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The insulating mixed-valent Ir$^{+3.66}$ compound Ba$_4$NbIr$_3$O$_{12}$ hosts two holes per Ir$_3$O$_{12}$ trimer unit. We address the electronic structure via resonant inelastic x-ray scattering (RIXS) at the Ir $L_3$ edge and exact diagonalization. The holes occupy quasimolecular orbitals that are delocalized over a trimer. This gives rise to a rich intra-$t_{2g}$ excitation spectrum that extends from 0.5 eV to energies larger than 2 eV. Furthermore, it yields a strong modulation of the RIXS intensity as a function of the transferred momentum q. A clear fingerprint of the quasimolecular trimer character is the observation of two modulation periods, $2\pi/d$ and $2\pi/2d$, where d and 2d denote the intratrimer Ir-Ir distances. We discuss how the specific modulation reflects the character of the wavefunction of an excited state. Our quantitative analysis shows that spin-orbit coupling $\lambda$ of about 0.4 eV is decisive for the character of the electronic states, despite a large hopping $t_{a_{1g}}$ of about 0.8 eV. The ground state of a single trimer is described very well by both holes occupying the bonding j=1/2 orbital, forming a vanishing quasimolecular moment with J=0., Comment: 19 pages, 13 figures

Mott insulators with spin-orbit entangled j=1/2 moments host intriguing magnetic properties. The j=1/2 wave function requires cubic symmetry, while a noncubic crystal field mixes j=1/2 and 3/2 character. Spectroscopic studies of $5d^5$ iridates typically claim noncubic symmetry, e.g., based on a splitting of the excited j=3/2 quartet. A sizable splitting is particularly puzzling in antifluorite-type K$_2$IrCl$_6$, a frustrated fcc quantum magnet with global cubic symmetry. It raises the fundamental question about the stability of j=1/2 moments against magneto-elastic coupling. Combining resonant inelastic x-ray scattering with optical spectroscopy, we demonstrate that the multi-peak line shape in K$_2$IrCl$_6$ reflects a vibronic character of the j=3/2 states rather than a noncubic crystal field. The quasimolecular crystal structure with well separated IrCl$_6$ octahedra explains the existence of well-defined sidebands that are usually smeared out in solids. Our results highlight the spin-orbital-lattice entangled character of cubic K$_2$IrCl$_6$ with ideal j=1/2 moments., Comment: 16 pages, 12 figures

We present a phenomenological theory of altermagnets, that captures their unique magnetization dynamics and allows modelling magnetic textures in this new magnetic phase. Focusing on the prototypical d-wave altermagnets, e.g. RuO$_2$, we can explain intuitively the characteristic lifted degeneracy of their magnon spectra, by the emergence of an effective sublattice-dependent anisotropic spin stiffness arising naturally from the phenomenological theory. We show that as a consequence the altermagnetic domain walls, in contrast to antiferromagnets, have a finite gradient of the magnetization, with its strength and gradient direction connected to the altermagnetic anisotropy, even for 180$^\circ$ domain walls. This gradient generates a ponderomotive force in the domain wall in the presence of a strongly inhomogeneous external magnetic field, which may be achieved through magnetic force microscopy techniques. The motion of these altermagentic domain walls is also characterized by an anisotropic Walker breakdown, with much higher speed limits of propagation than ferromagnets but lower than antiferromagnets.

Spin-orbit coupling locks spin direction and spatial orientation and generates, in semi-classical magnets, a local spin easy-axis and associated ordering. Quantum spin-1/2's defy this fate: rather than spins becoming locally anisotropic, the spin-spin interactions do. Consequently interactions become dependent on the spatial orientation of bonds between spins, prime theoretical examples of which are Kitaev magnets. Bond-directional interactions imply the existence of bond-directional magnetic modes, predicted spin excitations that render crystallographically equivalent bonds magnetically inequivalent, which yet have remained elusive experimentally. Here we show that resonant inelastic x-ray scattering allows us to explicitly probe the bond-directional character of magnetic excitations. To do so, we use a scattering plane spanned by one bond and the corresponding spin component and scan a range of momentum transfer that encompasses multiple Brillouin zones. Applying this approach to Na$_2$IrO$_3$ we establish the different bond-directional characters of magnetic excitations at 10 meV and 45 meV. Combined with the observation of spin-spin correlations that are confined to a single bond, this experimentally validates the Kitaev character of exchange interactions long proposed for this material., Comment: 6 pages, 5 figures, plus 4 pages Supplementary Information (incl. 5 figures)

Motivated by several claims of spin-orbit driven spin-liquid physics in hexagonal Ba$_3$Ti$_{3-x}$Ir$_x$O$_9$ hosting Ir2O9 dimers, we report on resonant inelastic x-ray scattering (RIXS) at the Ir L3 edge for different x. We demonstrate that magnetism in Ba$_3$Ti$_{3-x}$Ir$_x$O$_9$ is governed by an unconventional realization of strong disorder, where cation disorder affects the character of the local moments. RIXS interferometry, studying the RIXS intensity over a broad range of transferred momentum q, is ideally suited to assign different excitations to different Ir sites. We find pronounced Ir-Ti site mixing. Both ions are distributed over two crystallographically inequivalent sites, giving rise to a coexistence of quasimolecular singlet states on Ir2O9 dimers and spin-orbit entangled j=1/2 moments of 5d$^5$ Ir$^{4+}$ ions. RIXS reveals different kinds of strong magnetic couplings for different bonding geometries, highlighting the role of cation disorder for the suppression of long-range magnetic order in this family of compounds., Comment: 12 pages, 9 figures

The mixed-valent iridate Ba3InIr2O9 has been discussed as a promising candidate for quantum spin-liquid behavior. The compound exhibits Ir$^{4.5+}$ ions in face-sharing IrO6 octahedra forming Ir2O9 dimers with three t2g holes per dimer. Our results establish Ba3InIr2O9 as a cluster Mott insulator. Strong intra-dimer hopping delocalizes the three t2g holes in quasi-molecular dimer states while inter-dimer charge fluctuations are suppressed by Coulomb repulsion. The magnetism of Ba3InIr2O9 emerges from spin-orbit entangled quasi-molecular moments with yet unexplored interactions, opening up a new route to unconventional magnetic properties of 5d compounds. Using single-crystal x-ray diffraction we find the monoclinic space group C2/c already at room temperature. Dielectric spectroscopy shows insulating behavior. Resonant inelastic x-ray scattering (RIXS) reveals a rich excitation spectrum below 1.5 eV with a sinusoidal dynamical structure factor that unambiguously demonstrates the quasi-molecular character of the electronic states. Below 0.3 eV, we observe a series of excitations. According to exact diagonalization calculations, such low-energy excitations reflect the proximity of Ba3InIr2O9 to a hopping-induced phase transition based on the condensation of a quasi-molecular spin-orbit exciton. The dimer ground state roughly hosts two holes in a bonding j=1/2 orbital and the third hole in a bonding j=3/2 orbital., Comment: 14 pages, 10 figures, V2: published version, minor changes

To obtain a local description from highly accurate density functional theory codes that are based on modified plane wave bases, a transformation to a local orthonormal Wannier function basis is required. In order to do so while enforcing the constraints of the space group symmetry the Symmetry Conserving Maximally Projected Wannier Functions (SCMPWF) approach has been implemented in the Full-Potential-Local-Orbital code, FPLO. SCMPWFs represent the zeroth order approximation to maximally localized Wannier functions, projecting a subset of wave functions onto a set of suitably chosen local trial-functions with subsequent orthonormalization. The particular nature of the local orbitals in FPLO make them an ideal set of projectors, since they are constructed to be a chemical basis. While in many cases projection onto the FPLO basis orbitals is sufficient, the option is there to choose particular local linear combinations as projectors, in order to treat cases of bond centered Wannier functions. This choice turns out to lead to highly localized Wannier functions, which obey the space group symmetry of the crystal by construction. Furthermore we discuss the interplay of the Berry connection and position operator and especially its possible approximation, symmetries and the optimal choice of Bloch sum phase gauge in cases where the basis is not explicitly known. We also introduce various features which are accessible via the FPLO implementation of SCMPWFs, discuss and compare performance and provide example applications., Comment: 33 pages, 14 figures

Physically, one tends to think of non-Hermitian systems in terms of gain and loss: the decay or amplification of a mode is given by the imaginary part of its energy. Here, we introduce an alternative avenue to the realm of non-Hermitian physics, which involves neither gain nor loss. Instead, complex eigenvalues emerge from the amplitudes and phase-differences of waves backscattered from the boundary of insulators. We show that for any strong topological insulator in a Wigner-Dyson class, the reflected waves are characterized by a reflection matrix exhibiting the non-Hermitian skin effect. This leads to an unconventional Goos-H\"{a}nchen effect: due to non-Hermitian topology, waves undergo a lateral shift upon reflection, even at normal incidence. Going beyond systems with gain and loss vastly expands the set of experimental platforms that can access non-Hermitian physics and show signatures associated to non-Hermitian topology., Comment: 6 pages, 4 figures + 4 pages, 2 figures supplemental material; published version

Quantum phase transitions play an important role in shaping the phase diagram of high-temperature cuprate superconductors. These cuprates possess intertwined orders which interact strongly with superconductivity. However, the evidence for the quantum critical point associated with the charge order in the superconducting phase remains elusive. Here we show the short-range charge orders and the spectral signature of the quantum fluctuations in La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) near the optimal doping using high-resolution resonant inelastic X-ray scattering. On performing calculations through a diagrammatic framework, we discovered that the charge correlations significantly soften several branches of phonons. These results elucidate the role of charge order in the LSCO compound, providing evidence for quantum critical scaling and discommensurations associated with charge order., Comment: 9 pages, 4 figures

Triangular Heisenberg antiferromagnets are prototypes of geometric frustration, even if for nearest-neighbor interactions quantum fluctuations are not usually strong enough to destroy magnetic ordering: stronger frustration is required to stabilize a spin-liquid phase. On the basis of static magnetization and electron spin resonance measurements, we demonstrate the emergence of ${\tilde{j}_{\text{eff}}=\frac12}$ moments in the triangular-lattice magnet Na$_2$BaCo(PO$_4$)$_2$. These moments are subject to an extra source of frustration that causes magnetic correlations to set in far above both the magnetic ordering and Weiss temperatures. Corroborating the $\tilde{j}_{\text{eff}}=\frac12$ ground state, theory identifies ferromagnetic Kitaev exchange anisotropy as additional frustrating agent, altogether putting forward Na$_2$BaCo(PO$_4$)$_2$ as a promising Kitaev spin-liquid material., Comment: 6 pages, 4 figures (published version) + supplemental material (4 pages)

The recent discovery of magnetic topological insulators has opened new avenues to explore exotic states of matter that can emerge from the interplay between topological electronic states and magnetic degrees of freedom, be it ordered or strongly fluctuating. Motivated by the effects that the dynamics of the magnetic moments can have on the topological surface states, we investigate the magnetic fluctuations across the (MnBi$_{\text{2}}$Te$_{\text{4}}$)(Bi$_{\text{2}}$Te$_{\text{3}}$)$_{\text{n}}$ family. Our paramagnetic electron spin resonance experiments reveal contrasting Mn spin dynamics in different compounds, which manifests in a strongly anisotropic Mn spin relaxation in MnBi$_{\text{2}}$Te$_{\text{4}}$ while being almost isotropic in MnBi$_{\text{4}}$Te$_{\text{7}}$. Our density-functional calculations explain these striking observations in terms of the sensitivity of the local electronic structure to the Mn spin-orientation, and indicate that the anisotropy of the magnetic fluctuations can be controlled by the carrier density, which may directly affect the electronic topological surface states.

The low-energy physics of two-dimensional Quantum Anomalous Hall insulators like (Hg,Mn)Te quantum wells or magnetically doped (Bi,Sb)Te thin films can be effectively described by two Chern insulators, including a Dirac, as well as a momentum-dependent mass term. Each of those Chern insulators is directly related to the parity anomaly of planar quantum electrodynamics. In this work, we analyze the finite temperature Hall conductivity of a single Chern insulator in 2+1 space-time dimensions under the influence of a chemical potential and an out-of-plane magnetic field. At zero magnetic field, this non-dissipative transport coefficient originates from the parity anomaly of planar quantum electrodynamics. We show that the parity anomaly itself is not renormalized by finite temperature effects. However, it induces two terms of different physical origin in the effective action of a Chern insulator, which is proportional to the Hall conductivity. The first term is temperature and chemical potential independent, and solely encodes the intrinsic topological response. The second term specifies the non-topological thermal response of conduction and valence band states. In particular, we show that the relativistic mass of a Chern insulator counteracts finite temperature effects, whereas its non-relativistic mass enhances these corrections. Moreover, we extend our analysis to finite magnetic fields and relate the thermal response of a Chern insulator therein to the spectral asymmetry, which is a measure of the parity anomaly in orbital fields.

Using angle-resolved photoelectron spectroscopy (ARPES), we investigate the surface electronic structure of the magnetic van der Waals compounds MnBi$_4$Te$_7$ and MnBi$_6$Te$_{10}$, the $n=$~1 and 2 members of a modular (Bi$_2$Te$_3$)$_n$(MnBi$_2$Te$_4$) series, which have attracted recent interest as intrinsic magnetic topological insulators. Combining circular dichroic, spin-resolved and photon-energy-dependent ARPES measurements with calculations based on density functional theory, we unveil complex momentum-dependent orbital and spin textures in the surface electronic structure and disentangle topological from trivial surface bands. We find that the Dirac-cone dispersion of the topologial surface state is strongly perturbed by hybridization with valence-band states for Bi$_2$Te$_3$-terminated surfaces but remains preserved for MnBi$_2$Te$_4$-terminated surfaces. Our results firmly establish the topologically non-trivial nature of these magnetic van der Waals materials and indicate that the possibility of realizing a quantized anomalous Hall conductivity depends on surface termination.

We show that the cubic compound PtBi2, is a topological semimetal hosting a sixfold band touching point in close proximity to the Fermi level. Using angle-resolved photoemission spectroscopy, we map the bandstructure of the system, which is in good agreement with results from density functional theory. Further, by employing a low energy effective Hamiltonian valid close to the crossing point, we study the effect of a magnetic field on the sixfold fermion. The latter splits into a total of twenty Weyl cones for a Zeeman field oriented in the diagonal, [111] direction. Our results mark cubic PtBi2, as an ideal candidate to study the transport properties of gapless topological systems beyond Dirac and Weyl semimetals., Comment: 15 pages, 6 figures; this is the final, published version

Recently, several putative quantum spin liquid (QSL) states were discovered in ${\tilde S} = 1/2$ rare-earth based triangular-lattice antiferromagnets (TLAF) with the delafossite structure. A way to clarify the origin of the QSL state in these systems is to identify ways to tune them from the putative QSL state towards long-range magnetic order. Here, we introduce the Ce-based TLAF KCeS$_2$ and show via low-temperature specific heat and $\mu$SR investigations that it yields magnetic order below $T_{\mathrm N} = 0.38$ K despite the same delafossite structure. We identify a well separated ${\tilde S} = 1/2$ ground state for KCeS$_2$ from inelastic neutron scattering and embedded-cluster quantum chemical calculations. Magnetization and electron spin resonance measurements on single crystals indicate a strong easy-plane $g$~factor anisotropy, in agreement with the ab initio calculations. Finally, our specific-heat studies reveal an in-plane anisotropy of the magnetic field-temperature phase diagram which may indicate anisotropic magnetic interactions in KCeS$_2$., Comment: submission to Scipost Physics

In the quest for realizations of quantum spin liquids, the exploration of Kitaev materials - spin-orbit entangled Mott insulators with strong bond-directional exchanges - has taken center stage. However, in these materials the local spin-orbital j=1/2 moments typically show long-range magnetic order at low temperature, thus defying the formation of a spin-liquid ground state. Using resonant inelastic x-ray scattering (RIXS), we here report on a proximate spin liquid regime with clear fingerprints of Kitaev physics in the magnetic excitations of the honeycomb iridates alpha-Li2IrO3 and Na2IrO3. We observe a broad continuum of magnetic excitations that persists up to at least 300K, more than an order of magnitude larger than the magnetic ordering temperatures. We prove the magnetic character of this continuum by an analysis of the resonance behavior. RIXS measurements of the dynamical structure factor for energies within the continuum show that dynamical spin-spin correlations are restricted to nearest neighbors. Notably, these spectroscopic observations are also present in the magnetically ordered state for excitation energies above the conventional magnon excitations. Phenomenologically, our data agree with inelastic neutron scattering results on the related honeycomb compound RuCl3, establishing a common ground for a proximate Kitaev spin-liquid regime in these materials., Comment: 13 pages, 14 figures

Young's archetypal double-slit experiment forms the basis for modern diffraction techniques: the elastic scattering of waves yields an interference pattern that captures the real-space structure. Here, we report on an inelastic incarnation of Young's experiment and demonstrate that resonant inelastic x-ray scattering (RIXS) measures interference patterns which reveal the symmetry and character of electronic excited states in the same way as elastic scattering does for the ground state. A prototypical example is provided by the quasi-molecular electronic structure of insulating Ba3CeIr2O9 with structural Ir dimers and strong spin-orbit coupling. The double 'slits' in this resonant experiment are the highly localized core levels of the two Ir atoms within a dimer. The clear double-slit-type sinusoidal interference patterns that we observe allow us to characterize the electronic excitations, demonstrating the power of RIXS interferometry to unravel the electronic structure of solids containing, e.g., dimers, trimers, ladders, or other superstructures., Comment: 8 pages, 8 figures

We establish the double perovskite Ba$_2$CeIrO$_6$ as a nearly ideal model system for j=1/2 moments, with resonant inelastic x-ray scattering indicating a deviation of less than 1% from the ideally cubic j=1/2 state. The local j=1/2 moments form an fcc lattice and are found to order antiferromagnetically at $T_N$=14K, more than an order of magnitude below the Curie-Weiss temperature. Model calculations show that the geometric frustration of the fcc Heisenberg antiferromagnet is further enhanced by a next-nearest neighbor exchange, indicated by ab initio theory. Magnetic order is driven by a bond-directional Kitaev exchange and by local distortions via a strong magneto-elastic effect - both effects are typically not expected for j=1/2 compounds making Ba2CeIrO6 a riveting example for the rich physics of spin-orbit entangled Mott insulators., Comment: published version, 10 pages, 7 figures

High-resolution resonant inelastic x-ray scattering (RIXS) measurements ($\Delta$E = 46 meV) have been performed on Cd$_2$Os$_2$O$_7$ through the metal-to-insulator transition (MIT). A magnetic excitation at 125 meV evolves continuously through the MIT, in agreement with recent Raman scattering results, and provides further confirmation for an all-in, all-out magnetic ground state. Asymmetry of this feature is likely a result of coupling between the electronic and magnetic degrees of freedom. We also observe a broad continuum of interband excitations centered at 0.3 eV energy loss. This is indicative of significant hybridization between Os 5$d$ and O 2$p$ states, and concurrent itinerant nature of the system. In turn, this suggests a possible break down of the free-ion model for Cd$_2$Os$_2$O$_7$., Comment: Accepted in Physical Review B (10 pages)

We report a comprehensive experimental investigation on the magnetic anisotropy in bulk single crystals of Cr$_2$Ge$_2$Te$_6$, a quasi-two-dimensional ferromagnet belonging to the family of magnetic layered transition metal trichalcogenides that have attracted recently a big deal of interest with regard to the fundamental and applied aspects of two-dimensional magnetism. For this purpose electron spin resonance (ESR) and ferromagnetic resonance (FMR) measurements have been carried out over a wide frequency and temperature range. A gradual change in the angular dependence of the ESR linewidth at temperatures above the ferromagnetic transition temperature $T_{\rm c}$ reveals the development of two-dimensional spin correlations in the vicinity of $T_{\rm c}$ thereby proving the intrinsically low-dimensional character of spin dynamics in Cr$_2$Ge$_2$Te$_6$. Angular and frequency dependent measurements in the ferromagnetic phase clearly show an easy-axis type anisotropy of this compound. Furthermore, these experiments are compared with simulations based on a phenomenological approach, which takes into account results of static magnetization measurements as well as high temperature $g$ factors obtained from ESR spectroscopy in the paramagnetic phase. As a result the determined magnetocrystalline anisotropy energy density (MAE) $K_U$ is $(0.48 \pm 0.02) \times10^6$ erg/cm$^3$. This analysis is complemented by density functional calculations which yield the experimental MAE value for a particular value of the electronic correlation strength $U$. The analysis of the electronic structure reveals that the low-lying conduction band carries almost completely spin-polarized, quasi-homogeneous, two-dimensional states., Comment: 15 pages, 16 figures, accepted version

Platelike high-quality NaYbS$_{2}$ rhombohedral single crystals with lateral dimensions of a few mm have been grown and investigated in great detail by bulk methods like magnetization and specific heat, but also by local probes like nuclear magnetic resonance (NMR), electron-spin resonance (ESR), muon-spin relaxation ($\mu$SR), and inelastic neutron scattering (INS) over a wide field and temperature range. Our single-crystal studies clearly evidence a strongly anisotropic quasi-2D magnetism and an emerging spin-orbit entangled $S=1/2$ state of Yb towards low temperatures together with an absence of long-range magnetic order down to 260~mK. In particular, the clear and narrow Yb ESR lines together with narrow $^{23}$Na NMR lines evidence an absence of inherent structural distortions in the system, which is in strong contrast to the related spin-liquid candidate YbMgGaO$_{4}$ falling within the same space group $R\overline{3}m$. This identifies NaYbS$_{2}$ as a rather pure spin-1/2 triangular lattice magnet and a new putative quantum spin liquid.

Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been expressed in terms of a topological invariant computed using the eigenstates of the Wilson loop operator, a so called "nested Wilson loop" procedure. We show that, similar to the unitary Floquet operator describing periodically driven systems, the unitary Wilson loop operator can realize "anomalous" phases, that are topologically non-trivial despite having a trivial topological invariant. We introduce a concrete example of an anomalous HOTI, which has a quantized bulk quadrupole moment and fractional corner charges, but a vanishing nested Wilson loop index. A new invariant able to capture the topology of this phase is then constructed. Our work shows that anomalous topological phases, previously thought to be unique to periodically driven systems, can occur and be used to understand purely time-independent HOTIs., Comment: 7 pages, 2 figures + 9 pages, 5 figures appendix; This is the published version

The electronic ground state in many iridate materials is described by a complex wave-function in which spin and orbital angular momenta are entangled due to relativistic spin-orbit coupling (SOC). Such a localized electronic state carries an effective total angular momentum of $J_{eff}=1/2$. In materials with an edge-sharing octahedral crystal structure, such as the honeycomb iridates Li2IrO3 and Na2IrO3, these $J_{eff}=1/2$ moments are expected to be coupled through a special bond-dependent magnetic interaction, which is a necessary condition for the realization of a Kitaev quantum spin liquid. However, this relativistic electron picture is challenged by an alternate description, in which itinerant electrons are confined to a benzene-like hexagon, keeping the system insulating despite the delocalized nature of the electrons. In this quasi-molecular orbital (QMO) picture, the honeycomb iridates are an unlikely choice for a Kitaev spin liquid. Here we show that the honeycomb iridate Li2IrO3 is best described by a $J_{eff}=1/2$ state at ambient pressure, but crosses over into a QMO state under the application of small (~ 0.1 GPa) hydrostatic pressure. This result illustrates that the physics of iridates is extremely rich due to a delicate balance between electronic bandwidth, spin-orbit coupling, crystal field, and electron correlation., Comment: 7 pages, 5 figures, additional supplemental material included

We report a $^{75}$As nuclear magnetic resonance study in LaFeAsO single crystals, which undergoes nematic and antiferromagnetic transitions at $T_\text{nem}\sim 156$ K and $T_N \sim 138$ K, respectively. Below $T_\text{nem}$, the $^{75}$As spectrum splits sharply into two for an external magnetic field parallel to the orthorhombic $a$ or $b$ axis in the FeAs planes. Our analysis of the data demonstrates that the NMR line splitting arises from an electronically driven rotational symmetry breaking. The $^{75}$As spin-lattice relaxation rate as a function of temperature shows that spin fluctuations are strongly enhanced just below $T_\text{nem}$. These NMR findings indicate that nematic order promotes spin fluctuations in magnetically ordered LaFeAsO, as observed in non-magnetic and superconducting FeSe. We conclude that the origin of nematicity is identical in both FeSe and LaFeAsO regardless of whether or not a long range magnetic order develops in the nematic state., Comment: 5 pages, 4 figures, published as a rapid communication in PRB

Magnetization and high-resolution x-ray diffraction measurements of the Kitaev-Heisenberg material alpha-RuCl3 reveal a pressure-induced crystallographic and magnetic phase transition at a hydrostatic pressure of p=0.2 GPa. This structural transition into a triclinic phase is characterized by a very strong dimerization of the Ru-Ru bonds, accompanied by a collapse of the magnetic susceptibility. Ab initio quantum-chemistry calculations disclose a pressure-induced enhancement of the direct 4d-4d bonding on particular Ru-Ru links, causing a sharp increase of the antiferromagnetic exchange interactions. These combined experimental and computational data show that the Kitaev spin liquid phase in alpha-RuCl3 strongly competes with the crystallization of spin singlets into a valence bond solid.

A quantum spin-liquid might be realized in $\alpha$-RuCl$_{3}$, a honeycomb-lattice magnetic material with substantial spin-orbit coupling. Moreover, $\alpha$-RuCl$_{3}$ is a Mott insulator, which implies the possibility that novel exotic phases occur upon doping. Here, we study the electronic structure of this material when intercalated with potassium by photoemission spectroscopy, electron energy loss spectroscopy, and density functional theory calculations. We obtain a stable stoichiometry at K$_{0.5}$RuCl$_3$. This gives rise to a peculiar charge disproportionation into formally Ru$^{2+}$ (4$d^6$) and Ru$^{3+}$ (4$d^5$). Every Ru 4$d^5$ site with one hole in the $t_{2g}$ shell is surrounded by nearest neighbors of 4$d^6$ character, where the $t_{2g}$ level is full and magnetically inert. Thus, each type of Ru sites forms a triangular lattice and nearest-neighbor interactions of the original honeycomb are blocked., Comment: 6 pages, 4 figures

NaOsO$_{\text{3}}$ undergoes a metal-insulator transition (MIT) at 410 K, concomitant with the onset of antiferromagnetic order. The excitation spectra have been investigated through the MIT by resonant inelastic x-ray scattering (RIXS) at the Os L$_{\text{3}}$ edge. Low resolution ($\Delta E \sim$ 300 meV) measurements over a wide range of energies reveal that local electronic excitations do not change appreciably through the MIT. This is consistent with a picture in which structural distortions do not drive the MIT. In contrast, high resolution ($\Delta E \sim $ 56 meV) measurements show that the well-defined, low energy magnons in the insulating state weaken and dampen upon approaching the metallic state. Concomitantly, a broad continuum of excitations develops which is well described by the magnetic fluctuations of a nearly antiferromagnetic Fermi liquid. By revealing the continuous evolution of the magnetic quasiparticle spectrum as it changes its character from itinerant to localized, our results provide unprecedented insight into the nature of the MIT in \naoso. In particular, the presence of weak correlations in the paramagnetic phase implies a degree of departure from the ideal Slater limit., Comment: Joint submission with Physical Review Letters [Phys. Rev. Lett. 120, 227203 (2018), accepted version at arXiv:1805.03176]. This article includes further discussion about the calculations performed, models used, and so on

Within a Ginzburg-Landau formalism we establish analytically the necessary and sufficient conditions to realize a doubly degenerate superconducting ground state with broken time-reversal symmetry (BTRS) in a multi-band superconductor. Using these results we analyze the ground state of a three-band superconductor in the cylindrical geometry in an external magnetic field. We show that depending on the interband coupling constants, a magnetic flux can induce current density jumps in such superconducting geometries that are related to adiabatic or non-adiabatic transitions from BTRS to time-reversal symmetric states and vice versa. This unusual current induced magnetic flux response can in principle be used experimentally to detect superconducting BTRS ground states as well as corresponding metastable excited states., Comment: 7 pages, 7 figures

We report the first empirical demonstration that resonant inelastic x-ray scattering (RIXS) is sensitive to \emph{collective} magnetic excitations in $S=1$ systems by probing the Ni $L_3$-edge of La$_{2-x}$Sr$_x$NiO$_4$ ($x = 0, 0.33, 0.45$). The magnetic excitation peak is asymmetric, indicating the presence of single and multi spin-flip excitations. As the hole doping level is increased, the zone boundary magnon energy is suppressed at a much larger rate than that in hole doped cuprates. Based on the analysis of the orbital and charge excitations observed by RIXS, we argue that this difference is related to the orbital character of the doped holes in these two families. This work establishes RIXS as a probe of fundamental magnetic interactions in nickelates opening the way towards studies of heterostructures and ultra-fast pump-probe experiments., Comment: 8 pages, 4 figures, see ancillary files for the supplemental material

Recent breakthrough in search for the analogs of fundamental particles in condensed matter systems lead to experimental realizations of 3D Dirac and Weyl semimetals. Weyl state can be hosted either by non-centrosymmetric or magnetic materials and can be of the first or the second type. Several non-centrosymmetric materials have been proposed to be type-II Weyl semimetals, but in all of them the Fermi arcs between projections of multiple Weyl points either have not been observed directly or they were hardly distinguishable from the trivial surface states which significantly hinders the practical application of these materials. Here we present experimental evidence for type-II non-centrosymmetric Weyl state in TaIrTe$_4$ where it has been predicted theoretically. We find direct correspondence between ARPES spectra and calculated electronic structure both in the bulk and the surface and clearly observe the exotic surface states which support the quasi-1D Fermi arcs connecting only four Weyl points. Remarkably, these electronic states are spin-polarized in the direction along the arcs, thus highlighting TaIrTe$_4$ as a novel material with promising application potential., Comment: 9 pages, 4 figures

NaOsO3 hosts a rare manifestation of a metal-insulator transition driven by magnetic correlations, placing the magnetic exchange interactions in a central role. We use resonant inelastic x-ray scattering to directly probe these magnetic exchange interactions. A dispersive and strongly gapped (58 meV) excitation is observed indicating appreciable spin-orbit coupling in this 5d3 system. The excitation is well described within a minimal model Hamiltonian with strong anisotropy and Heisenberg exchange (J1=J2=13.9 meV). The observed behavior places NaOsO3 on the boundary between localized and itinerant magnetism.

Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of ${\alpha}$-RuCl$_3$, in which the Ru ions are in a d5 configuration and form a honeycomb lattice, by angle-resolved photoemission, x-ray photoemission and electron energy loss spectroscopy supported by density functional theory and multiplet calculations. We find that ${\alpha}$-RuCl$_3$ is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto Jeff states. This makes ${\alpha}$-RuCl$_3$ a promising candidate for the realization of Kitaev physics. Relevant electronic parameters such as the Hubbard energy U, the crystal field splitting 10Dq and the charge transfer energy are evaluated. Furthermore, we observe significant Cl photodesorption with time, which must be taken into account when interpreting photoemission and other surface sensitive experiments., Comment: 6 pages, 6 figures

Materials with a 5d4 electronic configuration are generally considered to have a nonmagnetic ground state (J=0). Interestingly, Sr2YIrO6 (Ir5+ having 5d4 electronic configuration) was recently reported to exhibit long-range magnetic order at low temperature and the distorted IrO6 octahedra were discussed to cause the magnetism in this material. Hence, a comparison of structurally distorted Sr2YIrO6 with cubic Ba2YIrO6 may shed light on the source of magnetism in such Ir5+ materials with 5d4 configuration. Besides, Ir5+ materials having 5d4 are also interesting in the context of recently predicted excitonic types of magnetism. Here we report a single-crystal-based analysis of the structural, magnetic, and thermodynamic properties of Ba2YIrO6. We observe that in Ba2YIrO6 for temperatures down to 0.4 K, long-range magnetic order is absent but at the same time correlated magnetic moments are present. We show that these moments are absent in fully relativistic ab initio band-structure calculations; hence, their origin is presently unclear., Comment: 8 pages, 9 figures

The rich physics manifested by 5d oxides falls outside the Mott-Hubbard paradigm used to successfully explain the electronic and magnetic properties of 3d oxides. Much consideration has been given to the extent to which strong spin-orbit coupling (SOC), in the limit of increased bandwidth and reduced electron correlation, drives the formation of novel electronic states, as manifested through the existence of metal-insulator transitions (MITs). SOC is believed to play a dominant role in 5d5 systems such as iridates (Ir4+), undergoing MITs which may or may not be intimately connected to magnetic order, with pyrochlore and perovksite systems being examples of the former and latter, respectively. However, the role of SOC for other 5d configurations is less clear. For example, 5d3 (e.g Os5+) systems are expected to have an orbital singlet and consequently a reduced effect of SOC in the groundstate. The pyrochlore osmate Cd2Os2O7 nonetheless exhibits a MIT intimately entwined with magnetic order with phenomena similar to pyrochlore iridates. Here we report the first resonant inelastic X-ray scattering (RIXS) measurements on an osmium compound, allowing us to determine the salient electronic and magnetic energy scales controlling the MIT in Cd2Os2O7, which we benchmark against detailed quantum chemistry calculations. In particular, we reveal the emergence at the MIT of a magnetic excitation corresponding to a superposition of multiple spin-flip processes from an Ising-like all-in/all-out magnetic groundstate. We discuss our results with respect to the role of SOC in magnetically mediated MITs in 5d systems

In condensed matter systems, out of a large number of interacting degrees of freedom emerge weakly coupled particles, in terms of which most physical properties are described. For example, Landau quasiparticles (QP) determine all electronic properties of a normal metal. The lack of identification of such QPs is major barrier for understanding myriad exotic properties of correlated electrons, such as unconventional superconductivity and non-Fermi liquid behaviours. Here, we report the observation of a composite particle in a Mott insulator Sr2IrO4---and exciton dressed with magnons---that propagates with the canonical characteristics of a QP: a finite QP residue and a lifetime longer than the hopping time scale. The dynamics of this charge-neutral bosonic excitation mirrors the fundamental process of the analogous one-hole propagation in the background of ordered spins, for which a well-defined QP has never been observed. The much narrower linewidth of the exciton reveals the same intrinsic dynamics that is obscured for the hole and is intimately related to the mechanism of high temperature superconductivity., Comment: submitted version

We present an ARPES study of the surface states of Ru$_2$Sn$_3$, a new type of a strong 3D topological insulator (TI). In contrast to currently known 3D TIs, which display two-dimensional Dirac cones with linear isotropic dispersions crossing through one point in the surface Brillouin Zone (SBZ), the surface states on Ru$_2$Sn$_3$ are highly anisotropic, displaying an almost flat dispersion along certain high-symmetry directions. This results in quasi-one dimensional (1D) Dirac electronic states throughout the SBZ that we argue are inherited from features in the bulk electronic structure of Ru$_2$Sn$_3$, where the bulk conduction bands are highly anisotropic. Unlike previous experimentally characterized TIs, the topological surface states of Ru$_2$Sn$_3$ are the result of a d-p band inversion rather than an s-p band inversion. The observed surface states are the topological equivalent to a single 2D Dirac cone at the surface Brillouin zone, Comment: 4 figures, includes supplementary information

The Skyrme-particle, the $skyrmion$, was introduced over half a century ago and used to construct field theories for dense nuclear matter. But with skyrmions being mathematical objects - special types of topological solitons - they can emerge in much broader contexts. Recently skyrmions were observed in helimagnets, forming nanoscale spin-textures that hold promise as information carriers. Extending over length-scales much larger than the inter-atomic spacing, these skyrmions behave as large, classical objects, yet deep inside they are of quantum origin. Penetrating into their microscopic roots requires a multi-scale approach, spanning the full quantum to classical domain. By exploiting a natural separation of exchange energy scales, we achieve this for the first time in the skyrmionic Mott insulator Cu$_2$OSeO$_3$. Atomistic ab initio calculations reveal that its magnetic building blocks are strongly fluctuating Cu$_4$ tetrahedra. These spawn a continuum theory with a skyrmionic texture that agrees well with reported experiments. It also brings to light a decay of skyrmions into half-skyrmions in a specific temperature and magnetic field range. The theoretical multiscale approach explains the strong renormalization of the local moments and predicts further fingerprints of the quantum origin of magnetic skyrmions that can be observed in Cu$_2$OSeO$_3$, like weakly dispersive high-energy excitations associated with the Cu$_4$ tetrahedra, a weak antiferromagnetic modulation of the primary ferrimagnetic order, and a fractionalized skyrmion phase., Comment: 5 pages, 3 figures

We report x-ray resonant magnetic scattering (XRMS) and resonant inelastic x-ray scattering (RIXS) studies of epitaxially-strained $\mathrm{Sr_2IrO_4}$ thin films. The films were grown on $\mathrm{SrTiO_3}$ and $\mathrm{(LaAlO_3)_{0.3}(Sr_2AlTaO_6)_{0.7}}$ substrates, under slight tensile and compressive strains, respectively. Although the films develop a magnetic structure reminiscent of bulk $\mathrm{Sr_2IrO_4}$, the magnetic correlations are extremely anisotropic, with in-plane correlation lengths significantly longer than the out-of-plane correlation lengths. In addition, the compressive (tensile) strain serves to suppress (enhance) the magnetic ordering temperature $\mathrm{T_N}$, while raising (lowering) the energy of the zone boundary magnon. Quantum chemical calculations show that the tuning of magnetic energy scales can be understood in terms of strain-induced change in bond lengths., Comment: 5 pages, 4 figures

We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in short-ranged spin correlations, a manifold of low-lying singlets (which can be understood as localized bound states of magnetic excitations), and the stabilization of valence bond crystals with resonating building blocks., Comment: Published version

From the measurement and analysis of the specific heat of high-quality K_(1-x)Na_xFe_2As_2 single crystals we establish the presence of large T^2 contributions with coefficients alpha_sc ~ 30 mJ/mol K^3 at low-T for both x=0 and 0.1. Together with the observed square root field behavior of the specific heat in the superconducting state both findings evidence d-wave superconductivity on almost all Fermi surface sheets with an average gap amplitude of Delta_0 in the range of 0.4 - 0.8 meV. The derived Delta_0 and the observed T_c agree well with the values calculated within the Eliashberg theory, adopting a spin-fluctuation mediated pairing in the intermediate coupling regime., Comment: 8 pages, 5 figures, field dependence of the specific heat added, slightly changed title, changed sequence of authors, one author added, accepted by Phys. Rev. B Rapid Communications

High resolution resonant inelastic x-ray scattering has been performed to reveal the role of lattice-coupling in a family of quasi-1D insulating cuprates, Ca$_{2+5x}$Y$_{2-5x}$Cu$_5$O$_{10}$. Site-dependent low energy excitations arising from progressive emissions of a 70 meV lattice vibrational mode are resolved for the first time, providing a direct measurement of electron-lattice coupling strength. We show that such electron-lattice coupling causes doping-dependent distortions of the Cu-O-Cu bond angle, which sets the intra-chain spin exchange interactions. Our results indicate that the lattice degrees of freedom are fully integrated into the electronic behavior in low dimensional systems., Comment: 5 pages, 4 figure

Motivated by the premise that superconductivity in iron-based superconductors is unconventional and mediated by spin fluctuations, an intense research effort has been focused on characterizing the spin excitation spectrum in the magnetically ordered parent phases of the Fe-pnictides2,3 and - chalcogenides4. For these undoped materials it is well-established that the spin excitation spectrum consists of a sharp, highly dispersive magnon spanning an energy range of up to 200 meV (ref. 3). The fate of these high-energy magnetic modes upon sizable doping is hitherto unresolved. Using resonant inelastic x-ray scattering we show that optimally doped superconducting Ba0.6K0.4Fe2As2 retains well defined, dispersive high-energy modes of magnetic origin. These paramagnon modes are softer than, though as intense as, the magnon of undoped antiferromagnetic BaFe2As2. The persistence of spin excitations well into the superconducting phase suggests that, if spin fluctuations are responsible for superconducting pairing, they originate from a distinctly correlated spin-state. This connects Fe-pnictide superconductors to the high-Tc cuprates, for which in spite of fundamental differences in the electronic structure, similar paramagnon modes are present5., Comment: 26 pages, 9 figures

The dynamics of S=1/2 quantum spins on a 2D square lattice lie at the heart of the mystery of the cuprates \cite{Hayden2004,Vignolle2007,Li2010,LeTacon2011,Coldea2001,Headings2010,Braicovich2010}. In bulk cuprates such as \LCO{}, the presence of a weak interlayer coupling stabilizes 3D N\'{e}el order up to high temperatures. In a truly 2D system however, thermal spin fluctuations melt long range order at any finite temperature \cite{Mermin1966}. Further, quantum spin fluctuations transfer magnetic spectral weight out of a well-defined magnon excitation into a magnetic continuum, the nature of which remains controversial \cite{Sandvik2001,Ho2001,Christensen2007,Headings2010}. Here, we measure the spin response of \emph{isolated one-unit-cell thick layers} of \LCO{}. We show that coherent magnons persist even in a single layer of \LCO{} despite the loss of magnetic order, with no evidence for resonating valence bond (RVB)-like spin correlations \cite{Anderson1987,Hsu1990,Christensen2007}. Thus these excitations are well described by linear spin wave theory (LSWT). We also observe a high-energy magnetic continuum in the isotropic magnetic response. This high-energy continuum is not well described by 2 magnon LSWT, or indeed any existing theories., Comment: Revised version to appear in Nature Materials; 6 pages,4 figures

The lack of structural symmetry which usually characterizes semiconductor quantum dots lifts the energetic degeneracy of the bright excitonic states and hampers severely their use as high fidelity sources of entangled photons. We demonstrate experimentally and theoretically that it is always possible to restore the excitonic degeneracy by the simultaneous application of large strain and electric fields, despite the fact that this possibility has fundamentally been doubted. This is achieved by using one external perturbation to align the polarization of the exciton emission along the axis of the second perturbation, which then erases completely the energy splitting of the states. This result, which holds for any QD structure, highlights the potential of combining complementary external fields to create artificial atoms meeting the stringent requirements posed by scalable semiconductor-based quantum-technology., Comment: 17 pages, 4 figures

Using resonant inelastic x-ray scattering, we observe in the bilayer iridate Sr3Ir2O7, a spin-orbit coupling driven magnetic insulator with a small charge gap, a magnon gap of ~92 meV for both acoustic and optical branches. This exceptionally large magnon gap exceeds the total magnon bandwidth of ~70 meV and implies a marked departure from the Heisenberg model, in stark contrast to the case of the single-layer iridate Sr2IrO4. Analyzing the origin of these observations, we find that the giant magnon gap results from bond-directional pseudo-dipolar interactions that are strongly enhanced near the metal-insulator transition boundary. This suggests that novel magnetism, such as that inspired by the Kitaev model built on the pseudo-dipolar interactions, may emerge in small charge-gap iridates.

Using resonant x-ray diffraction, we observe an easy c-axis collinear antiferromagnetic structure for the bilayer Sr$_3$Ir$_2$O$_7$, a significant contrast to the single layer Sr$_2$IrO$_4$ with in-plane canted moments. Based on a microscopic model Hamiltonian, we show that the observed spin-flop transition as a function of number of IrO$_2$ layers is due to strong competition among intra- and inter-layer bond-directional pseudo-dipolar interactions of the spin-orbit entangled $J_{eff}$=1/2 moments. With this we unravel the origin of anisotropic exchange interactions in a Mott insulator in the strong spin-orbit coupling regime, which holds the key to the various types of unconventional magnetism proposed in 5$d$ transition metal oxides.

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

To determine the strength of essential electronic and magnetic interactions in the iridates Sr$_2$IrO$_4$ and Ba$_2$IrO$_4$ - potential platforms for high-temperature superconductivity - we use many-body techniques from wavefunction-based electronic-structure theory. Multiplet physics, spin-orbit interactions, and Ir-O hybridization are all treated on equal footing, fully {\it ab initio}. Our calculations put the lowest d-d excitations of Sr$_2$IrO$_4$/Ba$_2$IrO$_4$ at 0.69/0.64 eV, substantially lower than in isostructural cuprates. Charge-transfer excitations start at 3.0/1.9 eV and the magnetic nearest-neighbor exchange coupling is 51/58 meV. Available experimental results are fully consistent with these values, which strongly constrains the parametrization of effective iridate Hamiltonians.

Ca2Y2Cu5O10 is build up from edge-shared CuO4 plaquettes forming spin chains. From inelastic neutron scattering data we extract an in-chain nearest neighbor exchange J1 approximately -170 K and the frustrating next neighbor J2 approximately 32 K interactions, both significantly larger than previous estimates. The ratio alpha= J2/J1 approximately 0.19 places the system very close to the critical point alpha_c=0.25 of the J1-J2 chain, but in the ferromagnetic regime. We establish that the vicinity to criticality only marginally affects the dispersion and coherence of the elementary spin-wave-like magnetic excitations, but instead results in a dramatic T-dependence of high-energy Zhang-Rice singlet excitation intensities., Comment: 4 pages, 5 figures, + supplement with 6 pages and 7 figures, 2 typos corrected

We used resonant inelastic x-ray scattering to reveal the nature of magnetic interactions in Sr2IrO4, a 5d transition-metal oxide with a spin-orbit entangled ground state and Jeff=1/2 magnetic momemts, referred to as 'isospins'. The magnon dispersion in Sr2IrO4 is well described by an antiferromagnetic Heisenberg model with isospin one-half moments on a square lattice, which renders the low-energy effective physics of Sr2IrO4 much akin to that in superconducting cuprates. This is further supported by the observation of exciton modes in Sr2IrO4 whose dispersion is strongly renormalized by magnons, which can be understood by analogy to the hole propagation in the background of antiferromagnetically ordered spins in the cuprates.