Collective Nature of Orbital Excitations in Layered Cuprates in the Absence of Apical Oxygens.

We have investigated the 3d orbital excitations in CaCuO_{2} (CCO), Nd_{2}CuO_{4} (NCO), and La_{2}CuO_{4} (LCO) using high-resolution resonant inelastic x-ray scattering. In LCO they behave as well-localized excitations, similarly to several other cuprates. On the contrary, in CCO and NCO the d_{xy} orbital clearly disperses, pointing to a collective character of this excitation (orbiton) in compounds without apical oxygen. We ascribe the origin of the dispersion as stemming from a substantial next-nearest-neighbor (NNN) orbital superexchange. Such an exchange leads to the liberation of the orbiton from its coupling to magnons, which is associated with the orbiton hopping between nearest neighbor copper sites. Finally, we show that the exceptionally large NNN orbital superexchange can be traced back to the absence of apical oxygens suppressing the charge transfer energy.

Strain engineering of the charge and spin-orbital interactions in Sr2IrO4.

In the high spin-orbit-coupled Sr2IrO4, the high sensitivity of the ground state to the details of the local lattice structure shows a large potential for the manipulation of the functional properties by inducing local lattice distortions. We use epitaxial strain to modify the Ir-O bond geometry in Sr2IrO4 and perform momentum-dependent resonant inelastic X-ray scattering (RIXS) at the metal and at the ligand sites to unveil the response of the low-energy elementary excitations. We observe that the pseudospin-wave dispersion for tensile-strained Sr2IrO4 films displays large softening along the [h,0] direction, while along the [h,h] direction it shows hardening. This evolution reveals a renormalization of the magnetic interactions caused by a strain-driven cross-over from anisotropic to isotropic interactions between the magnetic moments. Moreover, we detect dispersive electron-hole pair excitations which shift to lower (higher) energies upon compressive (tensile) strain, manifesting a reduction (increase) in the size of the charge gap. This behavior shows an intimate coupling between charge excitations and lattice distortions in Sr2IrO4, originating from the modified hopping elements between the t2g orbitals. Our work highlights the central role played by the lattice degrees of freedom in determining both the pseudospin and charge excitations of Sr2IrO4 and provides valuable information toward the control of the ground state of complex oxides in the presence of high spin-orbit coupling.

Silver route to cuprate analogs.

The parent compound of high-[Formula: see text] superconducting cuprates is a unique Mott insulator consisting of layers of spin-[Formula: see text] ions forming a square lattice and with a record high in-plane antiferromagnetic coupling. Compounds with similar characteristics have long been searched for without success. Here, we use a combination of experimental and theoretical tools to show that commercial [Formula: see text] is an excellent cuprate analog with remarkably similar electronic parameters to [Formula: see text] but larger buckling of planes. Two-magnon Raman scattering and inelastic neutron scattering reveal a superexchange constant reaching 70% of that of a typical cuprate. We argue that structures that reduce or eliminate the buckling of the [Formula: see text] planes could have an antiferromagnetic coupling that matches or surpasses the cuprates.

Unraveling the Orbital Physics in a Canonical Orbital System KCuF_{3}.

We explore the existence of the collective orbital excitations, orbitons, in the canonical orbital system KCuF_{3} using the Cu L_{3}-edge resonant inelastic x-ray scattering. We show that the nondispersive high-energy peaks result from the Cu^{2+} dd orbital excitations. These high-energy modes display good agreement with the ab initio quantum chemistry calculation, indicating that the dd excitations are highly localized. At the same time, the low-energy excitations present clear dispersion. They match extremely well with the two-spinon continuum following the comparison with Müller ansatz calculations. The localized dd excitations and the observation of the strongly dispersive magnetic excitations suggest that the orbiton dispersion is below the resolution detection limit. Our results can reconcile with the strong local Jahn-Teller effect in KCuF_{3}, which predominantly drives orbital ordering.

Jahn-Teller Effect in Systems with Strong On-Site Spin-Orbit Coupling.

When strong spin-orbit coupling removes orbital degeneracy, it would at the same time appear to render the Jahn-Teller mechanism ineffective. We discuss such a situation, the t_{2g} manifold of iridates, and show that, while the Jahn-Teller effect does indeed not affect the j_{eff}=1/2 antiferromagnetically ordered ground state, it leads to distinctive signatures in the j_{eff}=3/2 spin-orbit exciton. It allows for a hopping of the spin-orbit exciton between the nearest-neighbor sites without producing defects in the j_{eff}=1/2 antiferromagnet. This arises because the lattice-driven Jahn-Teller mechanism only couples to the orbital degree of freedom but is not sensitive to the phase of the wave function that defines isospin j_{z}. This contrasts sharply with purely electronic propagation, which conserves isospin, and the presence of Jahn-Teller coupling can explain some of the peculiar features of measured resonant inelastic x-ray scattering spectra of Sr_{2}IrO_{4}.

Orbital control of effective dimensionality: from spin-orbital fractionalization to confinement in the anisotropic ladder system CaCu(2)O(3).

Fractionalization of an electronic quasiparticle into spin, charge, and orbital parts is a fundamental and characteristic property of interacting electrons in one dimension. However, real materials are never strictly one dimensional and the fractionalization phenomena are hard to observe. Here we studied the spin and orbital excitations of the anisotropic ladder material CaCu_{2}O_{3}, whose electronic structure is not one dimensional. Combining high-resolution resonant inelastic x-ray scattering experiments with theoretical model calculations, we show that (i) spin-orbital fractionalization occurs in CaCu_{2}O_{3} along the leg direction x through the xz orbital channel as in a 1D system, and (ii) no fractionalization is observed for the xy orbital, which extends in both leg and rung direction, contrary to a 1D system. We conclude that the directional character of the orbital hopping can select different degrees of dimensionality. Using additional model calculations, we show that spin-orbital separation is generally far more robust than the spin-charge separation. This is not only due to the already mentioned selection realized by the orbital hopping, but also due to the fact that spinons are faster than the orbitons.

Resonant inelastic x-ray scattering as a probe of the phase and excitations of the order parameter of superconductors.

The capability to probe the dispersion of elementary spin, charge, orbital, and lattice excitations has positioned resonant inelastic x-ray scattering (RIXS) at the forefront of photon science. Here we develop the scattering theory for RIXS on superconductors, calculating its momentum-dependent scattering amplitude. Considering superconductors with different pairing symmetries, we show that the low-energy scattering is strongly affected by the superconducting gap and coherence factors. This establishes RIXS as a tool to disentangle pairing symmetries and to probe the elementary excitations of unconventional superconductors.

Unraveling orbital correlations with magnetic resonant inelastic x-ray scattering.

Although orbital degrees of freedom are a factor of fundamental importance in strongly correlated transition-metal compounds, orbital correlations and dynamics remain very difficult to access, in particular by neutron scattering. Via a direct calculation of scattering amplitudes we show that instead magnetic resonant inelastic x-ray scattering (RIXS) does reveal orbital correlations. In contrast to neutron scattering, the intensity of the magnetic excitations in RIXS depends very sensitively on the symmetry of the orbitals that spins occupy and on photon polarizations. We show in detail how this effect allows magnetic RIXS to distinguish between alternating orbital-ordered and ferro-orbital (or orbital liquid) states.

Limited Ferromagnetic Interactions in Monolayers of MPS3 (M = Mn and Ni).

We present a systematic study of the electronic and magnetic properties of two-dimensional ordered alloys, consisting of two representative hosts (MnPS3 and NiPS3) of transition metal phosphorus trichalcogenides doped with 3d elements. For both hosts, our DFT + U calculations are able to qualitatively reproduce the ratios and signs of all experimentally observed magnetic couplings. The relative strength of all antiferromagnetic exchange couplings, both in MnPS3 and in NiPS3, can successfully be explained using an effective direct exchange model: it reveals that the third-neighbor exchange dominates in NiPS3 due to the filling of the t2g subshell, whereas for MnPS3, the first-neighbor exchange prevails, owing to the presence of the t2g magnetism. On the other hand, the nearest neighbor ferromagnetic coupling in NiPS3 can only be explained using a more complex superexchange model and is (also) largely triggered by the absence of the t2g magnetism. For the doped systems, the DFT + U calculations revealed that magnetic impurities do not affect the magnetic ordering observed in the pure phases, and thus, in general in these systems, ferromagnetism may not be easily induced by such a kind of elemental doping. However, unlike for the hosts, the first and second (dopant-host) exchange couplings are of similar order of magnitude. This leads to frustration in the case of antiferromagnetic coupling and may be one of the reasons of the observed lower magnetic ordering temperature of the doped systems.

Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators.

We show how the general and basic asymmetry between two fundamental degrees of freedom present in strongly correlated oxides, spin and orbital, has very profound repercussions on the elementary spin and orbital excitations. Whereas the magnons remain largely unaffected, orbitons become inherently coupled with spin fluctuations in spin-orbital models with antiferromagnetic and ferro-orbital ordered ground states. The composite orbiton-magnon modes that emerge fractionalize again in one dimension, giving rise to spin-orbital separation in the peculiar regime where spinons are faster than orbitons.

Correlation induced electron-hole asymmetry in quasi- two-dimensional iridates.

The resemblance of crystallographic and magnetic structures of the quasi-two-dimensional iridates Ba2IrO4 and Sr2IrO4 to La2CuO4 points at an analogy to cuprate high-Tc superconductors, even if spin-orbit coupling is very strong in iridates. Here we examine this analogy for the motion of a charge (hole or electron) added to the antiferromagnetic ground state. We show that correlation effects render the hole and electron case in iridates very different. An added electron forms a spin polaron, similar to the cuprates, but the situation of a removed electron is far more complex. Many-body 5d 4 configurations form which can be singlet and triplet states of total angular momentum that strongly affect the hole motion. This not only has ramifications for the interpretation of (inverse-)photoemission experiments but also demonstrates that correlation physics renders electron- and hole-doped iridates fundamentally different.Some iridate compounds such as Sr2IrO4 have electronic and atomic structures similar to quasi-2D copper oxides, raising the prospect of high temperature superconductivity. Here, the authors show that there is significant electron-hole asymmetry in iridates, contrary to expectations from the cuprates.

Absence of hole confinement in transition-metal oxides with orbital degeneracy.

We investigate the spectral properties of a hole moving in a two-dimensional Hubbard model for strongly correlated t(2g) electrons. Although superexchange interactions are Ising-like, a quasi-one-dimensional coherent hole motion arises due to effective three-site terms. This mechanism is fundamentally different from the hole motion via quantum fluctuations in the conventional spin model with SU(2) symmetry. The orbital model describes also propagation of a hole in some e(g) compounds, and we argue that orbital degeneracy alone does not lead to hole self-localization.