Spin-Orbit Excitons in a Correlated Metal: Raman Scattering Study of Sr_{2}RhO_{4}.

Using Raman spectroscopy to study the correlated 4d-electron metal Sr_{2}RhO_{4}, we observe pronounced excitations at 220 meV and 240 meV with A_{1g} and B_{1g} symmetries, respectively. We identify them as transitions between the spin-orbit multiplets of the Rh ions, in close analogy to the spin-orbit excitons in the Mott insulators Sr_{2}IrO_{4} and α-RuCl_{3}. This observation provides direct evidence for the unquenched spin-orbit coupling in Sr_{2}RhO_{4}. A quantitative analysis of the data reveals that the tetragonal crystal field Δ in Sr_{2}RhO_{4} has a sign opposite to that in insulating Sr_{2}IrO_{4}, which enhances the planar xy orbital character of the effective J=1/2 wave function. This supports a metallic ground state, and suggests that c-axis compression of Sr_{2}RhO_{4} may transform it into a quasi-two-dimensional antiferromagnetic insulator.

Giant stress response of terahertz magnons in a spin-orbit Mott insulator.

Magnonic devices operating at terahertz frequencies offer intriguing prospects for high-speed electronics with minimal energy dissipation However, guiding and manipulating terahertz magnons via external parameters present formidable challenges. Here we report the results of magnetic Raman scattering experiments on the antiferromagnetic spin-orbit Mott insulator Sr2IrO4 under uniaxial stress. We find that the energies of zone-center magnons are extremely stress sensitive: lattice strain of 0.1% increases the magnon energy by 40%. The magnon response is symmetric with respect to the sign of the applied stress (tensile or compressive), but depends strongly on its direction in the IrO2 planes. A theory based on coupling of the spin-orbit-entangled iridium magnetic moments to lattice distortions provides a quantitative explanation of the Raman data and a comprehensive framework for the description of magnon-lattice interactions in magnets with strong spin-orbit coupling. The possibility to efficiently manipulate the propagation of terahertz magnons via external stress opens up multifold design options for reconfigurable magnonic devices.

Kitaev Spin Liquid in 3d Transition Metal Compounds.

We study the exchange interactions and resulting magnetic phases in the honeycomb cobaltates. For a broad range of trigonal crystal fields acting on Co^{2+} ions, the low-energy pseudospin-1/2 Hamiltonian is dominated by bond-dependent Ising couplings that constitute the Kitaev model. The non-Kitaev terms nearly vanish at small values of trigonal field Δ, resulting in spin liquid ground state. Considering Na_{3}Co_{2}SbO_{6} as an example, we find that this compound is proximate to a Kitaev spin liquid phase, and can be driven into it by slightly reducing Δ by ∼20 meV, e.g., via strain or pressure control. We argue that, due to the more localized nature of the magnetic electrons in 3d compounds, cobaltates offer the most promising search area for Kitaev model physics.

Nontrivial Triplon Topology and Triplon Liquid in Kitaev-Heisenberg-type Excitonic Magnets.

The combination of strong spin-orbit coupling and correlations, e.g., in ruthenates and iridates, has been proposed as a means to realize quantum materials with nontrivial topological properties. We discuss here Mott insulators where on-site spin-orbit coupling favors a local J_{tot}=0 singlet ground state. We investigate excitations into a low-lying triplet, triplons, and find them to acquire nontrivial band topology in a magnetic field. We also comment on magnetic states resulting from triplon condensation, where we find, in addition to the same ordered phases known from the J_{tot}=1/2 Kitaev-Heisenberg model, a triplon liquid taking the parameter space of Kitaev's spin liquid.

Pseudo-Jahn-Teller Effect and Magnetoelastic Coupling in Spin-Orbit Mott Insulators.

The consequences of the Jahn-Teller (JT) orbital-lattice coupling for magnetism of pseudospin J_{eff}=1/2 and J_{eff}=0 compounds are addressed. In the former case, represented by Sr_{2}IrO_{4}, this coupling generates, through the so-called pseudo-JT effect, orthorhombic deformations of a crystal concomitant with magnetic ordering. The orthorhombicity axis is tied to the magnetization and rotates with it under magnetic field. The theory resolves a number of puzzles in Sr_{2}IrO_{4} such as the origin of in-plane magnetic anisotropy and magnon gaps, metamagnetic transition, etc. In J_{eff}=0 systems, the pseudo-JT effect leads to spin-nematic transition well above magnetic ordering, which may explain the origin of "orbital order" in Ca_{2}RuO_{4}.

Raman Scattering from Higgs Mode Oscillations in the Two-Dimensional Antiferromagnet Ca_{2}RuO_{4}.

We present and analyze Raman spectra of the Mott insulator Ca_{2}RuO_{4}, whose quasi-two-dimensional antiferromagnetic order has been described as a condensate of low-lying spin-orbit excitons with angular momentum J_{eff}=1. In the A_{g} polarization geometry, the amplitude (Higgs) mode of the spin-orbit condensate is directly probed in the scalar channel, thus avoiding infrared-singular magnon contributions. In the B_{1g} geometry, we observe a single-magnon peak as well as two-magnon and two-Higgs excitations. Model calculations using exact diagonalization quantitatively agree with the observations. Together with recent neutron scattering data, our study provides strong evidence for excitonic magnetism in Ca_{2}RuO_{4} and points out new perspectives for research on the Higgs mode in two dimensions.

Doping-Induced Ferromagnetism and Possible Triplet Pairing in d(4) Mott Insulators.

We study the effects of electron doping in Mott insulators containing d(4) ions such as Ru(4+), Os(4+), Rh(5+), and Ir(5+) with J=0 singlet ground state. Depending on the strength of the spin-orbit coupling, the undoped systems are either nonmagnetic or host an unusual, excitonic magnetism arising from a condensation of the excited J=1 triplet states of t(2g)(4). We find that the interaction between J excitons and doped carriers strongly supports ferromagnetism, converting both the nonmagnetic and antiferromagnetic phases of the parent insulator into a ferromagnetic metal, and further to a nonmagnetic metal. Close to the ferromagnetic phase, the low-energy spin response is dominated by intense paramagnon excitations that may act as mediators of a triplet pairing.

Excitonic magnetism in Van Vleck-type d4 Mott insulators.

In Mott insulators with the t(2g)4 electronic configuration such as of Re3+, Ru4+, Os4+, and Ir5+ ions, spin-orbit coupling dictates a Van Vleck-type nonmagnetic ground state with an angular momentum J=0, and the magnetic response is governed by gapped singlet-triplet excitations. We derive the exchange interactions between these excitons and study their collective behavior on different lattices. In perovskites, a conventional Bose condensation of excitons into a magnetic state is found, while an unexpected one-dimensional behavior supporting spin-liquid states emerges in honeycomb lattices, due to the bond directional nature of exciton interactions in the case of 90° d-p-d bonding geometry.

Zigzag magnetic order in the iridium oxide Na2IrO3.

We explore the phase diagram of spin-orbit Mott insulators on a honeycomb lattice, within the Kitaev-Heisenberg model extended to its full parameter space. Zigzag-type magnetic order is found to occupy a large part of the phase diagram of the model, and its physical origin is explained as due to interorbital t(2g)-e(g) hopping. The magnetic susceptibility, spin wave spectra, and zigzag order parameter are calculated and compared to the experimental data, obtaining thereby the spin coupling constants in Na(2)IrO(3) and Li(2)IrO(3).

Spin-state crossover model for the magnetism of iron pnictides.

We propose a minimal model describing magnetic behavior of Fe-based superconductors. The key ingredient of the model is a dynamical mixing of quasidegenerate spin states of Fe(2+) ion by intersite electron hoppings, resulting in an effective local spin S(eff). The moments S(eff) tend to form singlet pairs and may condense into a spin nematic phase due to the emergent biquadratic exchange couplings. The long-range ordered part m of S(eff) varies widely, 0 ≤ m ≤ S(eff), but magnon spectra are universal and scale with S(eff), resolving the puzzle of large but fluctuating Fe moments. Unusual temperature dependences of a local moment and spin susceptibility are also explained.

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.

Kitaev-Heisenberg model on a honeycomb lattice: possible exotic phases in iridium oxides A2IrO3.

We derive and study a spin one-half Hamiltonian on a honeycomb lattice describing the exchange interactions between Ir4+ ions in a family of layered iridates A2IrO3 (A=Li,Na). Depending on the microscopic parameters, the Hamiltonian interpolates between the Heisenberg and exactly solvable Kitaev models. Exact diagonalization and a complementary spin-wave analysis reveal the presence of an extended spin-liquid phase near the Kitaev limit and a conventional Néel state close to the Heisenberg limit. The two phases are separated by an unusual stripy antiferromagnetic state, which is the exact ground state of the model at the midpoint between two limits.

Enhanced pairing correlations near oxygen dopants in cuprate superconductors.

Recent experiments on Bi-based cuprate superconductors have revealed an unexpected enhancement of the pairing correlations near the interstitial oxygen dopant ions. Here we propose a possible mechanism--based on local screening effects--by which the oxygen dopants do modify the electronic parameters within the CuO2 planes and strongly increase the superexchange coupling J. This enhances the spin pairing effects locally and may explain the observed spatial variations of the density of states and the pairing gap.

Magnetically hidden order of Kramers doublets in d;{1} systems: Sr2VO4.

We formulate and study an effective Hamiltonian for low-energy Kramers doublets of d;{1} ions on a square lattice. We find that the system exhibits a magnetically hidden order in which the expectation values of the local spin and orbital moments both vanish. The order parameter responsible for a time-reversal symmetry breaking has a composite nature and is a spin-orbital analog of a magnetic octupole. We argue that such a hidden order is realized in the layered perovskite Sr_{2}VO_{4}.

Origin of the spatial variation of the pairing gap in bi-based high temperature cuprate superconductors.

Recently, scanning tunneling microscopy on the Bi-2212 cuprate superconductor has revealed a spatial variation of the energy gap that is directly correlated with a modulation of the apical oxygen position. We identify two mechanisms by which out-of-plane oxygens can modulate the pairing interaction within the CuO2 layer: a covalency between the x2-y2 band and apical p orbital, and a screening of correlation U by apical oxygen polarization. Both effects strongly depend on the apical oxygen position, and their cooperative action explains the experiment.

Evolution of spin-orbital-lattice coupling in the RVO3 perovskites.

We introduce a microscopic model which unravels the physical mechanisms responsible for the observed phase diagram of the RVO3 perovskites. It reveals a nontrivial interplay between superexchange, the orbital-lattice coupling due to the GdFeO3-like rotations of the VO6 octahedra, and orthorhombic lattice distortions. We find that the lattice strain affects the onset of the magnetic and orbital order by partial suppression of orbital fluctuations. The present approach also provides a natural explanation of the observed reduction of magnon energies from LaVO3 to YVO3.

Orbital order and possible superconductivity in LaNiO3/LaMO3 superlattices.

A hypothetical layered oxide La2NiMO6 where NiO2 and MO2 planes alternate along the c axis of ABO3 perovskite lattice is considered theoretically. Here, M denotes a trivalent cation Al, Ga,... such that MO2 planes are insulating and suppress the c-axis charge transfer. We predict that correlated eg electrons in the NiO2 planes develop a planar x2-y2 orbital order driven by the reduced dimensionality and further supported by epitaxial strain from the substrate. Low-energy electronic states can be mapped to a single-band t - t' - J model, suggesting favorable conditions for high-Tc superconductivity.

Spin polaron theory for the photoemission spectra of layered cobaltates.

Recently, strong reduction of the quasiparticle peaks and pronounced incoherent structures have been observed in the photoemission spectra of layered cobaltates. Surprisingly, these many-body effects are found to increase near the band-insulator regime. We explain these unexpected observations in terms of a novel spin-polaron model for CoO2 planes, which is based on a fact of the spin-state quasidegeneracy of Co3+ ions in oxides. Scattering of the photoholes on spin-state fluctuations suppresses their coherent motion. The observed "peak-dip-hump" type line shapes are well reproduced by the theory.

Spin-orbital entanglement and violation of the Goodenough-Kanamori rules.

We point out that large composite spin-orbital fluctuations in Mott insulators with t(2g) orbital degeneracy are a manifestation of quantum entanglement of spin and orbital variables. This results in a dynamical nature of the spin superexchange interactions, which fluctuate over positive and negative values, and leads to an apparent violation of the Goodenough-Kanamori rules.

Dimerization versus orbital-moment ordering in a Mott insulator YVO3.

We use exact diagonalization combined with mean-field theory to investigate the phase diagram of the spin-orbital model for cubic vanadates. The spin-orbit coupling competes with Hund's exchange and triggers a novel phase, with the ordering of t(2g) orbital magnetic moments stabilized by the tilting of VO6 octahedra. It explains qualitatively spin canting and reduction of magnetization observed in YVO3. At finite temperature, an orbital instability in the C-type antiferromagnetic phase induces modulation of magnetic exchange constants even in the absence of lattice distortions. The calculated spin structure factor shows a magnon splitting at q-->=(0,0,pi / 2) due to the orbital dimerization.