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A procedure for quantifying the U $5f$ electrons' covalence and degree of localization in U intermetallic compounds is presented. To this end, bulk sensitive hard and soft x-ray photoelectron spectroscopy were utilized in combination with density-functional theory (DFT) plus dynamical mean-field theory (DMFT) calculations. The energy dependence of the photoionization cross-sections allows the disentanglement of the U\,$5f$ contribution to the valence band from the various other atomic subshells so that the computational parameters in the DFT\,+\,DMFT can be reliably determined. Applying this method to UGa$_2$ and UB$_2$ as model compounds from opposite ends of the (de)localization range, we have achieved excellent simulations of the valence band and core-level spectra. The width in the distribution of atomic U\,$5f$ configurations contributing to the ground state, as obtained from the calculations, quantifies the correlated nature and degree of localization of the U\,5$f$. The findings permit answering the longstanding question why different spectroscopic techniques give seemingly different numbers for the U 5$f$ valence in intermetallic U compounds., Comment: 14 pages, 9 figures

We investigate the topological superconductor candidate UTe$_2$ using high-resolution valence-band resonant inelastic x-ray scattering at the U $M_{4,5}$-edges. We observe atomic-like low-energy excitations that support the correlated nature of this unconventional superconductor. These excitations originate from the U $5f^2$ configuration, which is unexpected since the short Te2-Te2 distances exclude Te2 being 2-. By utilizing the photoionization cross-section dependence of the photoemission spectra in combination with band structure calculations, we infer that the stabilization of the U $5f^2$ configuration is due to the U $6d$ bonding states in the U-dimers acting as a charge reservoir. Our results emphasize that the description of the physical properties should commence with a $5f^2$ $ansatz$., Comment: 9 pages, 5 figures, article

The application of pressure as well as the successive substitution of Ru with Fe in the hidden order (HO) compound URu$_2$Si$_2$ leads to the formation of the large moment antiferromagnetic phase (LMAFM). Here we have investigated the substitution series URu$_{2-x}$Fe$_x$Si$_2$ from $x$\,=\,0.0 to 2.0 by U\,4$f$ core-level photoelectron spectroscopy and have observed non-monotonic changes in the spectra. The initial increase and subsequent decrease of the spectral weight of the 4$f$ core level satellite with increasing $x$ stands for a non-monotonic 5$f$ filling across the substitution series. The competition of chemical pressure and increase of the density of states at the Fermi energy, both due to substitution of Ru with Fe, can explain such a behavior. An extended Doniach phase diagram including the $x$ dependence of the density of states is proposed. Also in URu$_{2-x}$Fe$_x$Si$_2$ the ground state is a singlet or quasi-doublet state consisting of two singlets. Hence, the formation of magnetic order in the URu$_{2-x}$Fe$_x$Si$_2$ substitution series must be explained within a singlet magnetism model., Comment: 10 pages, 7 figures

CeRh$_2$As$_2$ is a new multiphase superconductor with strong suggestions for an additional itinerant multipolar ordered phase. The modeling of the low temperature properties of this heavy fermion compound requires a quartet Ce$^{3+}$ crystal-field ground state. Here we provide the evidence for the formation of such a quartet state using x-ray spectroscopy. Core-level photoelectron and x-ray absorption spectroscopy confirm the presence of Kondo hybridization in CeRh$_2$As$_2$. The temperature dependence of the linear dichroism unambiguously reveils the impact of Kondo physics for coupling the Kramer's doublets into an effective quasi-quartet. Non-resonant inelastic x-ray scattering data find that the $|\Gamma_7^- \rangle$ state with its lobes along the 110 direction of the tetragonal structure ($xy$ orientation) contributes most to the multi-orbital ground state of CeRh$_2$As$_2$., Comment: 8 pages, 7 figures

Using high resolution tender-x-ray resonant inelastic scattering and hard-x-ray non-resonant inelastic scattering beyond the dipole limit we were able to detect electronic excitations in intermetallic UGa$_2$ that are highly atomic in nature. Analysis of the spectral lineshape reveals that the local $5f^2$ configuration characterizes the correlated nature of this ferromagnet. The orientation and directional dependence of the spectra indicate that the ground state is made of the $\Gamma_1$ singlet and/or $\Gamma_6$ doublet symmetry. With the ordered moment in the $ab$ plane, we infer that the magnetism originates from the higher lying $\Gamma_6$ doublet being mixed with the $\Gamma_1$ singlet due to inter-site exchange, qualifying UGa$_2$ to be a true quantum magnet. The ability to observe atomic excitations is crucial to resolve the on-going debate about the degree of localization versus itineracy in U intermetallics., Comment: 9 pages, 7 figures

We investigated the electronic structure of the enigmatic CeRh$_3$B$_2$ using resonant inelastic scattering and x-ray absorption spectroscopy in combination with $ab$ $initio$ density functional calculations. We find that the Rh 4$d$ states are irrelevant for the high-temperature ferromagnetism and the Kondo effect. We also find that the Ce 4$f$ crystal-field strength is too small to explain the strong reduction of the Ce magnetic moment. The data reveal instead the presence of two different active Ce 4$f$ orbitals, with each coupling selectively to different bands in CeRh$_3$B$_2$. The inter-site hybridization of the |J=5/2,Jz=+/-1/2> crystal-field state and Ce 5$d$ band combined with the intra-site Ce 4$f$-5$d$ exchange creates the strong ferromagnetism, while hybridization between the |J=5/2,Jz=+/-5/2> and the B $sp$ in the $ab$-plane contributes to the Kondo interaction which causes the moment reduction. This orbital selective coupling explains the unique and seemingly contradictory properties of CeRh$_3$B$_2$., Comment: 15 pages, 14 figures

CeRhSn with the Ce atoms forming a quasikagome lattice in the hexagonal plane has recently been discussed in the context of quantum criticality driven by magnetic frustration. Furthermore, it has been reported that the successive substitution of Rh by Pd leads to magnetic order. Here we have investigated the change of the 4$f$ occupation in the substitution series CeRh$_{1-x}$Pd$_x$Sn for for $x$ = 0, 0.1, 0.3, 0.5, 0.75 by means of photoelectron spectroscopy with hard x-rays (HAXPES). The quantitative analysis of the core level spectra with a combined full multiplet and configuration interaction analysis shows a smooth decrease of the 4$f^0$ contribution with rising $x$ due to an increase of the effective 4$f$ binding energy $\varepsilon_{4f}$ and the reduction of the effective hybridization $V_\text{eff}$. We further compare valence band data with the calculated partial density of states and find that the Pd 4$d$ states are about 1eV further away from the Ce 4$f$ states at the Fermi energy than the Rh 4$d$ states. In fact, the effective binding energy $\varepsilon_{4f}$ of the 4$f$ states in the configuration interaction analysis of the core level spectra decreases by the same amount., Comment: 10 pages, 9 figures

CeRh$_3$Si$_2$ has been reported to exhibit metamagnetic transitions below 5~K, a giant crystal field splitting, and anisotropic magnetic properties from single crystal magnetization and heat capacity measurements. Here we report results of neutron and x-ray scattering studies of the magnetic structure and crystal-field excitations to further understand the magnetism of this compound. Inelastic neutron scattering (INS) and resonant inelastic x-ray scattering (RIXS) reveal a $J_z$\,=\,1/2 groundstate for Ce when considering the crystallographic $a$ direction as quantization axis, thus explaining the anisotropy of the static susceptibility. Furthermore, we find a total splitting of 78\,meV for the $J$\,=\,5/2 multiplet. The neutron diffraction study in zero field reveals that on cooling from the paramagnetic state, the system first orders at $T_{\text{N}_1}=4.7$\,K in a longitudinal spin density wave with ordered Ce moments along the $b$-axis (i.e. the [0 1 0] crystal direction) and an incommensurate propagation vector $\textbf{k}=(0,0.43,0$). Below the lower-temperature transition $T_{\text{N}_2}=4.48$\,K, the propagation vector locks to the commensurate value $\textbf{k}=(0,0.5,0)$, with a so-called lock-in transition. Our neutron diffraction study in applied magnetic field $H\parallel b$-axis shows a change in the commensurate propagation vector and development of a ferromagnetic component at $H=3$\,kOe, followed by a series of transitions before the fully field-induced ferromagnetic phase is reached at $H = 7$\,kOe. This explains the nature of the steps previously reported in field-dependent magnetization measurements. A very similar behaviour is also observed for the $H\parallel$ [0 1 1] crystal direction., Comment: 26 pages, 16 figures

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.

CeIrSn with a quasikagome Ce lattice in the hexagonal basal plane is a strongly valence fluctuating compound, as we confirm by hard x-ray photoelectron spectroscopy and inelastic neutron scattering, with a high Kondo temperature of $T_{\mathrm{K}}\sim 480$\,K. We report a negative in-plane thermal expansion $\alpha/T$ below 2\,K, which passes through a broad minimum near 0.75\,K. Volume and $a$-axis magnetostriction for $B \parallel a$ are markedly negative at low fields and change sign before a sharp metamagnetic anomaly at 6\,T. These behaviors are unexpected for Ce-based intermediate valence systems, which should feature positive expansivity. Rather they point towards antiferromagnetic correlations at very low temperatures. This is supported by muon spin relaxation measurements down to 0.1\,K, which provide microscopic evidence for a broad distribution of internal magnetic fields. Comparison with isostructural CeRhSn suggests that these antiferromagnetic correlations emerging at $T\ll T_{\mathrm{K}}$ result from geometrical frustration., Comment: to be published in Phys. Rev. Lett

The crystal-field ground state wave function of CeCu$_2$Si$_2$ has been investigated with linear polarized $M$-edge x-ray absorption spectroscopy from 250mK to 250K, thus covering the superconducting ($T_{\text{c}}$=0.6K), the Kondo ($T_{\text{K}}$$\approx$20K) as well as the Curie-Weiss regime. The comparison with full-multiplet calculations shows that the temperature dependence of the experimental linear dichroism is well explained with a $\Gamma_7^{(1)}$ crystal-field ground-state and the thermal population of excited states at around 30meV. The crystal-field scheme does not change throughout the entire temperature range thus making the scenario of orbital switching unlikely. Spectroscopic evidence for the presence of the Ce 4$f^0$ configuration in the ground state is consistent with the possibility for a multi-orbital character of the ground state. We estimate from the Kondo temperature and crystal-field splitting energies that several percents of the higher lying $\Gamma_6$ state and $\Gamma_7^{(2)}$ crystal-field states are mixed into the primarily $\Gamma_7^{(1)}$ ground state. This estimate is also supported by re-normalized band-structure calculations that uses the experimentally determined crystal-field scheme., Comment: 8 pages, 5 figures

The application of pressure as well as the successive substitution of Ru with Fe in the hidden order (HO) compound URu$_2$Si$_2$ leads to the formation of the large moment antiferromagnetic phase (LMAFM). Here we have investigated the substitution series URu$_{2-x}$Fe$_x$Si$_2$ with $x$ = 0.2 and 0.3 with non-resonant inelastic x-ray scattering (NIXS) and 4$f$ core-level photoelectron spectroscopy with hard x-rays (HAXPES). NIXS shows that the substitution of Fe has no impact on the symmetry of the ground-state wave function. In HAXPES we find no shift of spectral weight that would be indicative for a change of the 5$f$-electron count. Consequently, changes in the exchange interaction $\cal{J}$ due to substitution must be minor so that the conjecture of chemical pressure seems unlikely. An alternative scenario is discussed, namely the formation of long range magnetic order due the substitution induced local enhancement of the magnetization in the vicinity of the $f$-electron ions while the overall electronic structure remains unchanged., Comment: 6 pages, 3 figures

Using inelastic x-ray scattering beyond the dipole limit and hard x-ray photoelectron spectroscopy we establish the dual nature of the U $5f$ electrons in UM$_2$Si$_2$ (M = Pd, Ni, Ru, Fe), regardless of their degree of delocalization. We have observed that the compounds have in common a local atomic-like state that is well described by the U $5f^2$ configuration with the $\Gamma_1^{(1)}$ and $\Gamma_2$ quasi-doublet symmetry. The amount of the U 5$f^3$ configuration, however, varies considerably across the UM$_2$Si$_2$ series, indicating an increase of U5$f$ itineracy in going from M=Pd to Ni to Ru, and to the Fe compound. The identified electronic states explain the formation of the very large ordered magnetic moments in UPd$_2$Si$_2$ and UNi$_2$Si$_2$, the availability of orbital degrees of freedom needed for the hidden order in URu$_2$Si$_2$ to occur, as well as the appearance of Pauli paramagnetism in UFe$_2$Si$_2$. A unified and systematic picture of the U$M_2$Si$_2$ compounds may now be drawn, thereby providing suggestions for new experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered ThCr$_2$Si$_2$ structure.

The one-dimensional cobaltate Ca3Co2O6 is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, s-core-level non-resonant inelastic x-ray scattering (s-NIXS), we were able to image the atomic Co 3d orbital that is responsible for the Ising magnetism in this system. We show that we can directly observe that it is the complex d2 orbital occupied by the sixth electron at the high-spin Co-trig{3+} (d6) sites that generates this behavior. This is extremely rare in the research field of transition metal compounds, and is only made possible by the delicately balanced prismatic trigonal coordination. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system.

The spectacular physical properties of quantum materials based on transition metal, rare earth, and actinide elements continue to challenge our comprehension of solid state physics and chemistry. The electronic states of these materials are dominated by the $d$ and $f$ wave functions intertwined with the strong band formation of the solid. In order to estimate which wave functions contribute to the ground state formation, we have had to rely, until now, on theoretical calculations combined with spectroscopy. Here we show that $s$-core-level non-resonant inelastic x-ray scattering ($s$-NIXS) can directly image the active orbital in real space, without the necessity of any modeling. The power and accuracy of this new technique is shown using the text-book example, x$^2$-y$^2$/3$z^2$-r$^2$ orbital of the Ni$^{2+}$ ion in NiO single crystal., Comment: 6 pages, 4 figures

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

The crystal-field (CF) splitting of the $^6H_{5/2}$ Hund's rule ground state of Sm$^{3+}$ in the strongly correlated topological insulator SmB$_6$ has been determined with high resolution resonant inelastic x-ray scattering (RIXS) at the Sm M$_5$ edge. The valence selectivity of RIXS allows isolating the crystal-field-split excited multiplets of the Sm$^{3+}$ (4$f^5$) configuration from those of Sm$^{2+}$ (4$f^6$) in intermediate valent SmB$_6$. The very large energy range of RIXS allows the crystal-field analysis of a high lying multiplet at about 2.4\,eV that has the same total angular momentum $J$ as the ground state so that ambiguities due to the elastic tail can be avoided. We find that the $\Gamma_7$ doublet and $\Gamma_8$ quartet of the $^6H_{5/2}$ Hund's rule ground state are split by $\Delta^{CF}_{^6H_{5/2}}$\,=\,20$\pm$10\,meV which sets an upper limit for the 4$f$ band width. This indicates an extremely large mass renormalization from the band structure value, pointing out the need to consider the coefficients of fractional parentage for the hopping of the 4$f$ electrons., Comment: 8 pages, 6 figures

Nonresonant inelastic x-ray scattering (NIXS) has been performed on single crystals of UO$_2$ to study the direction dependence of higher-order-multipole scattering from the uranium $O_{4,5}$ edges (90--110 eV). By comparing the experimental results with theoretical calculations the symmetry of the ground state is confirmed directly as the crystal-field (CF) $\Gamma_5$ triplet state within the $J$ = 4 manifold. The results also demonstrate that the directional dichroism of the NIXS spectra is sensitive to the CF strength and establish NIXS as a tool for probing CF interactions quantitatively., Comment: preprint

We have investigated the local low-energy excitations in CeRu$_4$Sn$_6$, a material discussed recently in the framework of strongly correlated Weyl semimetals, by means of Ce $M_5$ resonant inelastic x-ray scattering (RIXS). The availability of both $^2$F$_\frac{5}{2}$ and $^2$F$_\frac{7}{2}$ excitations of the Ce $4f^1$ configuration in the spectra allows for the determination of the crystal-electric field parameters that explain quantitatively the temperature dependence and anisotropy of the magnetic susceptibility. The absence of an azimuthal dependence in the spectra indicates that all crystal-electric field states are close to being rotational symmetric. We show further that the non-negligible impact of the $\check A_6^0$ parameter on the ground state of CeRu$_4$Sn$_6$ leads to a reduction of the magnetic moment due to multiplet intermixing. The RIXS results are consistent with inelastic neutron scattering (INS) data and are compared to the predictions from \textsl{ab-initio} based electronic structure calculations., Comment: 9 pages and 7 figures, submitted

Yb$_2$Si$_2$Al may be a prototype for exploring different aspects of the Shastry-Sutherland lattice, formed by planes of orthogonally coupled Yb ions. Measurements of the magnetic susceptibility find incoherently fluctuating Yb$^{3+}$ moments coexisting with a weakly correlated metallic state that is confirmed by measurements of the electrical resistivity. Increasing signs of Kondo coherence are found with decreasing temperature, including an enhanced Sommerfeld coefficient and Kadowaki-Woods ratio that signal that the metallic state found at the lowest temperatures is a Fermi liquid where correlations have become significantly stronger. A pronounced peak in the electronic and magnetic specific heat indicates that the coupling of the Yb moments to the conduction electrons leads to an effective Kondo temperature that is approximately 30 K. The valence of Yb$_2$Si$_2$Al has been investigated with electron spectroscopy methods. Yb$_2$Si$_2$Al is found to be strongly intermediate valent ($v_F=2.68(2)$ at 80 K). Taken together, these experimental data are consistent with a scenario where a coherent Kondo lattice forms in Yb$_2$Si$_2$Al from an incoherently fluctuating ensemble of Yb moments with incomplete Kondo compensation, and strong intermediate valence character., Comment: Submitted to Physical Review B

Here we present linear and circular polarized soft x-ray absorption spectroscopy (XAS) data at the Ce $M_{4,5}$ edges of the electron (Ir) and hole-doped (Re) Kondo semiconductor CeOs$_2$Al$_{10}$. Both substitutions have a strong impact on the unusual high N$\acute{e}$el temperature, $T_N$=28.5\,K, and also the direction of the ordered moment in case of Ir. The substitution dependence of the linear dichroism is weak thus validating the crystal-field description of CeOs$_2$Al$_{10}$ being representative for the Re and Ir substituted compounds. The impact of electron- and hole-doping on the hybridization between conduction and 4$f$ electrons is related to the amount of $f^0$ in the ground state and reduction of x-ray magnetic circular dichroism. A relationship of $cf$-hybridization strength and enhanced $T_N$ is discussed. The direction and doping dependence of the circular dichroism is in agreement with strong Kondo screening along the crystallographic $a$ direction., Comment: 6 pagers, 6 figures

We present linear polarization-dependent soft x-ray absorption spectroscopy data at the Ce $M_{4,5}$ edges of Cd and Sn doped CeCoIn$_5$. The 4$f$ ground state wave functions have been determined for their superconducting, antiferromagnetic and paramagnetic ground states. The absence of changes in the wave functions in CeCo(In$_{1-x}$Cd$_x$)$_5$ suggests the 4$f$\,--\,conduction electron ($cf$) hybridization is not affected by globally Cd doping, thus supporting the interpretation of magnetic droplets nucleating long range magnetic order. This is contrasted by changes in the wave function due to Sn substitution. Increasing Sn in CeCo(In$_{1-y}$Sn$_y$)$_5$ compresses the 4$f$ orbitals into the tetragonal plane of these materials, suggesting enhanced $cf$ hybridization with the in-plane In(1) atoms and a homogeneous altering of the electronic structure. As these experiments show, the 4$f$ wave functions are a very sensitive probe of small changes in the hybridization of 4$f$ and conduction electrons, even conveying information about direction dependencies., Comment: 6 pages, 4 figures

We investigated the crystal-electric field ground state of the 4$f$ manifold in the strongly correlated topological insulator SmB$_6$ using core level non-resonant inelastic x-ray scattering (NIXS). The directional dependence of the scattering function that arises from higher multipole transitions establishes unambiguously that the $\Gamma_8$ quartet state of the Sm $f^5$ $J$=$5/2$ configuration governs the ground-state symmetry and hence the topological properties of SmB$_6$. Our findings contradict the results of density functional calculations reported so far., Comment: 9 pages, 9 figures

Bulk sensitive hard x-ray photoelectron spectroscopy data of the Ce 3$p$ core level of CeRu$_4$Sn$_6$ are presented. Using a combination of full multiplet and configuration iteration model we were able to obtain an accurate lineshape analysis of the data, thereby taking into account correlations for the strong plasmon intensities. We conclude that CeRu$_4$Sn$_6$ is a moderately mixed valence compound with a weight of 8% for the Ce $f^0$ configuration in the ground state., Comment: 4 pages, 3 figures, conference proceedings (SCES2016)

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