Nematic Spin Correlations Pervading the Phase Diagram of FeSe_{1-x}S_{x}.

We use resonant inelastic x-ray scattering (RIXS) at the Fe-L_{3} edge to study the spin excitations of uniaxial-strained and unstrained FeSe_{1-x}S_{x} (0≤x≤0.21) samples. The measurements on unstrained samples reveal dispersive spin excitations in all doping levels, which show only minor doping dependence in energy dispersion, lifetime, and intensity, indicating that high-energy spin excitations are only marginally affected by sulfur doping. RIXS measurements on uniaxial-strained samples reveal that the high-energy spin-excitation anisotropy observed previously in FeSe is also present in the doping range 0200 K in x=0.18 and reaches a maximum around the nematic quantum critical doping (x_{c}≈0.17). Since the spin-excitation anisotropy directly reflects the existence of nematic spin correlations, our results indicate that high-energy nematic spin correlations pervade the regime of nematicity in the phase diagram and are enhanced by the nematic quantum criticality. These results emphasize the essential role of spin fluctuations in driving electronic nematicity and highlight the capability of uniaxial strain in tuning spin excitations in quantum materials hosting strong magnetoelastic coupling and electronic nematicity.

Cuts through the manifold of molecular H2O potential energy surfaces in liquid water at ambient conditions.

The fluctuating hydrogen bridge bonded network of liquid water at ambient conditions entails a varied ensemble of the underlying constituting H2O molecular moieties. This is mirrored in a manifold of the H2O molecular potentials. Subnatural line width resonant inelastic X-ray scattering allowed us to quantify the manifold of molecular potential energy surfaces along the H2O symmetric normal mode and the local asymmetric O-H bond coordinate up to 1 and 1.5 Å, respectively. The comparison of the single H2O molecular potentials and spectroscopic signatures with the ambient conditions liquid phase H2O molecular potentials is done on various levels. In the gas phase, first principles, Morse potentials, and stepwise harmonic potential reconstruction have been employed and benchmarked. In the liquid phase the determination of the potential energy manifold along the local asymmetric O-H bond coordinate from resonant inelastic X-ray scattering via the bound state oxygen 1s to [Formula: see text] resonance is treated within these frameworks. The potential energy surface manifold along the symmetric stretch from resonant inelastic X-ray scattering via the oxygen 1s to [Formula: see text] resonance is based on stepwise harmonic reconstruction. We find in liquid water at ambient conditions H2O molecular potentials ranging from the weak interaction limit to strongly distorted potentials which are put into perspective to established parameters, i.e., intermolecular O-H, H-H, and O-O correlation lengths from neutron scattering.

Hydrogen bond effects in multimode nuclear dynamics of acetic acid observed via resonant x-ray scattering.

A theoretical and experimental study of the gas phase and liquid acetic acid based on resonant inelastic x-ray scattering (RIXS) spectroscopy is presented. We combine and compare different levels of theory for an isolated molecule for a comprehensive analysis, including electronic and vibrational degrees of freedom. The excitation energy scan over the oxygen K-edge absorption reveals nuclear dynamic effects in the core-excited and final electronic states. The theoretical simulations for the monomer and two different forms of the dimer are compared against high-resolution experimental data for pure liquid acetic acid. We show that the theoretical model based on a dimer describes the hydrogen bond formation in the liquid phase well and that this bond formation sufficiently alters the RIXS spectra, allowing us to trace these effects directly from the experiment. Multimode vibrational dynamics is accounted for in our simulations by using a hybrid time-dependent stationary approach for the quantum nuclear wave packet simulations, showing the important role it plays in RIXS.

Vibrational resonant inelastic X-ray scattering in liquid acetic acid: a ruler for molecular chain lengths.

Quenching of vibrational excitations in resonant inelastic X-ray scattering (RIXS) spectra of liquid acetic acid is observed. At the oxygen core resonance associated with localized excitations at the O-H bond, the spectra lack the typical progression of vibrational excitations observed in RIXS spectra of comparable systems. We interpret this phenomenon as due to strong rehybridization of the unoccupied molecular orbitals as a result of hydrogen bonding, which however cannot be observed in x-ray absorption but only by means of RIXS. This allows us to address the molecular structure of the liquid, and to determine a lower limit for the average molecular chain length.

In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe2As2.

A small in-plane external uniaxial pressure has been widely used as an effective method to acquire single domain iron pnictide BaFe2As2, which exhibits twin-domains without uniaxial strain below the tetragonal-to-orthorhombic structural (nematic) transition temperature Ts. Although it is generally assumed that such a pressure will not affect the intrinsic electronic/magnetic properties of the system, it is known to enhance the antiferromagnetic (AF) ordering temperature TN ( < Ts) and create in-plane resistivity anisotropy above Ts. Here we use neutron polarization analysis to show that such a strain on BaFe2As2 also induces a static or quasi-static out-of-plane (c-axis) AF order and its associated critical spin fluctuations near TN/Ts. Therefore, uniaxial pressure necessary to detwin single crystals of BaFe2As2 actually rotates the easy axis of the collinear AF order near TN/Ts, and such effects due to spin-orbit coupling must be taken into account to unveil the intrinsic electronic/magnetic properties of the system.

Anisotropic spin fluctuations in detwinned FeSe.

Superconductivity in FeSe emerges from a nematic phase that breaks four-fold rotational symmetry in the iron plane. This phase may arise from orbital ordering, spin fluctuations or hidden magnetic quadrupolar order. Here we use inelastic neutron scattering on a mosaic of single crystals of FeSe, detwinned by mounting on a BaFe2As2 substrate to demonstrate that spin excitations are most intense at the antiferromagnetic wave vectors QAF = (±1, 0) at low energies E = 6-11 meV in the normal state. This two-fold (C2) anisotropy is reduced at lower energies, 3-5 meV, indicating a gapped four-fold (C4) mode. In the superconducting state, however, the strong nematic anisotropy is again reflected in the spin resonance (E = 3.6 meV) at QAF with incommensurate scattering around 5-6 meV. Our results highlight the extreme electronic anisotropy of the nematic phase of FeSe and are consistent with a highly anisotropic superconducting gap driven by spin fluctuations.

Probing hydrogen bond strength in liquid water by resonant inelastic X-ray scattering.

Local probes of the electronic ground state are essential for understanding hydrogen bonding in aqueous environments. When tuned to the dissociative core-excited state at the O1s pre-edge of water, resonant inelastic X-ray scattering back to the electronic ground state exhibits a long vibrational progression due to ultrafast nuclear dynamics. We show how the coherent evolution of the OH bonds around the core-excited oxygen provides access to high vibrational levels in liquid water. The OH bonds stretch into the long-range part of the potential energy curve, which makes the X-ray probe more sensitive than infra-red spectroscopy to the local environment. We exploit this property to effectively probe hydrogen bond strength via the distribution of intramolecular OH potentials derived from measurements. In contrast, the dynamical splitting in the spectral feature of the lowest valence-excited state arises from the short-range part of the OH potential curve and is rather insensitive to hydrogen bonding.

Compatibility of quantitative X-ray spectroscopy with continuous distribution models of water at ambient conditions.

The phase diagram of water harbors controversial views on underlying structural properties of its constituting molecular moieties, its fluctuating hydrogen-bonding network, as well as pair-correlation functions. In this work, long energy-range detection of the X-ray absorption allows us to unambiguously calibrate the spectra for water gas, liquid, and ice by the experimental atomic ionization cross-section. In liquid water, we extract the mean value of 1.74 ± 2.1% donated and accepted hydrogen bonds per molecule, pointing to a continuous-distribution model. In addition, resonant inelastic X-ray scattering with unprecedented energy resolution also supports continuous distribution of molecular neighborhoods within liquid water, as do X-ray emission spectra once the femtosecond scattering duration and proton dynamics in resonant X-ray-matter interaction are taken into account. Thus, X-ray spectra of liquid water in ambient conditions can be understood without a two-structure model, whereas the occurrence of nanoscale-length correlations within the continuous distribution remains open.

Strain-Induced Spin-Nematic State and Nematic Susceptibility Arising from 2×2 Fe Clusters in KFe_{0.8}Ag_{1.2}Te_{2}.

Spin nematics break spin-rotational symmetry while maintaining time-reversal symmetry, analogous to liquid crystal nematics that break spatial rotational symmetry while maintaining translational symmetry. Although several candidate spin nematics have been proposed, the identification and characterization of such a state remain challenging because the spin-nematic order parameter does not couple directly to experimental probes. KFe_{0.8}Ag_{1.2}Te_{2} (K_{5}Fe_{4}Ag_{6}Te_{10}, KFAT) is a local-moment magnet consisting of well-separated 2×2 Fe clusters, and in its ground state the clusters order magnetically, breaking both spin-rotational and time-reversal symmetries. Using uniform magnetic susceptibility and neutron scattering measurements, we find a small strain induces sizable spin anisotropy in the paramagnetic state of KFAT, manifestly breaking spin-rotational symmetry while retaining time-reversal symmetry, resulting in a strain-induced spin-nematic state in which the 2×2 clusters act as the spin analog of molecules in a liquid crystal nematic. The strain-induced spin anisotropy in KFAT allows us to probe its nematic susceptibility, revealing a divergentlike increase upon cooling, indicating the ordered ground state is driven by a spin-orbital entangled nematic order parameter.

Spin Waves in Detwinned BaFe_{2}As_{2}.

Understanding magnetic interactions in the parent compounds of high-temperature superconductors forms the basis for determining their role for the mechanism of superconductivity. For parent compounds of iron pnictide superconductors such as AFe_{2}As_{2} (A=Ba, Ca, Sr), although spin excitations have been mapped out throughout the entire Brillouin zone, the respective measurements were carried out on twinned samples and did not allow for a conclusive determination of the spin dynamics. Here we use inelastic neutron scattering to completely map out spin excitations of ∼100% detwinned BaFe_{2}As_{2}. By comparing observed spectra with theoretical calculations, we conclude that the spin excitations can be well described by an itinerant model when taking into account moderate electronic correlation effects.

Oxygen redox chemistry without excess alkali-metal ions in Na2/3[Mg0.28Mn0.72]O2.

The search for improved energy-storage materials has revealed Li- and Na-rich intercalation compounds as promising high-capacity cathodes. They exhibit capacities in excess of what would be expected from alkali-ion removal/reinsertion and charge compensation by transition-metal (TM) ions. The additional capacity is provided through charge compensation by oxygen redox chemistry and some oxygen loss. It has been reported previously that oxygen redox occurs in O 2p orbitals that interact with alkali ions in the TM and alkali-ion layers (that is, oxygen redox occurs in compounds containing Li+-O(2p)-Li+ interactions). Na2/3[Mg0.28Mn0.72]O2 exhibits an excess capacity and here we show that this is caused by oxygen redox, even though Mg2+ resides in the TM layers rather than alkali-metal (AM) ions, which demonstrates that excess AM ions are not required to activate oxygen redox. We also show that, unlike the alkali-rich compounds, Na2/3[Mg0.28Mn0.72]O2 does not lose oxygen. The extraction of alkali ions from the alkali and TM layers in the alkali-rich compounds results in severely underbonded oxygen, which promotes oxygen loss, whereas Mg2+ remains in Na2/3[Mg0.28Mn0.72]O2, which stabilizes oxygen.

Two-Dimensional Massless Dirac Fermions in Antiferromagnetic AFe_{2}As_{2} (A=Ba,Sr).

We report infrared studies of AFe_{2}As_{2} (A=Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a sqrt[B] dependence of the LL transition energies, the zero-energy intercepts at B=0 T under the linear extrapolations of the transition energies and the energy ratio (∼2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe_{2}As_{2}. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction k_{z} indicate that massless Dirac fermions in BaFe_{2}As_{2} are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe_{2}As_{2} by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.

Zone plates as imaging analyzers for resonant inelastic x-ray scattering.

We have implemented and successfully tested an off-axis transmission Fresnel zone plate as a novel type of analyzer optics for resonant inelastic x-ray scattering (RIXS). We achieved a spectral resolution of 64 meV at the nitrogen K-edge (E/dE = 6200), closely matching theoretical predictions. The fundamental advantage of transmission optics is the fact that it can provide stigmatic imaging properties. This opens up a variety of advanced RIXS configurations, such as efficient scanning RIXS, parallel detection for varying incident energy and time-resolved measurements.

Doping Evolution of Magnetic Order and Magnetic Excitations in (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7}.

We use resonant elastic and inelastic x-ray scattering at the Ir-L_{3} edge to study the doping-dependent magnetic order, magnetic excitations, and spin-orbit excitons in the electron-doped bilayer iridate (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} (0≤x≤0.065). With increasing doping x, the three-dimensional long range antiferromagnetic order is gradually suppressed and evolves into a three-dimensional short range order across the insulator-to-metal transition from x=0 to 0.05, followed by a transition to two-dimensional short range order between x=0.05 and 0.065. Because of the interactions between the J_{eff}=1/2 pseudospins and the emergent itinerant electrons, magnetic excitations undergo damping, anisotropic softening, and gap collapse, accompanied by weakly doping-dependent spin-orbit excitons. Therefore, we conclude that electron doping suppresses the magnetic anisotropy and interlayer couplings and drives (Sr_{1-x}La_{x})_{3}Ir_{2}O_{7} into a correlated metallic state with two-dimensional short range antiferromagnetic order. Strong antiferromagnetic fluctuations of the J_{eff}=1/2 moments persist deep in this correlated metallic state, with the magnon gap strongly suppressed.

Effect of Nematic Order on the Low-Energy Spin Fluctuations in Detwinned BaFe_{1.935}Ni_{0.065}As_{2}.

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,π) should decrease with decreasing temperature below the structural transition temperature T_{s}. Here, we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe_{1.935}Ni_{0.065}As_{2} under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,π) happens just below T_{s}, suggesting the strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

Nematic Quantum Critical Fluctuations in BaFe_{2-x}Ni_{x}As_{2}.

We have systematically studied the nematic fluctuations in the electron-doped iron-based superconductor BaFe_{2-x}Ni_{x}As_{2} by measuring the in-plane resistance change under uniaxial pressure. While the nematic quantum critical point can be identified through the measurements along the (110) direction, as studied previously, quantum and thermal critical fluctuations cannot be distinguished due to similar Curie-Weiss-like behaviors. Here we find that a sizable pressure-dependent resistivity along the (100) direction is present in all doping levels, which is against the simple picture of an Ising-type nematic model. The signal along the (100) direction becomes maximum at optimal doping, suggesting that it is associated with nematic quantum critical fluctuations. Our results indicate that thermal fluctuations from striped antiferromagnetic order dominate the underdoped regime along the (110) direction. We argue that either there is a strong coupling between the quantum critical fluctuations and the fermions, or more exotically, a higher symmetry may be present around optimal doping.

Structural and Magnetic Phase Transitions near Optimal Superconductivity in BaFe2(As(1-x)Px)2.

We use nuclear magnetic resonance (NMR), high-resolution x-ray, and neutron scattering studies to study structural and magnetic phase transitions in phosphorus-doped BaFe2(As(1-x)P(x)2. Previous transport, NMR, specific heat, and magnetic penetration depth measurements have provided compelling evidence for the presence of a quantum critical point (QCP) near optimal superconductivity at x=0.3. However, we show that the tetragonal-to-orthorhombic structural (T{s}) and paramagnetic to antiferromagnetic (AF, TN) transitions in BaFe2(As(1-x)Px)2 are always coupled and approach T{N}≈T{s}≥T{c} (≈29 K) for x=0.29 before vanishing abruptly for x≥0.3. These results suggest that AF order in BaFe_{2}(As(1-x)Px)2 disappears in a weakly first-order fashion near optimal superconductivity, much like the electron-doped iron pnictides with an avoided QCP.

Superconductivity. Nematic spin correlations in the tetragonal state of uniaxial-strained BaFe(2-x)Ni(x)As2.

Understanding the microscopic origins of electronic phases in high-transition temperature (high-T(c)) superconductors is important for elucidating the mechanism of superconductivity. In the paramagnetic tetragonal phase of BaFe(2-x)T(x)As2 (where T is Co or Ni) iron pnictides, an in-plane resistivity anisotropy has been observed. Here, we use inelastic neutron scattering to show that low-energy spin excitations in these materials change from fourfold symmetric to twofold symmetric at temperatures corresponding to the onset of the in-plane resistivity anisotropy. Because resistivity and spin excitation anisotropies both vanish near optimal superconductivity, we conclude that they are likely intimately connected.

Doping dependence of spin excitations and its correlations with high-temperature superconductivity in iron pnictides.

High-temperature superconductivity in iron pnictides occurs when electrons and holes are doped into their antiferromagnetic parent compounds. Since spin excitations may be responsible for electron pairing and superconductivity, it is important to determine their electron/hole-doping evolution and connection with superconductivity. Here we use inelastic neutron scattering to show that while electron doping to the antiferromagnetic BaFe2As2 parent compound modifies the low-energy spin excitations and their correlation with superconductivity (<50 meV) without affecting the high-energy spin excitations (>100 meV), hole-doping suppresses the high-energy spin excitations and shifts the magnetic spectral weight to low-energies. In addition, our absolute spin susceptibility measurements for the optimally hole-doped iron pnictide reveal that the change in magnetic exchange energy below and above T(c) can account for the superconducting condensation energy. These results suggest that high-T(c) superconductivity in iron pnictides is associated with both the presence of high-energy spin excitations and a coupling between low-energy spin excitations and itinerant electrons.