Krzysztof Wohlfeld

Spin-orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3

When viewed as an elementary particle, the electron has spin and charge. When binding to the atomic nucleus, it also acquires an angular momentum quantum number corresponding to the quantized atomic orbital it occupies. 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. The hallmark of one-dimensional physics is a breaking up of the elementary electron into its separate degrees of freedom. The separation of the electron into independent quasi-particles that carry either spin (spinons) or charge (holons) was first observed fifteen years ago. Here we report observation of the separation of the orbital degree of freedom (orbiton) using resonant inelastic X-ray scattering on the one-dimensional Mott insulator Sr2CuO3. We resolve an orbiton separating itself from spinons and propagating through the lattice as a distinct quasi-particle with a substantial dispersion in energy over momentum, of about 0.2 electronvolts, over nearly one Brillouin zone.

Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering

How coherent quasiparticles emerge by doping quantum antiferromagnets is a key question in correlated electron systems, whose resolution is needed to elucidate the phase diagram of copper oxides. Recent resonant inelastic X-ray scattering (RIXS) experiments in hole-doped cuprates have purported to measure high-energy collective spin excitations that persist well into the overdoped regime and bear a striking resemblance to those found in the parent compound, challenging the perception that spin excitations should weaken with doping and have a diminishing effect on superconductivity. Here we show that RIXS at the Cu L3-edge indeed provides access to the spin dynamical structure factor once one considers the full influence of light polarization. Further we demonstrate that high-energy spin excitations do not correlate with the doping dependence of Tc, while low-energy excitations depend sensitively on doping and show ferromagnetic correlations. This suggests that high-energy spin excitations are marginal to pairing in cuprate superconductors.

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.

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.

Orbitally induced string formation in the spin-orbital polarons

We study the spectral function of a single hole doped into the ab plane of the Mott insulator LaVO3, with antiferromagnetic (AF) spin order of S = 1 spins accompanied by alternating orbital (AO) order of active {dyz,dzx} orbitals. Starting from the respective t-J model, with spin-orbital superexchange and effective three-site hopping terms, we derive the polaron Hamiltonian and show that a hole couples simultaneously to the collective excitations of the AF/AO phase, magnons and orbitons. Next, we solve this polaron problem using the self-consistent Born approximation and find a stable quasiparticle solution — a spin-orbital polaron. We show that the spin-orbital polaron resembles the orbital polaron found in eg systems, as e.g. in K2CuF4 or (to some extent) in LaMnO3, and that the hole may be seen as confined in a string-like potential. However, the spins also play a crucial role in the formation of this polaron — we explain how the orbital degrees of freedom: (i) confine the spin dynamics acting on the hole as the classical Ising spins, and (ii) generate the string potential which is of the joint spin-orbital character. Finally, we discuss the impact of the results presented here on the understanding of the phase diagrams of the lightly doped cubic vanadates.

Phase diagram and spin correlations of the Kitaev-Heisenberg model: Importance of quantum effects

We explore the phase diagram of the Kitaev-Heisenberg model with nearest neighbor interactions on the honeycomb lattice using the exact diagonalization of finite systems combined with the cluster mean field approximation, and supplemented by the insights from analytic approaches: the linear spin-wave and second-order perturbation theories. This study confirms that by varying the balance between the Heisenberg and Kitaev term, frustrated exchange interactions stabilize in this model either one of four phases with magnetic long range order: Neel phase, ferromagnetic phase, and two other phases with coexisting antiferromagnetic and ferromagnetic bonds, zigzag and stripy phase, or one of two distinct spin-liquid phases. Out of these latter disordered phases, the one with ferromagnetic Kitaev interactions has a substantially broader range of stability as the neighboring competing ordered phases, ferromagnetic and stripy, have very weak quantum fluctuations. Focusing on the quantum spin-liquid phases, we study spatial spin correlations and dynamic spin structure factor of the model by the exact diagonalization technique, and discuss the evolution of gapped low-energy spin response across the quantum phase transitions between the disordered spin liquid and phases with long range magnetic order.

Raman and fluorescence characteristics of resonant inelastic X-ray scattering from doped superconducting cuprates

Measurements of spin excitations are essential for an understanding of spin-mediated pairing for superconductivity; and resonant inelastic X-ray scattering (RIXS) provides a considerable opportunity to probe high-energy spin excitations. However, whether RIXS correctly measures the collective spin excitations of doped superconducting cuprates remains under debate. Here we demonstrate distinct Raman- and fluorescence-like RIXS excitations of Bi1.5Pb0.6Sr1.54CaCu2O8+δ. Combining photon-energy and momentum dependent RIXS measurements with theoretical calculations using exact diagonalization provides conclusive evidence that the Raman-like RIXS excitations correspond to collective spin excitations, which are magnons in the undoped Mott insulators and evolve into paramagnons in doped superconducting compounds. In contrast, the fluorescence-like shifts are due primarily to the continuum of particle-hole excitations in the charge channel. Our results show that under the proper experimental conditions RIXS indeed can be used to probe paramagnons in doped high-Tc cuprate superconductors.

Using RIXS to uncover elementary charge and spin excitations

Despite significant progress in resonant inelastic x-ray scattering (RIXS) experiments on cuprates at the Cu L-edge, a theoretical understanding of the cross-section remains incomplete in terms of elementary excitations and the connection to both charge and spin structure factors. Here we use state-of-the-art, unbiased numerical calculations to study the low energy excitations probed by RIXS in undoped and doped Hubbard model relevant to the cuprates. The results highlight the importance of scattering geometry, in particular both the incident and scattered x-ray photon polarization, and demonstrate that on a qualitative level the RIXS spectral shape in the cross-polarized channel approximates that of the spin dynamical structure factor. However, in the parallel-polarized channel the complexity of the RIXS process beyond a simple two-particle response complicates the analysis, and demonstrates that approximations and expansions which attempt to relate RIXS to less complex correlation functions can not reproduce the full diversity of RIXS spectral features.

Orbital superexchange and crystal field simultaneously at play in YVO3: resonant inelastic x-ray scattering at the V L edge and the O K edge

We report on the observation of orbital excitations in YVO3 by means of resonant inelastic x-ray scattering (RIXS) at energies across the vanadium L-3 and oxygen K absorption edges. At the V L3 edge, we are able to resolve the full spectrum of orbital excitations up to 5 eV. In order to unravel the effect of superexchange interactions and the crystal field on the orbital excitations, we analyzed the energy and temperature dependence of the intra-t(2g) excitations at 0.1-0.2 eV in detail. While these results suggest a dominant influence of the crystal field, peak shifts of about 13-20 meV observed as a function of the transferred momentum q parallel to a reflect a finite dispersion of the orbital excitations. This is puzzling since theoretical models based on superexchange interactions predict a dispersion only for q parallel to c. Furthermore, we demonstrate that RIXS at the O K edge is very sensitive to intersite excitations. At the O K edge, we observe excitations across the Mott-Hubbard gap and an additional feature at 0.4 eV, which we attribute to two-orbiton scattering, i.e., an exchange of orbitals between adjacent sites. Altogether, our results indicate that both superexchange interactions and the crystal field are important for a quantitative understanding of the orbital excitations in YVO3.

Microscopic origin of spin-orbital separation in Sr2CuO3

Recently performed resonant inelastic x-ray scattering experiment (RIXS) at the copper L3 edge in the quasi-1D Mott insulator Sr2CuO3 has revealed a significant dispersion of a single orbital excitation (orbiton). This large and unexpected orbiton dispersion has been explained using the concept of spin-orbital fractionalization in which orbiton, which is intrinsically coupled to the spinon in this material, liberates itself from the spinon due to the strictly 1D nature of its motion. Here we investigate this mechanism in detail by: (i) deriving the microscopic spin-orbital superexchange model from the charge transfer model for the CuO3 chains in Sr2CuO3, (ii) mapping the orbiton motion in the obtained spin-orbital model into a problem of a single hole moving in an effective half-filled antiferromagnetic chain t-J model, and (iii) solving the latter model using the exact diagonalization and obtaining the orbiton spectral function. Finally, the RIXS cross section is calculated based on the obtained orbiton spectral function and compared with the RIXS experiment.