Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1307.6180 · Physical Review B

Microscopic origin of spin-orbital separation in Sr 2 CuO 3

Krzysztof Wohlfeld, Satoshi Nishimoto, M. W. Haverkort, Jeroen van den Brink

Published Nov 20, 2013• 52 citations
arXivHTMLPDF

Abstract

A recently performed resonant inelastic x-ray scattering experiment (RIXS) at the copper ${L}_{3}$ edge in the quasi-one-dimensional Mott insulator Sr${}_{2}$CuO${}_{3}$ 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 CuO${}_{3}$ chains in Sr${}_{2}$CuO${}_{3}$, (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 $t$-$J$ 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.

DOI
10.1103/physrevb.88.195138

Related papers

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

Aaron Müller, Francesco Grandi, Martin Eckstein

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.

arXiv:2111.12514•Physical review. B./Physical review. B•Sep 15, 2022•6 citations

Multi-spinon and antiholon excitations probed by resonant inelastic x-ray scattering on doped one-dimensional antiferromagnets

Umesh Kumar, Alberto Nocera, Elbio R. Dagotto +1 more

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.

arXiv:1803.01955•New Journal of Physics•Jun 29, 2018•27 citations

Orbital Control of Effective Dimensionality: From Spin-Orbital Fractionalization to Confinement in the Anisotropic Ladder System CaCu2O3

Valentina Bisogni, Krzysztof Wohlfeld, Satoshi Nishimoto +11 more

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.

arXiv:1310.8346•Physical Review Letters•Mar 4, 2015•38 citations

Probing multi-spinon excitations outside of the two-spinon continuum in the antiferromagnetic spin chain cuprate Sr2CuO3

Justine Schlappa, U. Kumar, K. J. Zhou +8 more

Abstract One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and emergent phenomena. The spin-1/2 Heisenberg chain with antiferromagnetic nearest neighbour interactions is an important reference system; its elementary magnetic excitations are spin-1/2 quasiparticles called spinons that are created in even numbers. However, while the excitation continuum associated with two-spinon states is routinely observed, the study of four-spinon and higher multi-spinon states is an open area of research. Here we show that four-spinon excitations can be accessed directly in Sr2CuO3 using resonant inelastic x-ray scattering (RIXS) in a region of phase space clearly separated from the two-spinon continuum. Our finding is made possible by the fundamental differences in the correlation function probed by RIXS in comparison to other probes. This advance holds promise as a tool in the search for novel quantum states and quantum spin liquids.

arXiv:1802.09329•Nature Communications•Dec 13, 2018•72 citations

Collective Magnetic Excitations in the Spin Ladder Sr14Cu24O41 Measured Using High-Resolution Resonant Inelastic X-Ray Scattering

Justine Schlappa, Thorsten Schmitt, F. Vernay +13 more

We investigate magnetic excitations in the spin-ladder compound Sr_{14}Cu_{24}O_{41} using high-resolution Cu L_{3} edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as 100 +/- 30 meV. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.

arXiv:0901.1331•Physical Review Letters•Jul 21, 2009•111 citations

Spin and charge dynamics of doped one-dimensional Mott insulators

Takami Tohyama, Hiroki Maeda, Kenji Tsutsui +2 more

Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.

arXiv:2404.11412•Physical review. B./Physical review. B•Sep 3, 2024•2 citations
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.
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 $t\text{\ensuremath{-}}J$ 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.
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.
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.
Abstract One-dimensional (1D) magnetic insulators have attracted significant interest as a platform for studying quasiparticle fractionalization, quantum criticality, and emergent phenomena. The spin-1/2 Heisenberg chain with antiferromagnetic nearest neighbour interactions is an important reference system; its elementary magnetic excitations are spin-1/2 quasiparticles called spinons that are created in even numbers. However, while the excitation continuum associated with two-spinon states is routinely observed, the study of four-spinon and higher multi-spinon states is an open area of research. Here we show that four-spinon excitations can be accessed directly in Sr2CuO3 using resonant inelastic x-ray scattering (RIXS) in a region of phase space clearly separated from the two-spinon continuum. Our finding is made possible by the fundamental differences in the correlation function probed by RIXS in comparison to other probes. This advance holds promise as a tool in the search for novel quantum states and quantum spin liquids.
We investigate magnetic excitations in the spin-ladder compound Sr_{14}Cu_{24}O_{41} using high-resolution Cu L_{3} edge resonant inelastic x-ray scattering (RIXS). Our findings demonstrate that RIXS couples to two-triplon collective excitations. In contrast to inelastic neutron scattering, the RIXS cross section changes only moderately over the entire Brillouin zone, revealing high sensitivity also at small momentum transfers, allowing determination of the two-triplon energy gap as 100 +/- 30 meV. Our results are backed by calculations within an effective Hubbard model for a finite-size cluster, and confirm that optical selection rules are obeyed for excitations from this spherically symmetric quantum spin-liquid ground state.
Recent angle-resolved photoemission spectroscopy (ARPES) for a newly discovered doped one-dimensional (1D) Mott insulator ${\mathrm{Ba}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{3+\ensuremath{\delta}}$ proposed the presence of attractive charge interactions between neighboring sites if a 1D Hubbard model is employed to describe the material. On the other hand, long-range repulsive charge interactions were proposed to be crucial for understanding the optical excitations of undoped 1D Mott insulators. Motivated by these contrasting proposals, we perform density-matrix renormalization group calculations of the single-particle spectral function as well as dynamical spin and charge structure factors for two kinds of extended 1D Hubbard models. The spectral function for the long-range repulsive model less agrees with the ARPES data as compared with that for the attractive one. The dynamical spin and charge structure factors also exhibit contrasting behaviors between the two models: The attractive model shows less momentum dependence of the integrated weight in the dynamical spin structure factor and more accumulation of the weight on the upper edge of particle-hole-type excitation in the dynamical charge structure factor. These features give a good criterion of an appropriate model for doped 1D Mott insulators, which can be judged by resonant-inelastic x-ray scattering experiments.