Evolution of the Magnetic Excitations in Electron-Doped La_{2-x}Ce_{x}CuO_{4}.

We investigated the high energy spin excitations in electron-doped La_{2-x}Ce_{x}CuO_{4}, a cuprate superconductor, by resonant inelastic x-ray scattering (RIXS) measurements. Efforts were paid to disentangle the paramagnon signal from non-spin-flip spectral weight mixing in the RIXS spectrum at Q_{∥}=(0.6π,0) and (0.9π,0) along the (1 0) direction. Our results show that, for doping level x from 0.07 to 0.185, the variation of the paramagnon excitation energy is marginal. We discuss the implication of our results in connection with the evolution of the electron correlation strength in this system.

Emergence of Spinons in Layered Trimer Iridate Ba_{4}Ir_{3}O_{10}.

Spinons are well known as the elementary excitations of one-dimensional antiferromagnetic chains, but means to realize spinons in higher dimensions is the subject of intense research. Here, we use resonant x-ray scattering to study the layered trimer iridate Ba_{4}Ir_{3}O_{10}, which shows no magnetic order down to 0.2 K. An emergent one-dimensional spinon continuum is observed that can be well described by XXZ spin-1/2 chains with a magnetic exchange of ∼55 meV and a small Ising-like anisotropy. With 2% isovalent Sr doping, magnetic order appears below T_{N}=130 K along with sharper excitations in (Ba_{1-x}Sr_{x})_{4}Ir_{3}O_{10}. Combining our data with exact diagonalization calculations, we find that the frustrated intratrimer interactions effectively reduce the system into decoupled spin chains, the subtle balance of which can be easily tipped by perturbations such as chemical doping. Our results put Ba_{4}Ir_{3}O_{10} between the one-dimensional chain and two-dimensional quantum spin liquid scenarios, illustrating a new way to suppress magnetic order and realize fractional spinons.

Charge Condensation and Lattice Coupling Drives Stripe Formation in Nickelates.

Revealing the predominant driving force behind symmetry breaking in correlated materials is sometimes a formidable task due to the intertwined nature of different degrees of freedom. This is the case for La_{2-x}Sr_{x}NiO_{4+δ}, in which coupled incommensurate charge and spin stripes form at low temperatures. Here, we use resonant x-ray photon correlation spectroscopy to study the temporal stability and domain memory of the charge and spin stripes in La_{2-x}Sr_{x}NiO_{4+δ}. Although spin stripes are more spatially correlated, charge stripes maintain a better temporal stability against temperature change. More intriguingly, charge order shows robust domain memory with thermal cycling up to 250 K, far above the ordering temperature. These results demonstrate the pinning of charge stripes to the lattice and that charge condensation is the predominant factor in the formation of stripe orders in nickelates.

Strong Superexchange in a d

The discovery of superconductivity in a d^{9-δ} nickelate has inspired disparate theoretical perspectives regarding the essential physics of this class of materials. A key issue is the magnitude of the magnetic superexchange, which relates to whether cuprate-like high-temperature nickelate superconductivity could be realized. We address this question using Ni L-edge and O K-edge spectroscopy of the reduced d^{9-1/3} trilayer nickelates R_{4}Ni_{3}O_{8} (where R=La, Pr) and associated theoretical modeling. A magnon energy scale of ∼80 meV resulting from a nearest-neighbor magnetic exchange of J=69(4) meV is observed, proving that d^{9-δ} nickelates can host a large superexchange. This value, along with that of the Ni-O hybridization estimated from our O K-edge data, implies that trilayer nickelates represent an intermediate case between the infinite-layer nickelates and the cuprates. Layered nickelates thus provide a route to testing the relevance of superexchange to nickelate superconductivity.

Strongly Correlated Charge Density Wave in La_{2-x}Sr_{x}CuO_{4} Evidenced by Doping-Dependent Phonon Anomaly.

The discovery of charge-density-wave-related effects in the resonant inelastic x-ray scattering spectra of cuprates holds the tantalizing promise of clarifying the interactions that stabilize the electronic order. Here, we report a comprehensive resonant inelastic x-ray scattering study of La_{2-x}Sr_{x}CuO_{4} finding that charge-density wave effects persist up to a remarkably high doping level of x=0.21 before disappearing at x=0.25. The inelastic excitation spectra remain essentially unchanged with doping despite crossing a topological transition in the Fermi surface. This indicates that the spectra contain little or no direct coupling to electronic excitations near the Fermi surface, rather they are dominated by the resonant cross section for phonons and charge-density-wave-induced phonon softening. We interpret our results in terms of a charge-density wave that is generated by strong correlations and a phonon response that is driven by the charge-density-wave-induced modification of the lattice.

High-temperature charge density wave correlations in La1.875Ba0.125CuO4 without spin-charge locking.

Although all superconducting cuprates display charge-ordering tendencies, their low-temperature properties are distinct, impeding efforts to understand the phenomena within a single conceptual framework. While some systems exhibit stripes of charge and spin, with a locked periodicity, others host charge density waves (CDWs) without any obviously related spin order. Here we use resonant inelastic X-ray scattering to follow the evolution of charge correlations in the canonical stripe-ordered cuprate La1.875Ba0.125CuO4 across its ordering transition. We find that high-temperature charge correlations are unlocked from the wavevector of the spin correlations, signaling analogies to CDW phases in various other cuprates. This indicates that stripe order at low temperatures is stabilized by the coupling of otherwise independent charge and spin density waves, with important implications for the relation between charge and spin correlations in the cuprates.

Direct Detection of Dimer Orbitals in Ba_{5}AlIr_{2}O_{11}.

The electronic states of many Mott insulators, including iridates, are often conceptualized in terms of localized atomic states such as the famous "J_{eff}=1/2 state." Although orbital hybridization can strongly modify such states and dramatically change the electronic properties of materials, probing this process is highly challenging. In this Letter, we directly detect and quantify the formation of dimer orbitals in an iridate material Ba_{5}AlIr_{2}O_{11} using resonant inelastic x-ray scattering. Sharp peaks corresponding to the excitations of dimer orbitals are observed and analyzed by a combination of density functional theory calculations and theoretical simulations based on an Ir-Ir cluster model. Such partially delocalized dimer states lead to a redefinition of the angular momentum of the electrons and changes in the magnetic and electronic behaviors of the material. We use this to explain the reduction of the observed magnetic moment with respect to predictions based on atomic states. This study opens new directions to study dimerization in a large family of materials, including solids, heterostructures, molecules, and transient states.

Phononic Helical Nodal Lines with PT Protection in MoB_{2}.

While condensed matter systems host both fermionic and bosonic quasiparticles, reliably predicting and empirically verifying topological states is only mature for Fermionic electronic structures, leaving topological Bosonic excitations sporadically explored. This is unfortunate, as Bosonic systems such as phonons offer the opportunity to assess spinless band structures where nodal lines can be realized without invoking special additional symetries to protect against spin-orbit coupling. Here we combine first-principles calculations and meV-resolution inelastic x-ray scattering to demonstrate the first realization of parity-time reversal symmetry protected helical nodal lines in the phonon spectrum of MoB_{2}. This structure is unique to phononic systems as the spin-orbit coupling present in electronic systems tends to lift the degeneracy away from high-symmetry locations. Our study establishes a protocol to accurately identify topological Bosonic excitations, opening a new route to explore exotic topological states in crystalline materials.

Ultrafast dynamics of spin and orbital correlations in quantum materials: an energy- and momentum-resolved perspective.

Many remarkable properties of quantum materials emerge from states with intricate coupling between the charge, spin and orbital degrees of freedom. Ultrafast photo-excitation of these materials holds great promise for understanding and controlling the properties of these states. Here, we introduce time-resolved resonant inelastic X-ray scattering (tr-RIXS) as a means of measuring the charge, spin and orbital excitations out of equilibrium. These excitations encode the correlations and interactions that determine the detailed properties of the states generated. After outlining the basic principles and instrumentations of tr-RIXS, we review our first observations of transient antiferromagnetic correlations in quasi two dimensions in a photo-excited Mott insulator and present possible future routes of this fast-developing technique. The increasing number of X-ray free electron laser facilities not only enables tackling long-standing fundamental scientific problems, but also promises to unleash novel inelastic X-ray scattering spectroscopies. This article is part of the theme issue 'Measurement of ultrafast electronic and structural dynamics with X-rays'.

Observation of Double Weyl Phonons in Parity-Breaking FeSi.

Condensed matter systems have now become a fertile ground to discover emerging topological quasiparticles with symmetry protected modes. While many studies have focused on fermionic excitations, the same conceptual framework can also be applied to bosons yielding new types of topological states. Motivated by Zhang et al.'s recent theoretical prediction of double Weyl phonons in transition metal monosilicides [Phys. Rev. Lett. 120, 016401 (2018)PRLTAO0031-900710.1103/PhysRevLett.120.016401], we directly measure the phonon dispersion in parity-breaking FeSi using inelastic x-ray scattering. By comparing the experimental data with theoretical calculations, we make the first observation of double Weyl points in FeSi, which will be an ideal material to explore emerging bosonic excitations and its topologically nontrivial properties.

Decoupling Carrier Concentration and Electron-Phonon Coupling in Oxide Heterostructures Observed with Resonant Inelastic X-Ray Scattering.

We report the observation of multiple phonon satellite features in ultrathin superlattices of the form nSrIrO_{3}/mSrTiO_{3} using resonant inelastic x-ray scattering (RIXS). As the values of n and m vary, the energy loss spectra show a systematic evolution in the relative intensity of the phonon satellites. Using a closed-form solution for the RIXS cross section, we extract the variation in the electron-phonon coupling strength as a function of n and m. Combined with the negligible carrier doping into the SrTiO_{3} layers, these results indicate that the tuning of the electron-phonon coupling can be effectively decoupled from doping. This work both showcases a feasible method to extract the electron-phonon coupling in superlattices and unveils a potential route for tuning this coupling, which is often associated with superconductivity in SrTiO_{3}-based systems.

Ultrafast energy- and momentum-resolved dynamics of magnetic correlations in the photo-doped Mott insulator Sr2IrO4.

Measuring how the magnetic correlations evolve in doped Mott insulators has greatly improved our understanding of the pseudogap, non-Fermi liquids and high-temperature superconductivity. Recently, photo-excitation has been used to induce similarly exotic states transiently. However, the lack of available probes of magnetic correlations in the time domain hinders our understanding of these photo-induced states and how they could be controlled. Here, we implement magnetic resonant inelastic X-ray scattering at a free-electron laser to directly determine the magnetic dynamics after photo-doping the Mott insulator Sr2IrO4. We find that the non-equilibrium state, 2 ps after the excitation, exhibits strongly suppressed long-range magnetic order, but hosts photo-carriers that induce strong, non-thermal magnetic correlations. These two-dimensional (2D) in-plane Néel correlations recover within a few picoseconds, whereas the three-dimensional (3D) long-range magnetic order restores on a fluence-dependent timescale of a few hundred picoseconds. The marked difference in these two timescales implies that the dimensionality of magnetic correlations is vital for our understanding of ultrafast magnetic dynamics.

Two-Dimensional J_{eff}=1/2 Antiferromagnetic Insulator Unraveled from Interlayer Exchange Coupling in Artificial Perovskite Iridate Superlattices.

We report an experimental investigation of the two-dimensional J_{eff}=1/2 antiferromagnetic Mott insulator by varying the interlayer exchange coupling in [(SrIrO_{3})_{1}, (SrTiO_{3})_{m}] (m=1, 2 and 3) superlattices. Although all samples exhibited an insulating ground state with long-range magnetic order, temperature-dependent resistivity measurements showed a stronger insulating behavior in the m=2 and m=3 samples than the m=1 sample which displayed a clear kink at the magnetic transition. This difference indicates that the blocking effect of the excessive SrTiO_{3} layer enhances the effective electron-electron correlation and strengthens the Mott phase. The significant reduction of the Néel temperature from 150 K for m=1 to 40 K for m=2 demonstrates that the long-range order stability in the former is boosted by a substantial interlayer exchange coupling. Resonant x-ray magnetic scattering revealed that the interlayer exchange coupling has a switchable sign, depending on the SrTiO_{3} layer number m, for maintaining canting-induced weak ferromagnetism. The nearly unaltered transition temperature between the m=2 and the m=3 demonstrated that we have realized a two-dimensional antiferromagnet at finite temperatures with diminishing interlayer exchange coupling.

Doping Dependence of Collective Spin and Orbital Excitations in the Spin-1 Quantum Antiferromagnet La_{2-x}Sr_{x}NiO_{4} Observed by X Rays.

We report the first empirical demonstration that resonant inelastic x-ray scattering (RIXS) is sensitive to 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 ultrafast pump-probe experiments.

Remarkable Stability of Charge Density Wave Order in La_{1.875}Ba_{0.125}CuO_{4}.

The occurrence of charge-density-wave (CDW) order in underdoped cuprates is now well established, although the precise nature of the CDW and its relationship with superconductivity is not. Theoretical proposals include contrasting ideas such as that pairing may be driven by CDW fluctuations or that static CDWs may intertwine with a spatially modulated superconducting wave function. We test the dynamics of CDW order in La_{1.825}Ba_{0.125}CuO_{4} by using x-ray photon correlation spectroscopy at the CDW wave vector, detected resonantly at the Cu L_{3} edge. We find that the CDW domains are strikingly static, with no evidence of significant fluctuations up to 2 ¾ h. We discuss the implications of these results for some of the competing theories.

Orbital Engineering in Nickelate Heterostructures Driven by Anisotropic Oxygen Hybridization rather than Orbital Energy Levels.

Resonant inelastic x-ray scattering is used to investigate the electronic origin of orbital polarization in nickelate heterostructures taking LaTiO_{3}-LaNiO_{3}-3×(LaAlO_{3}), a system with exceptionally large polarization, as a model system. We find that heterostructuring generates only minor changes in the Ni 3d orbital energy levels, contradicting the often-invoked picture in which changes in orbital energy levels generate orbital polarization. Instead, O K-edge x-ray absorption spectroscopy demonstrates that orbital polarization is caused by an anisotropic reconstruction of the oxygen ligand hole states. This provides an explanation for the limited success of theoretical predictions based on tuning orbital energy levels and implies that future theories should focus on anisotropic hybridization as the most effective means to drive large changes in electronic structure and realize novel emergent phenomena.

First-Order Melting of a Weak Spin-Orbit Mott Insulator into a Correlated Metal.

The electronic phase diagram of the weak spin-orbit Mott insulator (Sr(1-x)La(x))(3)Ir(2)O(7) is determined via an exhaustive experimental study. Upon doping electrons via La substitution, an immediate collapse in resistivity occurs along with a narrow regime of nanoscale phase separation comprised of antiferromagnetic, insulating regions and paramagnetic, metallic puddles persisting until x≈0.04. Continued electron doping results in an abrupt, first-order phase boundary where the Néel state is suppressed and a homogenous, correlated, metallic state appears with an enhanced spin susceptibility and local moments. As the metallic state is stabilized, a weak structural distortion develops and suggests a competing instability with the parent spin-orbit Mott state.

Persistence of magnetic excitations in La(2-x)Sr(x)CuO4 from the undoped insulator to the heavily overdoped non-superconducting metal.

One of the most intensely studied scenarios of high-temperature superconductivity (HTS) postulates pairing by exchange of magnetic excitations. Indeed, such excitations have been observed up to optimal doping in the cuprates. In the heavily overdoped regime, neutron scattering measurements indicate that magnetic excitations have effectively disappeared, and this has been argued to cause the demise of HTS with overdoping. Here we use resonant inelastic X-ray scattering, which is sensitive to complementary parts of reciprocal space, to measure the evolution of the magnetic excitations in La(2-x)Sr(x)CuO4 across the entire phase diagram, from a strongly correlated insulator (x = 0) to a non-superconducting metal (x = 0.40). For x = 0, well-defined magnon excitations are observed. These magnons broaden with doping, but they persist with a similar dispersion and comparable intensity all the way to the non-superconducting, heavily overdoped metallic phase. The destruction of HTS with overdoping is therefore caused neither by the general disappearance nor by the overall softening of magnetic excitations. Other factors, such as the redistribution of spectral weight, must be considered.

Magnetically propagating Hund's exciton in van der Waals antiferromagnet NiPS3.

Magnetic van der Waals (vdW) materials have opened new frontiers for realizing novel many-body phenomena. Recently NiPS3 has received intense interest since it hosts an excitonic quasiparticle whose properties appear to be intimately linked to the magnetic state of the lattice. Despite extensive studies, the electronic character, mobility, and magnetic interactions of the exciton remain unresolved. Here we address these issues by measuring NiPS3 with ultra-high energy resolution resonant inelastic x-ray scattering (RIXS). We find that Hund's exchange interactions are primarily responsible for the energy of formation of the exciton. Measuring the dispersion of the Hund's exciton reveals that it propagates in a way that is analogous to a double-magnon. We trace this unique behavior to fundamental similarities between the NiPS3 exciton hopping and spin exchange processes, underlining the unique magnetic characteristics of this novel quasiparticle.

Spin excitations in a single La2CuO4 layer.

Cuprates and other high-temperature superconductors consist of two-dimensional layers that are crucial to their properties. The dynamics of the quantum spins in these layers lie at the heart of the mystery of the cuprates. In bulk cuprates such as La(2)CuO(4), the presence of a weak coupling between the two-dimensional layers stabilizes a three-dimensional magnetic order up to high temperatures. In a truly two-dimensional system however, thermal spin fluctuations melt long-range order at any finite temperature. Here, we measure the spin response of isolated layers of La(2)CuO(4) that are only one-unit-cell-thick. We show that coherent magnetic excitations, magnons, known from the bulk order, persist even in a single layer of La(2)CuO(4), with no evidence for more complex correlations such as resonating valence bond correlations. These magnons are, therefore, well described by spin-wave theory (SWT). On the other hand, we also observe a high-energy magnetic continuum in the isotropic magnetic response that is not well described by two-magnon SWT, or indeed any existing theories.