Spectroscopic Evidence of Kondo-Induced Quasiquartet in CeRh_{2}As_{2}.

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 reveals the impact of Kondo physics for coupling the Kramer's doublets into an effective quasiquartet. Nonresonant inelastic x-ray scattering data find that the |Γ_{7}^{-}⟩ state with its lobes along the 110 direction of the tetragonal structure (xy orientation) contributes most to the multiorbital ground state of CeRh_{2}As_{2}.

Orbital Magnetic Moment and Single-Ion Magnetic Anisotropy of the S = 1/2 K3[Fe(CN)6] Compound: A Case Where the Orbital Magnetic Moment Dominates the Spin Magnetic Moment.

The potassium hexacyanoferrate(III), K3[FeIII(CN)6], is known for its exceptional magnetic anisotropy among the 3d transition metal series. The Fe(III) ions are in the S = 1/2 low spin state imposed by the strong crystal field of the cyanido ligands. A large orbital magnetic moment is expected from previous publications. In the present work, X-ray magnetic circular dichroism was recorded for a powder sample, allowing direct measurement of the Fe(III) orbital magnetic moment. A combination of molecular multiconfigurational ab initio and atomic ligand field multiplets calculations provides the spin and orbital magnetic moments for the [FeIII(CN)6]3- isolated cluster, the crystallographic unit cell, and the powder sample. The calculations of the angular dependencies of the spin and orbital magnetic moments with the external magnetic induction direction reveal easy magnetization axes for each S = 1/2 molecular entity and the crystal. It also shows that the orbital magnetic moment dominates the spin magnetic moment for all directions. Our measurements confirm that the orbital magnetic moment contributes to 60% of the total magnetization for the powder, which is in excellent agreement with our theoretical predictions. An orbital magnetic moment greater than the spin magnetic moment is exceptional for 3d transition metal ions. The impact of crystal field strength and distortion, π back-bonding, spin-orbit coupling, and external magnetic induction was analyzed, leading to a deeper understanding of the spin and orbital magnetic anisotropies.

Magnetic excitations beyond the single- and double-magnons.

A photon carrying one unit of angular momentum can change the spin angular momentum of a magnetic system with one unit (ΔMs = ±1) at most. This implies that a two-photon scattering process can manipulate the spin angular momentum of the magnetic system with a maximum of two units. Herein we describe a triple-magnon excitation in α-Fe2O3, which contradicts this conventional wisdom that only 1- and 2-magnon excitations are possible in a resonant inelastic X-ray scattering experiment. We observe an excitation at exactly three times the magnon energy, along with additional excitations at four and five times the magnon energy, suggesting quadruple and quintuple-magnons as well. Guided by theoretical calculations, we reveal how a two-photon scattering process can create exotic higher-rank magnons and the relevance of these quasiparticles for magnon-based applications.

Intermixing-Driven Surface and Bulk Ferromagnetism in the Quantum Anomalous Hall Candidate MnBi6 Te10.

The recent realizations of the quantum anomalous Hall effect (QAHE) in MnBi2 Te4 and MnBi4 Te7 benchmark the (MnBi2 Te4 )(Bi2 Te3 )n family as a promising hotbed for further QAHE improvements. The family owes its potential to its ferromagnetically (FM) ordered MnBi2 Te4 septuple layers (SLs). However, the QAHE realization is complicated in MnBi2 Te4 and MnBi4 Te7 due to the substantial antiferromagnetic (AFM) coupling between the SLs. An FM state, advantageous for the QAHE, can be stabilized by interlacing the SLs with an increasing number n of Bi2 Te3 quintuple layers (QLs). However, the mechanisms driving the FM state and the number of necessary QLs are not understood, and the surface magnetism remains obscure. Here, robust FM properties in MnBi6 Te10 (n = 2) with Tc ≈ 12 K are demonstrated and their origin is established in the Mn/Bi intermixing phenomenon by a combined experimental and theoretical study. The measurements reveal a magnetically intact surface with a large magnetic moment, and with FM properties similar to the bulk. This investigation thus consolidates the MnBi6 Te10 system as perspective for the QAHE at elevated temperatures.

Laser Control of Electronic Exchange Interaction within a Molecule.

Electronic interactions play a fundamental role in atoms, molecular structure and reactivity. We introduce a general concept to control the effective electronic exchange interaction with intense laser fields via coupling to excited states. As an experimental proof of principle, we study the SF_{6} molecule using a combination of soft x-ray and infrared (IR) laser pulses. Increasing the IR intensity increases the effective exchange energy of the core hole with the excited electron by 50%, as observed by a characteristic spin-orbit branching ratio change. This work demonstrates altering electronic interactions by targeting many-particle quantum properties.

Tensor description of X-ray magnetic dichroism at the Fe L2,3-edges of Fe3O4.

A procedure to build the optical conductivity tensor that describes the full magneto-optical response of the system from experimental measurements is presented. Applied to the Fe L2,3-edge of a 38.85 nm Fe3O4/SrTiO3 (001) thin-film, it is shown that the computed polarization dependence using the conductivity tensor is in excellent agreement with that experimentally measured. Furthermore, the magnetic field angular dependence is discussed using a set of fundamental spectra expanded on spherical harmonics. It is shown that the convergence of this expansion depends on the details of the ground state of the system in question and in particular on the valence-state spin-orbit coupling. While a cubic expansion up to the third order explains the angular-dependent X-ray magnetic linear dichroism of Fe3+ well, higher-order terms are required for Fe2+ when the orbital moment is not quenched.

From antiferromagnetic and hidden order to Pauli paramagnetism in UM 2Si2 compounds with 5f electron duality.

Using inelastic X-ray scattering beyond the dipole limit and hard X-ray photoelectron spectroscopy we establish the dual nature of the U [Formula: see text] electrons in U[Formula: see text] (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 [Formula: see text] configuration with the [Formula: see text] and [Formula: see text] quasi-doublet symmetry. The amount of the U 5[Formula: see text] configuration, however, varies considerably across the U[Formula: see text] series, indicating an increase of U 5f 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 [Formula: see text] and [Formula: see text], the availability of orbital degrees of freedom needed for the hidden order in [Formula: see text] to occur, as well as the appearance of Pauli paramagnetism in [Formula: see text] A unified and systematic picture of the U[Formula: see text] compounds may now be drawn, thereby providing suggestions for additional experiments to induce hidden order and/or superconductivity in U compounds with the tetragonal body-centered [Formula: see text] structure.

Origin of Ising magnetism in Ca3Co2O6 unveiled by orbital imaging.

The one-dimensional cobaltate Ca[Formula: see text]Co[Formula: see text]O[Formula: see text] is an intriguing material having an unconventional magnetic structure, displaying quantum tunneling phenomena in its magnetization. Using a newly developed experimental method, [Formula: see text]-core-level non-resonant inelastic x-ray scattering ([Formula: see text]-NIXS), we were able to image the atomic Co [Formula: see text] orbital that is responsible for the Ising magnetism in this system. We can directly observe that corrections to the commonly accepted ideal prismatic trigonal crystal field scheme occur in Ca[Formula: see text]Co[Formula: see text]O[Formula: see text], and it is the complex [Formula: see text] orbital occupied by the sixth electron at the high-spin Co[Formula: see text] ([Formula: see text]) sites that generates the Ising-like behavior. The ability to directly relate the orbital occupation with the local crystal structure is essential to model the magnetic properties of this system.

Magnetic Contrast at Spin-Flip Excitations: An Advanced X-Ray Spectroscopy Tool to Study Magnetic-Ordering.

The determination of the local orientation and magnitude of the magnetization in spin textures plays a pivotal role in understanding and harnessing magnetic properties for technological applications. Here, we show that by employing the polarization dependence of resonant inelastic X-ray scattering (RIXS), we can directly probe the spin ordering with chemical and site selectivity. Applied on the prototypical ferrimagnetic mixed-valence system, magnetite ([Fe3+]A[Fe3+,Fe2+]BO4), we can distinguish spin-flip excitations at the A and B antiferromagnetically coupled Fe3+ sublattices and quantify the exchange field. Furthermore, it is possible to determine the orbital contribution to the magnetic moment from detailed angular dependence measurements. RIXS dichroism measurements performed at spin-flip excitations with nanometer spatial resolution will offer a powerful mapping contrast suitable for the characterization of magnetic ordering at interfaces and engineered spin textures.

Quanty4RIXS: a program for crystal field multiplet calculations of RIXS and RIXS-MCD spectra using Quanty.

Some initial instructions for the Quanty4RIXS program written in MATLAB® are provided. The program assists in the calculation of 1s 2p RIXS and 1s 2p RIXS-MCD spectra using Quanty. Furthermore, 1s XAS and 2p 3d RIXS calculations in different symmetries can also be performed. It includes the Hartree-Fock values for the Slater integrals and spin-orbit interactions for several 3d transition metal ions that are required to create the .lua scripts containing all necessary parameters and quantum mechanical definitions for the calculations. The program can be used free of charge and is designed to allow for further adjustments of the scripts.

Nonperturbative Series Expansion of Green's Functions: The Anatomy of Resonant Inelastic X-Ray Scattering in the Doped Hubbard Model.

We present a nonperturbative, divergence-free series expansion of Green's functions using effective operators. The method is especially suited for computing correlators of complex operators as a series of correlation functions of simpler forms. We apply the method to study low-energy excitations in resonant inelastic x-ray scattering (RIXS) in doped one- and two-dimensional single-band Hubbard models. The RIXS operator is expanded into polynomials of spin, density, and current operators weighted by fundamental x-ray spectral functions. These operators couple to different polarization channels resulting in simple selection rules. The incident photon energy dependent coefficients help to pinpoint main RIXS contributions from different degrees of freedom. We show in particular that, with parameters pertaining to cuprate superconductors, local spin excitation dominates the RIXS spectral weight over a wide doping range in the cross-polarization channel.

Direct bulk-sensitive probe of 5f symmetry in URu2Si2.

The second-order phase transition into a hidden order phase in URu2Si2 goes along with an order parameter that is still a mystery, despite 30 years of research. However, it is understood that the symmetry of the order parameter must be related to the symmetry of the low-lying local electronic [Formula: see text]-states. Here, we present results of a spectroscopic technique, namely core-level nonresonant inelastic X-ray scattering (NIXS). This method allows for the measurement of local high-multipole excitations and is bulk-sensitive. The observed anisotropy of the scattering function unambiguously shows that the 5[Formula: see text] ground-state wave function is composed mainly of the [Formula: see text] with majority [Formula: see text] = [Formula: see text] + [Formula: see text] and/or [Formula: see text] singlet states. The incomplete dichroism indicates the possibility that quantum states of other irreducible representation are mixed into the ground state.

CeRu4Sn6: a strongly correlated material with nontrivial topology.

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 CeRu4Sn6 is a strongly correlated material with non-trivial topology.

Element specific monolayer depth profiling.

The electronic phase behavior and functionality of interfaces and surfaces in complex materials are strongly correlated to chemical composition profiles, stoichiometry and intermixing. Here a novel analysis scheme for resonant X-ray reflectivity maps is introduced to determine such profiles, which is element specific and non-destructive, and which exhibits atomic-layer resolution and a probing depth of hundreds of nanometers.

Orbital reflectometry of oxide heterostructures.

The occupation of d orbitals controls the magnitude and anisotropy of the inter-atomic electron transfer in transition-metal oxides and hence exerts a key influence on their chemical bonding and physical properties. Atomic-scale modulations of the orbital occupation at surfaces and interfaces are believed to be responsible for massive variations of the magnetic and transport properties, but could not thus far be probed in a quantitative manner. Here we show that it is possible to derive quantitative, spatially resolved orbital polarization profiles from soft-X-ray reflectivity data, without resorting to model calculations. We demonstrate that the method is sensitive enough to resolve differences of ~3% in the occupation of Ni e(g) orbitals in adjacent atomic layers of a LaNiO(3)-LaAlO(3) superlattice, in good agreement with ab initio electronic-structure calculations. The possibility to quantitatively correlate theory and experiment on the atomic scale opens up many new perspectives for orbital physics in transition-metal oxides.