Cu<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>K</mml:mi></mml:math>-edge resonant inelastic x-ray scattering in edge-sharing cuprates

Vernay, F.; Moritz, Brian; Elfimov, Ilya; Geck, J.; Hawthorn, D. G.; Devereaux, T. P.; Sawatzky, G. A.

doi:10.1103/physrevb.77.104519

Cited by 39 publications

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References 43 publications

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“…The relatively large separation in energy from the valence levels as well as the large spatial extent of the 4p orbital are believed to prevent the photoelectron from interacting with the valence system, and this type of RIXS is in turn referred to as indirect. 6 Accordingly, theoretical models of this type of RIXS accordingly do not include possible interactions of the 4p photoelectron with the valence system, 12-15 which is commonly referred to as the '4p-as-spectator' approximation.RIXS investigations of the photon polarization effects have so far concluded that the incident polarization does not affect the probed valence band excitations, but only determines their specific resonance energies based on the crystal field levels of the 4p photoelectron, 14,16,17 in accordance with the 4p-as-spectator approximation. Nonetheless, there still exists no quantitative experimental evidence for an incident-photon polarization independence.…”

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Polarization dependence and symmetry analysis in indirectK-edge RIXS

et al. 2010

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We present a study of the charge-transfer excitations in undoped Nd 2 CuO 4 using resonant inelastic X-ray scattering (RIXS) at the Cu K-edge. At the Brillouin zone center, azimuthal scans that rotate the incidentphoton polarization within the CuO 2 planes reveal weak fourfold oscillations. A comparison of spectra taken in different Brillouin zones reveals a spectral weight decrease at high energy loss from forward-to back-scattering. We show that these are scattered-photon polarization effects related to the properties of the observed electronic excitations. Each of the two effects constitutes about 10% of the inelastic signal while the '4p-as-spectator' approximation describes the remaining 80%. Raman selection rules can accurately model our data, and we conclude that the observed polarization-dependent RIXS features correspond to E g and B 1g charge-transfer excitations to non-bonding oxygen 2p bands, above 2.5 eV energy-loss, and to an E g d → d excitation at 1.65 eV.Raman scattering and optical spectroscopy have enabled tremendous contributions to the study of condensed matter systems. Both probes use ∼ 1 eV light and are limited to essentially zero momentum transfer. In order to investigate the charge response of a material throughout the Brillouin zone, photons in the X-ray regime must be used. X-ray Raman scattering, more commonly referred to as resonant inelastic X-ray scattering (RIXS), allows the measurement of the momentum dependence of charge excitations. Even though it has successfully been used to study the physics of a wide array of systems, 1-5 this resonant technique is relatively new and there is still much to learn about the details of its cross section.One of the strengths of conventional Raman scattering derives from the fact that the technique allows the determination of the symmetry of excitations by selecting the polarization of the incident and scattered photons. Only polarization dependent soft (or direct 6 ) X-ray RIXS studies, at the O K-edge or the Cu L-and M-edges of the cuprates, 7-11 have shown that photon polarization can be used to select different electronic excitations. In these cases, the photon polarization effects are understood to come from the direct interaction of the photoelectron, excited into the valence system, with the valence electrons. This is why this type of RIXS is commonly referred to as direct. 6 On the other hand, tuning the incident energy to the Cu K-edge excites the photoelectron into the Cu 4p band approximately 10-20 eV above the 3d valence levels. The relatively large separation in energy from the valence levels as well as the large spatial extent of the 4p orbital are believed to prevent the photoelectron from interacting with the valence system, and this type of RIXS is in turn referred to as indirect. 6 Accordingly, theoretical models of this type of RIXS accordingly do not include possible interactions of the 4p photoelectron with the valence system, 12-15 which is commonly referred to as the '4p-as-spectator' approximation.RIXS investigations of ...

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Polarization dependence and symmetry analysis in indirectK-edge RIXS

et al. 2010

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“…Spectral intensities were calculated using the KramersHeisenberg formula [11] with the optical transition operator expressed in the hole representation: O k ¼ P j; p y j; d j; e ikÁr j , d removing a hole in the 3d band and p y creating one in the Cu 2p shell. The presence of a Cu 2p core-hole in the intermediate states was accounted for by an on-site Coulomb interaction [33]. The calculated RIXS profiles for the accessible k points are displayed in Fig.…”

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Collective Magnetic Excitations in the Spin LadderSr14Cu24O41Measured Using High-Resolution Resonant Inelastic X-Ray Scattering

et al. 2009

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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 AE 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. DOI: 10.1103/PhysRevLett.103.047401 PACS numbers: 78.70.En, 71.10.Pm, 75.25.+z, 75.30.Ds Collective excitations in strongly correlated electron materials remain a pivotal challenge in contemporary solid state physics. It is widely debated whether magnetic excitations provide the pairing interaction in the hightemperature and unconventional superconductors [1,2]. From that perspective quantum spin systems attract considerable interest. While most such materials, e.g., the cuprate superconductors, exhibit enormous complexity, the two-leg spin ladder is easier to tract theoretically [3][4][5][6]. It consists of two parallel chains (legs) with a transverse (rung) exchange coupling. This system features a singlet ground state and dispersive triplet excitations (triplons), that both have quantum mechanical origin without any classical counterpart. To date, mainly two techniques have been established as momentum-and energy-resolved probes of the dispersion of collective excitations: angleresolved photoelectron spectroscopy and inelastic neutron scattering (INS) for charge and spin degrees of freedom, respectively [7,8]. Because of the latest instrumental improvements [9,10], the energy scale of magnetic exchange is becoming readily accessible for resonant inelastic x-ray scattering (RIXS) [11][12][13][14], which is promising to give information on both, spin and charge degrees of freedom, and in addition is an element-specific technique. Furthermore, RIXS requires only small sample volumes (<0:1 mm 3 ). Recent RIXS studies were performed on long-range ordered magnets with spin-wave excitations [15][16][17].In this Letter, we report a study of the two-leg quantum spin ladder Sr 14 Cu 24 O 41 [18,19] by means of momentumresolved high-resolution RIXS at the Cu L 3 edge. Given that Cu L 3 scattering experiments have been already shown to contain valuable information about the charge degrees of freedom [20], an outstanding question we would like to address here is: how can RIXS provide information on magnetic excitations from a quantum ground state. In the ladder system of Sr 14 Cu 24 O 41 no symmetry breaking occurs-neither in spin-nor in real-space-in contrast to, e.g., a magnetically ordered state, where both symmetries are broken and the direction of the ordered moments dictates the quantization axi...

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“…The most exciting puzzle addressed here is the missing of the ZhangRice singlet peak (ZRS) in reflectivity and electron energy loss spectroscopy (EELS) data at T = 300 K 1,2 . Its detection in resonant inelastic x-ray scattering (RIXS) spectra is under debate, too 4,5 . There is also no consensus on the role of two scenarios for the FM in-chain order below the Néel temperature T N = 9 K. Scenario I is given by a dominant FM J 1 9 defined by the inequality α = −J 2 /J 1 < α c ≈ 0.25, if J 3 is weak 13 , where α c marks the transition from a high-spin FM to a lowspin spiral-like ground state (GS).…”

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“…This will cause a strong T -dependence of various response functions, here presented for the case of the optical conductivity σ(ω). For an illustration of our approach we consider Li 2 CuO 2 being of current interest 1,2,3,4,5,6,7,8,9,10,11,12 , structurally simple, and most importantly, where single crystal data are available in a broad ω-range 1,2 . This system stands for a class of frustrated spin-1/2 chain materials with both small ferromagnetic (FM) NN Cu-Cu exchange coupling J 1 and AFM next-nearest neighbor (NNN) Cu-Cu in-chain exchange J 2 1,3 in terms of a 1D spin-1/2 Heisenberg model…”

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Temperature-dependent optical conductivity of undoped cuprates with weak exchange

et al. 2008

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The optical conductivity σ(ω) is calculated at finite temperature T for CuO2 chain clusters within a pd-Hubbard model. Data at T = 300 K for Li2CuO2 are reanalyzed within this approach. The relative weights of Zhang-Rice singlet and triplet charge excitations near 2.5 and 4 eV, respectively, depend strongly on T , and a rather dramatic dependence of σ(ω) on the ratio of the 1 st to 2 nd neighbor exchange integrals is predicted. On the basis of these results, information about exchange interactions for frustrated edge-shared cuprates can be obtained from T -dependent optical spectra. Our results are also relevant for magnetically weakly coupled wide-gap insulators in general.PACS numbers: 71.15. Mb, 71.27.+a, 74.72.Jt, 75.10.Jm, 75.10.Pq, Standard wisdom on wide gap insulators says that their optical spectra above 1 eV excitation energy are hardly affected by temperature T , magnetic fields H, and by the magnetic nature of their ground state (GS). Moreover, spin and charge degrees of freedom are often decoupled in one dimension (1D). Here, we present exact theoretical results qualitatively valid for several cuprates to be specified below which prove just the opposite in all these respects. Our study bases on the fact that different magnetic states with different symmetries obey different selection rules, which -in case of soft magnetic materials -can lead to sizable T -dependence of the optical spectra. For systems with small enough exchange integrals, the energy difference between the GS and the excited magnetic states of the system will be small enough so that they can be thermally populated. This will cause a strong T -dependence of various response functions, here presented for the case of the optical conductivity σ(ω). For an illustration of our approach we consider Li 2 CuO 2 being of current interest 1,2,3,4,5,6,7,8,9,10,11,12 , structurally simple, and most importantly, where single crystal data are available in a broad ω-range 1,2 . This system stands for a class of frustrated spin-1/2 chain materials with both small ferromagnetic (FM) NN Cu-Cu exchange coupling J 1 and AFM next-nearest neighbor (NNN) Cu-Cu in-chain exchange J 2 1,3 in terms of a 1D spin-1/2 Heisenberg modelIn Li 2 CuO 2 chains running along the b-axis are formed by the edge-sharing of CuO 4 plaquettes. The most exciting puzzle addressed here is the missing of the ZhangRice singlet peak (ZRS) in reflectivity and electron energy loss spectroscopy (EELS) data at T = 300 K 1,2 . Its detection in resonant inelastic x-ray scattering (RIXS) spectra is under debate, too 4,5 . There is also no consensus on the role of two scenarios for the FM in-chain order below the Néel temperature T N = 9 K. Scenario I is given by a dominant FM J 1 9 defined by the inequality α = −J 2 /J 1 < α c ≈ 0.25, if J 3 is weak 13 , where

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CuK-edge resonant inelastic x-ray scattering in edge-sharing cuprates

Cited by 39 publications

References 43 publications

Polarization dependence and symmetry analysis in indirectK-edge RIXS

Polarization dependence and symmetry analysis in indirectK-edge RIXS

Collective Magnetic Excitations in the Spin LadderSr14Cu24O41Measured Using High-Resolution Resonant Inelastic X-Ray Scattering

Temperature-dependent optical conductivity of undoped cuprates with weak exchange

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