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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., 6 pages, 4 figures (published version) + supplemental material (4 pages)

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., 15 pages, 16 figures, accepted version

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., 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.

Magnetization and high-resolution x-ray diffraction measurements of the Kitaev-Heisenberg material α− 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 α−RuCl3 strongly competes with the crystallization of spin singlets into a valence bond solid., This research has been supported by the DFG via SFB 1143 and WO 1532/3-2 and by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No 796048. M. Mezouar is acknowledged for providing beamtime at ID27 at the ESRF and for fruitful discussions. S.P.L. is grateful to CONICET for financial support during her stay at the ESRF. R.Y. and L.H. acknowledge Ulrike Nitzsche for technical support as concerns the ab initio calculations. P.L.K and D.G.M. were supported by the Gordon and Betty Moore Foundation EPiQS Initiative Grant No. GBMF4416. S.N. was supported by the U.S. Department of Energy, Basic Energy Sciences, Scientific User Facilities Division under contract DE-AC0500OR22725 with the Oak Ridge National Laboratory.

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.

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

Novel ground states might be realized in honeycomb lattices with strong spin-orbit coupling. Here we study the electronic structure of $��$-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 $��$-RuCl$_3$ is a Mott insulator with significant spin-orbit coupling, whose low energy electronic structure is naturally mapped onto Jeff states. This makes $��$-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., 6 pages, 6 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

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

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., 35 pages, 8 figures

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., 4 pages, 5 figures, + supplement with 6 pages and 7 figures, 2 typos corrected

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.

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.

We study the dynamical, momentum dependent two- and four-spin response functions in doped and undoped 1D cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t-J$ system the four-spin response vanishes at $\pi$, whereas the two-spin correlator is peaked around $\pi/2$, with generally larger spectral weight. Upon doping spectra tend to soften and broaden, with a transfer of spectral weight towards higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\pi$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta the higher-energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions., Comment: 7 pages, 5 figures

We assess the capabilities of magnetic Resonant Inelastic X-ray Scattering (RIXS) at the O $K$ edge in undoped cuprates by taking La_{2}CuO_{4} as a benchmark case, based on a series of RIXS measurements that we present here. By combining the experimental results with basic theory we point out the fingerprints of bimagnon in the O $K$ edge RIXS spectra. These are a dominant peak around 450 meV, the almost complete absence of dispersion both with $\pi$ and $\sigma$ polarization and the almost constant intensity vs. the transferred momentum with $\sigma$ polarization. This behavior is quite different from Cu $L_3$ edge RIXS giving a strongly dispersing bimagnon tending to zero at the center of the Brillouin zone. This is clearly shown by RIXS measurements at the Cu $L_3$ edge that we present. The Cu $L_3$ bimagnon spectra and those at Cu $K$ edge - both from the literature and from our data - however, have the same shape. These similarities and differences are understood in terms of different sampling of the bimagnon continuum. This panorama points out the unique possibilities offered by O $K$ RIXS in the study of magnetic excitations in cuprates near the center of the BZ.

We show that LiVCuO4 should be described by strongly ferromagnetically coupled Heisenberg antiferromagnetic chains (HAC) in sharp contrast with the effective exchange integrals Ji given in Enderle et al., Phys. Rev. Lett. vol. 104, 237207 (2010), and the main issues of that work, namely, (i) LiVCuO4 is well described by two weakly ferromagnetically coupled interpenetrating Heisenberg antiferromagnetic spin-1/2 chains, (ii) the extracted exchange integrals J1, J2 agree with a previous spin-wave description (Enderle et al., Euphys. Lett. vol. 70, 237 (2005)), (iii) the spectral density of inelastic neutron scattering (INS) above 10 meV is ascribed to a 4-spinon continuum. Applying exact diagonalization and DMRG methods to fit their INS and magnetization M(H) data, supported by two independent microscopic methods (5-band Hubbard model and LSDA+U calculations), we demonstrate that LiCuVO4 exhibits strong inchain frustration with alpha =-J2/J1 < 1, i.e. strong coupling of the HAC at odds with (i). An alternative phenomenological set in accord with various experimental results is proposed. In view of the recent possible discovery of quantum-spin nematics and Bose condensation of two-magnon bound states (M. Zhitomirsky et al. arXiv:1003.4096v2 (2010), L. Svistov et al. ibid. 1005.5668v2 (2010)) in LiCuVO4 precise knowledge of the main J-values is of key importance., 1 page, 1 figure, revised comment, analysis of magnetization data included, one author added; response to arXiv:1009.1564 by Enderle et al., changed abstract

Coupled frustrated spin-1/2 chains in high magnetic fields described within the ferro- antiferromagnetic J1-J2 Heisenberg model are studied by the DMRG, the hard core boson, and the spin wave theory approaches. Multipolar phases related to magnon bound states are destroyed (supported) by weak antiferromagnetic (ferromagnetic) interchain couplings Jic. We show that quantum spin nematics might be found for LiVCuO4 whereas for Li(Na)Cu2O2 it is prevented by a sizeable antiferromagnetic Jic. Also for Li2ZrCuO4 with a small antiferromagnetic Jic expected triatic or quartic phases are unlikely, too. The saturation field is found to be strongly affected even by a relatively small Jic., Comment: 5 pages, 4 figures, as compared with the 1st version: new title, inclusion of 2D-phase diagrams, as well as addition of exact hard core boson results for nematics

Using high-resolution resonant inelastic x-ray scattering (RIXS), we performed a momentum-resolved study of magnetic excitations in the model spin-1/2 2D antiferromagnetic insulator Sr_2CuCl_2O_2. We identify both a single-spin-wave feature and a multi-magnon continuum, and show that the X-ray polarization can be used to distinguish these two contributions in the cross-section. The spin-waves display a large (70 meV) dispersion between the zone-boundary points ($\pi$,0) and ($\pi$/2,$\pi$/2). Employing an extended $t$-$t'$-$t"$-$U$ one-band Hubbard model, we find significant electronic hopping beyond nearest-neighbor Cu ions. We conclude that sizeable extended magnetic interactions are present in \scoc{} and probably important in all undoped cuprates., Comment: 4 pages, 4 figures

We show that, contrary to common lore, in resonant inelastic x-ray scattering (RIXS) at the copper L- and M-edge direct spin-flip scattering is in principle allowed. We demonstrate how this possibility can be exploited to probe the momentum dependent magnetic properties of cuprates such as the high Tc superconductors and compute in detail the relevant local and momentum dependent magnetic scattering amplitudes, which we compare to the elastic and $dd$-excitation scattering intensities. For cuprates these results put RIXS as a technique on the same footing as neutron scattering., 4 pages, 3 figures

We probe the collective magnetic modes of La$_2$CuO$_4$ (LCO) and underdoped La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) by momentum resolved Resonant Inelastic X-ray Scattering (RIXS) at the Cu $L_3$ edge. In LCO the single magnon dispersion measured by RIXS coincides with the one determined by inelastic neutron scattering. For LSCO the spin dynamics shows a branch dispersing up to $\sim$400 meV coexisting with a branch at lower energy. Only the latter has been observed with neutrons so far and is considered a key signature of doped cuprates. The presence of the high-energy branch indicates that LSCO is in a dynamic inhomogeneous spin state., Comment: 5 pages, 4 figures

The electronic, magnetic and orbital structures of KCrF3 are determined in all its recently identified crystallographic phases (cubic, tetragonal, and monoclinic) with a set of ab initio local spin density approximation (LSDA) and LSDA+U calculations. The high-temperature undistorted cubic phase appears as a metal from LSDA, but it is a Mott insulator with a gap of 1.72 eV at the LSDA+U level. The tetragonal and monoclinic phases of KCrF3 exhibit cooperative Jahn-Teller distortions concomitant with staggered 3x2−r2/3y2−r2 orbital order. We find that the energy gains due to the Jahn-Teller distortion are 82 and 104 meV per chromium ion in the tetragonal and monoclinic phases, respectively. These phases show A-type magnetic ordering and have a band gap of 2.48 eV. In this Mott insulating state, KCrF3 has a substantial conduction bandwidth leading to the possibility for the kinetic energy of charge carriers in electron- or hole-doped derivatives of KCrF3 to overcome the polaron localization at low temperatures, in analogy with the situation encountered in the colossal magnetoresistive manganites.

In the early days of high temperature superconductivity it was already recognized that magnetic properties of these materials are intimately related to the superconducting ones . When doped, the long-range ordered antiferromagnetic background of pristine copper-oxide insulators melts away and makes room for a spin liquid and superconductivity. By resonant inelastic x-ray scattering (RIXS) in the soft regime we probe the hitherto inaccessible dynamical multiple-spin correlations of the magnetic background in a series of parent compounds and in high Tc materials [NCCO (Nd2-xCexCuO4) and LSCO (La2-xSrxCuO4)]. High resolution measurements allows the clear observation of dispersing bimagnon excitations. In the undoped compounds the theory, fits the data on these coherent spin excitations without free parameters. In nearly optimally doped LSCO we observe the appearance of a new collective excitation at an energy of 250 +/- 60 meV having the signature of a coupled bimagnon-charge mode. It has a strongly reduced dispersion and lies in a so far unexplored region of momentum and energy space in the mid-infrared., Comment: 16 pages, 3 figures embedded

We study with the Raman scattering technique two types of phase transitions in the pyroxene compounds NaMSi$_2$O$_6$ (with M=Ti, V, and Cr). In the quasi one-dimensional S=1/2 system NaTiSi$_2$O$_6$ we observe anomalous high-temperature phonon broadening and large changes of the phonon energies and line-widths across the phase transition at 210 K. The phonon anomalies originate from an orbital order-disorder phase transition and these results --combined with theoretical considerations-- indicate that the high temperature dynamical Jahn-Teller phase of NaTiSi$_2$O$_6$ exhibits a spontaneous breaking of translational symmetry into a dimerized, Jahn-Teller distorted, orbital ordered state under the formation of spin valence bonds. In S=1 NaVSi$_2$O$_6$ orbital degrees of freedom are strongly suppressed and the magnetic excitations are well described within a Heisenberg model, indicating that at T$_N$=19K this system orders antiferromagnetically., Comment: 4 pages, 4 figures embedded

The elementary excitations of a model Hamiltonian that captures the low energy behavior of a simple two-fold degenerate Hubbard Hamiltonian with Hund's rule coupling, is studied. The phase diagram in the mean-field limit and in a two-site approach reveals a rich variety of phases where both the orbital and the spin degrees of freedom are ordered. We show that besides usual spin waves (magnons) there exist also orbital waves (orbitons) and, most interestingly, in a completely ferromagnetically coupled system, a combined spin-orbital excitation which can be visualized as a bound state of magnons and orbitons. For a completely degenerate system the bound states are found to be the lowest lying elementary excitations, both in one- and two-dimensions. Finally we extend our treatment to almost-degenerate systems. This can serve as an example that the elementary excitations in orbitally degenerate strongly correlated electron systems in general carry both spin and orbital character., Comment: 7 pages, 8 figures

Resonant Inelastic X-ray Scattering (RIXS) is an X-ray in, X-ray out technique that enables one to study the dispersion of excitations in solids. In this thesis, we investigated how various elementary excitations of transition metal oxides show up in RIXS spectra.