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arXiv:1104.5588 · Physical Review B

Doping dependence of magnetic excitations of one-dimensional cuprates as probed by resonant inelastic x-ray scattering

Filomena Forte, Mario Cuoco, Canio Noce, Jeroen van den Brink

Published Jun 28, 2011• 25 citations
arXivHTMLPDF

Abstract

We study the dynamical, momentum-dependent two- and four-spin response functions in doped and undoped one-dimensional cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped $t$--$J$ system, the four-spin response vanishes at $\ensuremath{\pi}$, whereas the two-spin correlator is peaked around $\ensuremath{\pi}/2$, with generally larger spectral weight. Upon doping, spectra tend to soften and broaden, with a transfer of spectral weight toward higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at $\ensuremath{\pi}$ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta, the higher energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.

DOI
10.1103/physrevb.83.245133

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We study the dynamical, momentum-dependent two- and four-spin response functions in doped and undoped one-dimensional cuprates, as probed by resonant inelastic x-ray scattering, using an exact numerical diagonalization procedure. In the undoped ttt--JJJ system, the four-spin response vanishes at \ensuremathπ\ensuremath{\pi}\ensuremathπ, whereas the two-spin correlator is peaked around \ensuremathπ/2\ensuremath{\pi}/2\ensuremathπ/2, with generally larger spectral weight. Upon doping, spectra tend to soften and broaden, with a transfer of spectral weight toward higher energy. However, the total spectral weight and average peak position of either response are only weakly affected by doping up to a concentration of 1/8. Only the two-spin response at \ensuremathπ\ensuremath{\pi}\ensuremathπ changes strongly, with a large reduction of spectral weight and enhancement of excitation energy. At other momenta, the higher energy, generic features of the magnetic response are robust against doping. It signals the presence of strong short-range antiferromagnetic correlations, even after doping mobile holes into the system. We expect this to hold also in higher dimensions.
We study the impact of next-nearest-neighbor (NNN) hopping on the low-energy collective excitations of strongly correlated doped antiferromagnetic cuprate spin chains. Specifically, we use exact diagonalization and the density matrix renormalization group method to study the single-particle spectral function, the dynamical spin and charge structure factors, and the Cu LLL-edge resonant inelastic x-ray scattering (RIXS) intensity of the doped $t\text{\ensuremath{-}}t\ensuremath{'}\text{\ensuremath{-}}J$ model for a set of $t\ensuremath{'}$ values. We find evidence that the spin and charge degrees of freedom of the doped holes are not strictly separated anymore as $|t\ensuremath{'}|$ increases and identify the consequences of this in the dynamical response functions. The inclusion of NNN hopping couples the spinon and holon excitations, resulting in the formation of a spin polaron, where a ferromagnetic spin-polarization cloud dresses the doped carrier. The spin polaron manifests itself as additional spectral weight in the dynamical correlation functions, which appear simultaneously in the spin- and charge-sensitive channels. We also demonstrate that RIXS can provide a unique view of the spin polaron, due to its sensitivity to both the spin and charge degrees of freedom.
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Resonant inelastic x-ray scattering (RIXS) has become an important tool for studying elementary excitations in correlated materials. Here, we present a systematic theoretical investigation of the Cu LLL-edge RIXS spectra of undoped and doped cuprate two-leg spin-ladders in both the non-spin-conserving (NSC) and spin-conserving (SC) channels. The spectra are rich and host many exotic excitations. In the NSC channel of the undoped case, we identify one-triplon and bound triplet two-triplon excitations in the strong rung coupling limit, as well as confined spinons in the weak rung coupling limit. In the doped case, we observe a quasiparticle excitation formed from a bound charge and spin-1/21/21/2 in the strong rung coupling limit. In the SC channel, we also identify several new features, including bound singlet two-triplon excitations and confined spinons in the undoped ladders in the strong and weak rung coupling limits, respectively. Conversely, in the doped case, the SC channel primarily probes both gapless and gapped charge excitations. Finally, we revisit the available data for the ladder compound Sr14Cu24O41{\mathrm{Sr}}_{14}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}Sr14​Cu24​O41​ in the context of our results.
Magnetic interactions are widely believed to play a crucial role in the microscopic mechanism leading to high critical temperature superconductivity. It is therefore important to study the signatures of pairing in the magnetic excitation spectrum of simple models known to show unconventional superconducting tendencies. Using the density matrix renormalization group technique, we calculate the dynamical spin structure factor $S(\mathbf{k},\ensuremath{\omega})$ of a generalized $t\ensuremath{-}U\ensuremath{-}J$ Hubbard model away from half filling in a two-leg ladder geometry. The addition of JJJ enhances pairing tendencies. We analyze quantitatively the signatures of pairing in the magnetic excitation spectra. We found that the superconducting pair-correlation strength, that can be estimated independently from ground state properties, is closely correlated with the integrated low-energy magnetic spectral weight in the vicinity of $(\ensuremath{\pi},\ensuremath{\pi})$. In this wave-vector region, robust spin incommensurate features develop with increasing doping. The branch of the spectrum with rung direction wave vector krung=0{k}_{\mathrm{rung}}=0krung​=0 does not change substantially with doping where pairing dominates and thus plays a minor role. We discuss the implications of our results for neutron scattering experiments, where the spin excitation dynamics of hole-doped quasi-one-dimensional magnetic materials can be measured and also address implications for recent resonant inelastic x-ray scattering experiments.
We have analyzed experimental evidence for an anomalous transfer of spectral weight from high- to low-energy scales in both electron- and hole-doped cuprates as a function of doping. X-ray scattering, optical, and photoemission spectra are all found to show that the high-energy spectral weight decreases with increasing doping at a rate much faster than predictions of the large UUU-limit calculations. The observed doping evolution is however well described by an intermediate coupling scenario where the effective Hubbard UUU is comparable to the bandwidth. The experimental spectra across various spectroscopies are inconsistent with fixed-UUU exact diagonalization or quantum Monte Carlo calculations, and suggest a significant doping dependence of the effective UUU in the cuprates.