hbar/2 and charge e. When binding to the atomic nucleus it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies (e.g., s, p or d). Even if electrons in solids form bands and delocalize from the nuclei, in Mott insulators they retain their three fundamental quantum numbers: spin, charge and orbital[1]. The hallmark of one-dimensional (1D) physics is a breaking up of the elementary electron into its separate degrees of freedom[2]. The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago[3]. Using Resonant Inelastic X-ray Scattering on the 1D Mott-insulator Sr2CuO3 we now observe also the orbital degree of freedom separating. We resolve an orbiton liberating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion of ~0.2 eV., Comment: 35 pages, 8 figures

We have successfully determined the hitherto unknown sign of the B44 Stevens crystal-field parameter of the tetragonal heavy-fermion compound CeCu2Si2 using vector q dependent non-resonant inelastic x-ray scattering (NIXS) experiments at the cerium N4,5 edge. The observed difference between the two different directions q||[100] and q||[110] is due to the anisotropy of the crystal-field ground state in the (001) plane and is observable only because of the utilization of higher than dipole transitions possible in NIXS. This approach allows us to go beyond the specific limitations of dc magnetic susceptibility, inelastic neutron scattering, and soft x-ray spectroscopy, and provides us with a reliable information about the orbital state of the 4f electrons relevant for the quantitative modeling of the quasi-particles and their interactions in heavy-fermion systems.

We study the magnetic susceptibility of mixed-valent La2-xSrxCoO4 single crystals in the doping range of 0.5<= x <= 0.8 for temperatures up to 1000 K. The magnetism below room temperature is described by paramagnetic Co2+ in the high-spin state and by Co3+ in the non-magnetic low-spin state. Above room temperature, an increase in susceptibility compared to the behavior expected from Co2+ is seen, which we attribute to a spin-state transition of Co3+. The susceptibility is analyzed by comparison to full-multiplet calculations for the thermal population of the high- and intermediate-spin states of Co3+.

We demonstrate how ab initio cluster calculations including the full Coulomb vertex can be done in the basis of the localized, generalized Wannier orbitals which describe the low-energy density functional (LDA) band structure of the infinite crystal, e.g. the transition metal 3d and oxygen 2p orbitals. The spatial extend of our 3d Wannier orbitals (orthonormalized Nth order muffin-tin orbitals) is close to that found for atomic Hartree-Fock orbitals. We define Ligand orbitals as those linear combinations of the O 2p Wannier orbitals which couple to the 3d orbitals for the chosen cluster. The use of ligand orbitals allows for a minimal Hilbert space in multiplet ligand-field theory calculations, thus reducing the computational costs substantially. The result is a fast and simple ab initio theory, which can provide useful information about local properties of correlated insulators. We compare results for NiO, MnO and SrTiO3 with x-ray absorption, inelastic x-ray scattering, and photoemission experiments. The multiplet ligand field theory parameters found by our ab initio method agree within ~10% to known experimental values.

X-ray absorption spectroscopy is a well established tool for obtaining information about orbital and spin degrees of freedom in transition metal- and rare earth-compounds. For this purpose usually the dipole transitions of the L- (2p to 3d) and M- (3d to 4f) edges are employed, whereas higher order transitions such as quadrupolar 1s to 3d in the K-edge are rarely studied in that respect. This is due to the fact that usually such quadrupolar transitions are overshadowed by dipole allowed 1s to 4p transitions and, hence, are visible only as minor features in the pre-edge region. Nonetheless, these features carry a lot of valuable information, similar to the dipole L-edge transition, which is not accessible in experiments under pressure due to the absorption of the diamond anvil pressurecell. We recently performed a theoretical and experimental analysis of such a situation for the metal insulator transition of (V(1-x)Crx)2O3. Since the importance of the orbital degrees of freedom in this transition is widely accepted, a thorough understanding of quadrupole transitions of the vanadium K-pre-edge provides crucial information about the underlying physics. Moreover, the lack of inversion symetry at the vanadium site leads to onsite mixing of vanadium 3d- and 4p- states and related quantum mechanical interferences between dipole and quadrupole transitions. Here we present a theoretical analysis of experimental high resolution x-ray absorption spectroscopy at the V pre-K edge measured in partial fluorescence yield mode for single crystals. We carried out density functional as well as configuration interaction calculations in order to capture effects coming from both, itinerant and atomic limits.

V2O3 is an archetypal system for the study of correlation induced, Mott-Hubbard metal-insulator transitions. Despite decades of extensive investigations, the accurate description of its electronic properties remains an open problem in the physics of strongly correlated materials, also because of the lack of detailed experimental data on its electronic structure over the whole phase diagram. We present here a high resolution X-ray absorption spectroscopy study at the V K-edge of (V(1-x)Crx)2O3 to probe its electronic structure as a function of temperature, doping and pressure, providing an accurate picture of the electronic changes over the whole phase diagram. We also discuss the relevance of the parallel evolution of the lattice parameters, determined with X-ray diffraction. This allows us to draw two conclusions of general interest: first, the transition under pressure presents peculiar properties, related to a more continuous evolution of the lattice and electronic structure; second, the lattice mismatch is a good parameter describing the strength of the first order transition, and is consequently related to the tendency of the system towards the coexistence of different phases. Our results show that the evolution of the electronic structure while approaching a phase transition, and not only while crossing it, is also a key element to unveil the underlying physical mechanisms of Mott materials .

We describe procedures to obtain the electronic structure of disordered systems using either tight binding like models or quite directly from ab inito density functional band structure calculations. The band structure is calculated using super cells much larger than those containing a single minority component atom. We average over a large number of different super cell calculations containing different randomly positioned minority component atoms in the super cell as well as a varying total number of minority component atoms, weighted by the statistical probability. We develop an efficient and simple algorithm for unfolding of these bands, based on Bloch's theorem. The unfolded band-structure obtained in this way exhibits momentum and energy broadened structures replacing the gaps observed in often used single super cell calculations. Using the super cell averaged band-structure one can introduce a self-energy, resulting from the scattering of randomly positioned alloy components. The self-energy is causal, and shows strong energy and some momentum dependence. The self-energy shows rather non-trivial behavior and is in general non-zero at the Fermi-energy, resulting in an ill or undefined Fermi surface. The real-part of the self-energy at the Fermi-energy relates to an apparent violation of Luttinger's theorem. There is no simple relation between the apparent Fermi-surface volume and the electron count. Examples introducing these effects both for model and real binary alloy systems are presented.

In the search for the mechanism of high-temperature superconductivity, intense research has been focused on the evolution of the spin excitation spectrum upon doping from the antiferromagnetic insulating to the superconducting states of the cuprates. Because of technical limitations, the experimental investigation of doped cuprates has been largely focused on low-energy excitations in a small range of momentum space. Here we use resonant inelastic x-ray scattering to show that a large family of superconductors, encompassing underdoped YBa$_2$Cu$_4$O$_8$ and overdoped YBa$_2$Cu$_3$O$_{7}$, exhibits damped spin excitations (paramagnons) with dispersions and spectral weights closely similar to those of magnons in undoped cuprates. %The results are in excellent agreement with the spin excitations obtained by exact diagonalization of the $\bf t-J$ Hamiltonian on finite-sized clusters. The comprehensive experimental description of this surprisingly simple spectrum permits quantitative tests of magnetic Cooper pairing models. A numerical solution of the Eliashberg equations for the magnetic spectrum of YBa$_2$Cu$_3$O$_{7}$ reproduces its superconducting transition temperature within a factor of two, a level of agreement comparable to Eliashberg theories of conventional superconductors., Comment: Main text (11 pages, 4 figures) + supplementary information (4 pages, 4 figures, 1 table). An updated version will appear in Nature Physics

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 thus far not 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 LaNiO3-LaAlO3 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 d-electron materials.

We compare different methods for performing analytical continuation of spectral data from the imaginary time or frequency axis to the real frequency axis for the optical conductivity sigma(omega). We compare the maximum entropy (MaxEnt), singular value decomposition (SVD), sampling and Pade methods for analytical continuation. We also study two direct methods for obtaining sigma(0). For the MaxEnt approach we focus on a recent modification. The data are split up in batches, a separate MaxEnt calculation is done for each batch and the results are averaged. For the problems studied here, we find that typically the SVD, sampling and modified MaxEnt methods give comparable accuracy, while the Pade approximation is usually less reliable., Comment: 10 pages, 7 figures

We report on the local electronic structure of Fe impurities in MgO thin films. Using soft x-ray absorption spectroscopy (XAS) we verified that the Fe impurities are all in the 2+ valence state. The fine details in the line shape of the Fe $L_{2,3}$ edges provide direct evidence for the presence of a dynamical Jahn-Teller distortion. We are able to determine the magnitude of the effective $D_{4h}$ crystal field energies. We also observed a strong temperature dependence in the spectra which we can attribute to the thermal population of low-lying excited states that are present due to the spin-orbit coupling in the Fe 3d. Using this Fe$^{2+}$ impurity system as an example, we show that an accurate measurement of the orbital moment in Fe$_3$O$_4$ will provide a direct estimate for the effective local low-symmetry crystal fields on the Fe$^{2+}$ sites, important for the theoretical modeling of the formation of orbital ordering.

We improve on Fourier transforms (FT) between imaginary time $\tau$ and imaginary frequency $\omega_n$ used in certain quantum cluster approaches using the Hirsch-Fye method. The asymptotic behavior of the electron Green's function can be improved by using a "sumrule" boundary condition for a spline. For response functions a two-dimensional FT of a singular function is required. We show how this can be done efficiently by splitting off a one-dimensional part containing the singularity and by performing a semi-analytical FT for the remaining more innocent two-dimensional part., Comment: 4 pages, 3 figures

We report nonresonant inelastic x-ray scattering from the semi-core 5d levels of several actinide compounds. Dipole-forbidden, high-multipole features form a rich bound-state spectrum dependent on valence electron configuration and spin-orbit and Coulomb interactions. Cross-material comparisons, together with the anomalously high Coulomb screening required for agreement between atomic multiplet theory and experiment, demonstrate sensitivity to the neighboring electronic environment, such as is needed to address long-standing questions of electronic localization and bonding in 5f compounds., Comment: LA-UR 09-07829

We develop the theory for shallow-core to valence excitations when the multiplet spread is larger than the core-hole attraction, e.g., if the core and valence orbitals have the same principal quantum number. This results in a cross-over from bound to virtual-bound excited states with increasing energy and in large differences between dipole and high-order multipole transitions, as observed in inelastic x-ray scattering. The theory is important to obtain ground state information from x-ray spectroscopies of strongly correlated transition metal, rare-earth and actinide systems., Comment: 5 pages, 3 figures. Submitted to Phys. Rev. Lett

We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic error, due to deviations of the default function, used in the MaxEnt approach, from the exact spectrum. We find that the MaxEnt approach in its classical formulation can lead to a nonoptimal balance between the two types of errors, leading to an unnecessary large statistical error. The statistical error can be reduced by splitting up the data in several batches, performing a MaxEnt calculation for each batch and averaging. This can outweigh an increase in the systematic error resulting from this approach. The output from the MaxEnt result can be used as a default function for a new MaxEnt calculation. Such iterations often lead to worse results due to an increase in the statistical error. By splitting up the data in batches, the statistical error is reduced and and the increase resulting from iterations can be outweighed by a decrease in the systematic error. Finally we consider a linearized version to obtain a better understanding of the method., Comment: 10 pages and 8 figures