Collective Nature of Spin Excitations in Superconducting Cuprates Probed by Resonant Inelastic X-Ray Scattering

We used resonant inelastic x-ray scattering (RIXS) with and without analysis of the scattered photon polarization, to study dispersive spin excitations in the high temperature superconductor ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+x}$ over a wide range of doping levels ($0.1\le x\le 1$). The excitation profiles were carefully monitored as the incident photon energy was detuned from the resonant condition, and the spin excitation energy was found to be independent of detuning for all $x$. These findings demonstrate that the largest fraction of the spin-flip RIXS profiles in doped cuprates arises from magnetic collective modes, rather than from incoherent particle-hole excitations as recently suggested theoretically [Benjamin et al. Phys. Rev. Lett. 112, 247002 (2014)]. Implications for the theoretical description of the electron system in the cuprates are discussed.

Figure 1

Scheme of the scattering geometries allowing maximal momentum transfer with (a) grazing incident photons or (b) grazing emitted photons. Polarization resolved measurements of underdoped ${\mathrm{YBCO}}_{6.35}$ taken with incident $\pi$ (c) and $\sigma$ (e) polarized light. Polarization resolved measurements of overdoped $\mathrm{YBCO}+\mathrm{Ca}$ taken with incident $\pi$ (d) and $\sigma$ (f) polarized light.

Figure 2

Raw RIXS spectra measured with $\pi$ polarization in the configuration of Fig. 1 and excited at selected incident energies across the corresponding $\mathrm{Cu}\text{−}{L}_3$ edge XAS profile (a) for ${\mathrm{YBCO}}_{6.1}$ (b), ${\mathrm{YBCO}}_{6.55}$ (c), ${\mathrm{YBCO}}_{6.79}$ (d), ${\mathrm{YBCO}}_{6.99}$ (e), and $\mathrm{YBCO}+\mathrm{Ca}$ (f). At each doping we plot the spectra for the following incident energies: 931.35 eV ($L_3$, dark gray squares), 931.475 eV ($L_3+0.125\mathrm{eV}$, blue circles), 931.6 eV ($L_3+0.250\mathrm{eV}$, green diamonds), and 931.725 eV ($L_3+0.375\mathrm{eV}$, red triangles).

Figure 3

(a) Examples of fitting for ${\mathrm{YBCO}}_{6.55}$ excited at selected incident energies. The symbols are the raw data while the black solid lines represent the results of least-squares fits based on a Gaussian line shape for the quasielastic signal (green shaded peak) and an antisymmetrized Voigt function for the paramagnon (orange shaded peak), on top of a Voigt fit of the tail of $dd$ excitations (dashed line). (b) Spectral weight of the paramagnon peak for all YBCO samples, as a function of incident photon energy. The magnetic integrated intensity is normalized to the area of the $dd$ excitations [42] as excited at the L3 peak (i.e., the maximum of the absorption spectrum, orange solid line) and set to 100. Notice how the spectral weight is modulated by the x-ray absorption spectrum (orange solid line). (c) and (d) Experimental paramagnon peak position and width for all YBCO samples, as a function of incident photon energy, compared to the theoretical prediction of Ref. [25].

Figure 4

Color map of the energy dependence of the RIXS intensity for (a),(b) antiferromagnetic ${\mathrm{YBCO}}_{6.1}$ and (c),(d) overdoped $\mathrm{YBCO}+\mathrm{Ca}$ with $\pi$ (a),(c) and $\sigma$ (b),(d) polarizations. The horizontal dashed black lines highlight the energy independence of the magnetic peak position, while the inclined dashed green line is a guide to the eye underlining the fluorescence behavior of charge excitations from the doped holes.