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arXiv:1106.3108 · Physical Review B

Proposal for detecting spin-chirality terms in Mott insulators via resonant inelastic x-ray scattering

Wing-Ho Ko, Patrick A. Lee

Published Sep 1, 2011• 21 citations
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Abstract

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 $\text{U}(1)$ Dirac spin liquid.

DOI
10.1103/physrevb.84.125102

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Proposal for detecting spin-chirality terms in Mott insulators via resonant inelastic x-ray scattering

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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 Si\ifmmode⋅\else\textperiodcentered\fi(Sj\ifmmode×\else\texttimes\fiSk){\mathbf{S}}_{i}\ifmmode\cdot\else\textperiodcentered\fi{}({\mathbf{S}}_{j}\ifmmode\times\else\texttimes\fi{}{\mathbf{S}}_{k})Si​\ifmmode⋅\else\textperiodcentered\fi(Sj​\ifmmode×\else\texttimes\fiSk​) 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.
We calculate the resonant inelastic x-ray scattering (RIXS) response of the Kitaev honeycomb model, an exactly solvable quantum-spin-liquid model with fractionalized Majorana and flux excitations. We find that the fundamental RIXS channels, the spin-conserving (SC) and the non-spin-conserving (NSC) ones, do not interfere and give completely different responses. SC RIXS picks up exclusively the Majorana sector with a pronounced momentum dispersion, whereas NSC RIXS also creates immobile fluxes, thereby rendering the response only weakly momentum dependent, as in the spin structure factor measured by inelastic neutron scattering. RIXS can, therefore, pick up the fractionalized excitations of the Kitaev spin liquid separately, making it a sensitive probe to detect spin-liquid character in potential material incarnations of the Kitaev honeycomb model.
We propose that resonant inelastic x-ray scattering (RIXS) is an effective probe of the fractionalized excitations in three-dimensional (3D) Kitaev spin liquids. While the non-spin-conserving RIXS responses are dominated by the gauge-flux excitations and reproduce the inelastic-neutron-scattering response, the spin-conserving (SC) RIXS response picks up the Majorana-fermion excitations and detects whether they are gapless at Weyl points, nodal lines, or Fermi surfaces. As a signature of symmetry fractionalization, the SC RIXS response is suppressed around the Γ point. On a technical level, we calculate the exact SC RIXS responses of the Kitaev models on the hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices, arguing that our main results also apply to generic 3D Kitaev spin liquids beyond these exactly solvable models.
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.
Motivated by the ongoing effort to search for high-resolution signatures of quantum spin liquids, we investigate the temperature dependence of the indirect resonant inelastic x-ray scattering (RIXS) response for the Kitaev honeycomb model. We find that, as a result of spin fractionalization, the RIXS response changes qualitatively at two well-separated temperature scales, TL{T}_{L}TL​ and TH{T}_{H}TH​, which correspond to the characteristic energies of the two kinds of fractionalized excitations, Z2{\mathbb{Z}}_{2}Z2​ gauge fluxes and Majorana fermions, respectively. While thermally excited Z2{\mathbb{Z}}_{2}Z2​ gauge fluxes at temperature TL{T}_{L}TL​ lead to a general broadening and softening of the response, the thermal proliferation of Majorana fermions at temperature ${T}_{H}\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}{T}_{L}$ results in a significant shift of the spectral weight, both in terms of energy and momentum. Due to its exclusively indirect nature, the RIXS process we consider gives rise to a universal magnetic response and, from an experimental perspective, it directly corresponds to the KKK-edge of Ru3+{\mathrm{Ru}}^{3+}Ru3+ in the Kitaev candidate material $\ensuremath{\alpha}\ensuremath{-}{\mathrm{RuCl}}_{3}$.
We study a spin-orbital model for 4d14{d}^{1}4d1 or 5d15{d}^{1}5d1 Mott insulators in ordered double perovskites with strong spin-orbit coupling. This model is conveniently written in terms of pseudospin and pseudo-orbital operators representing multipoles of the effective j=32j=\frac{3}{2}j=23​ angular momentum. Similarities between this model and the effective theories of Kitaev materials motivate the proposal of a chiral spin-orbital liquid with Majorana fermion excitations. The thermodynamic and spectroscopic properties of this quantum spin liquid are characterized using parton mean-field theory. The heat capacity, spin-lattice relaxation rate, and dynamic structure factor for inelastic neutron scattering are calculated and compared with the experimental data for the spin liquid candidate Ba2YMoO6{\mathrm{Ba}}_{2}{\mathrm{YMoO}}_{6}Ba2​YMoO6​. Moreover, based on a symmetry analysis, we discuss the operators involved in resonant inelastic x-ray scattering (RIXS) amplitudes for double-perovskite compounds. In general, the RIXS cross sections allow one to selectively probe pseudospin and pseudo-orbital degrees of freedom. For the chiral spin-orbital liquid in particular, these cross sections provide information about the spectrum for different flavors of Majorana fermions.