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arXiv:2111.12514 · Physical review. B./Physical review. B

Ultrafast control of spin-orbital separation probed with time-resolved resonant inelastic x-ray scattering

Aaron Müller, Francesco Grandi, Martin Eckstein

Published Sep 15, 2022• 6 citations
arXivHTMLPDF

Abstract

Quasi-one-dimensional systems exhibit many-body effects elusive in higher dimensions. A prime example is spin-orbital separation, which has been measured by resonant inelastic x-ray scattering (RIXS) in ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$. Here, we theoretically analyze the time-resolved RIXS spectrum of ${\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}$ under the action of a time-dependent electric field. We show that the external field can reversibly modify the parameters in the effective $t\text{\ensuremath{-}}J$ model used to describe spinon and orbiton dynamics in the material. For strong driving amplitudes, we find that the spectrum changes qualitatively as a result of reversing the relative spinon to orbiton velocity. The analysis shows that in general, the spin-orbital dynamics in Mott insulators in combination with time-resolved RIXS should provide a suitable platform to explore the reversible control of many-body physics in the solid with strong laser fields.

DOI
10.1103/physrevb.106.l121107

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Quasi-one-dimensional systems exhibit many-body effects elusive in higher dimensions. A prime example is spin-orbital separation, which has been measured by resonant inelastic x-ray scattering (RIXS) in Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​. Here, we theoretically analyze the time-resolved RIXS spectrum of Sr2CuO3{\mathrm{Sr}}_{2}{\mathrm{CuO}}_{3}Sr2​CuO3​ under the action of a time-dependent electric field. We show that the external field can reversibly modify the parameters in the effective t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model used to describe spinon and orbiton dynamics in the material. For strong driving amplitudes, we find that the spectrum changes qualitatively as a result of reversing the relative spinon to orbiton velocity. The analysis shows that in general, the spin-orbital dynamics in Mott insulators in combination with time-resolved RIXS should provide a suitable platform to explore the reversible control of many-body physics in the solid with strong laser fields.
A recently performed resonant inelastic x-ray scattering experiment (RIXS) at the copper L3{L}_{3}L3​ edge in the quasi-one-dimensional Mott insulator Sr2{}_{2}2​CuO3{}_{3}3​ 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 the orbiton, which is intrinsically coupled to the spinon in this material, liberates itself from the spinon due to the strictly one-dimensional 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{}_{3}3​ chains in Sr2{}_{2}2​CuO3{}_{3}3​, (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 ttt-JJJ 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.
Resonant inelastic x-ray scattering (RIXS) at the oxygen K -edge has recently accessed multi-spinon excitations in the one-dimensional antiferromagnet (1D-AFM) Sr 2 CuO 3 , where four-spinon excitations are resolved separately from the two-spinon continuum. This technique, therefore, provides new opportunities to study fractionalized quasiparticle excitations in doped 1D-AFMs. To this end, we carried out exact diagonalization studies of the doped t – J model and provided predictions for oxygen K -edge RIXS experiments on doped 1D-AFMs. We show that the RIXS spectra are rich, containing distinct two- and four-spinon excitations, dispersive antiholon excitations, and combinations thereof. Our results highlight how RIXS complements inelastic neutron scattering experiments by accessing additional charge and spin components of fractionalized quasiparticles.
Abstract Resonant inelastic X-ray scattering (RIXS) detects various types of high- and low-energy elementary excitations in correlated solids, and this tool will play an increasingly important role in investigations of time-dependent phenomena in photo-excited systems. While theoretical frameworks for the computation of equilibrium RIXS spectra are well established, the development of appropriate methods for nonequilibrium simulations is an active research field. Here, we apply a recently developed nonequilibrium dynamical mean field theory (DMFT) based approach to compute the RIXS response of photo-excited two-orbital Mott insulators. The results demonstrate the feasibility of multi-orbital nonequilibrium RIXS calculations and the sensitivity of the quasi-elastic fluorescence-like features and excitation peaks on the nonequilibrium population of the Hubbard bands.
We consider the question of whether resonant inelastic x-ray scattering (RIXS) can be used to detect many-body excitations that are coupled to the spin-chirality terms ${\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}({\mathbf{S}}_{j}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{k})$ in a Mott insulator. We find that while the spin-chirality terms are in general absent in the usual experimental setups of RIXS, there are prospects of realizing such terms if one considers instead the scattering near a pre-edge. We then perform detailed analyses for the square and the kagome lattices, and brief analyses for the triangular and the honeycomb lattices, in which we show that the spin-chirality terms are indeed present in all the above lattices, but that they occur at a higher order in our expansion for the kagome and the honeycomb lattices. The merit of using RIXS in addition to Raman spectroscopy to detect excitations that are coupled to the spin-chirality terms is also briefly discussed in the context of the emergent gauge boson in the U(1)\text{U}(1)U(1) Dirac spin liquid.
We consider the question of whether resonant inelastic x-ray scattering (RIXS) can be used to detect many-body excitations that are coupled to the spin-chirality terms S[subscript i]·(S[subscript j]×S[subscript k]) in a Mott insulator. We find that while the spin-chirality terms are in general absent in the usual experimental setups of RIXS, there are prospects of realizing such terms if one considers instead the scattering near a pre-edge. We then perform detailed analyses for the square and the kagome lattices, and brief analyses for the triangular and the honeycomb lattices, in which we show that the spin-chirality terms are indeed present in all the above lattices, but that they occur at a higher order in our expansion for the kagome and the honeycomb lattices. The merit of using RIXS in addition to Raman spectroscopy to detect excitations that are coupled to the spin-chirality terms is also briefly discussed in the context of the emergent gauge boson in the U(1) Dirac spin liquid.
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.