Doping dependence of the magnetic excitations in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$

The magnetic correlations within the cuprates have undergone intense scrutiny as part of efforts to understand high-temperature superconductivity. We explore the evolution of the magnetic correlations along the nodal direction of the Brillouin zone in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, spanning the doping phase diagram from the antiferromagnetic Mott insulator at $x=0$ to the metallic phase at $x=0.26$. Magnetic excitations along this direction are found to be systematically softened and broadened with doping, at a higher rate than the excitations along the antinodal direction. This phenomenology is discussed in terms of the nature of the magnetism in the doped cuprates. Survival of the high-energy magnetic excitations, even in the overdoped regime, indicates that these excitations are marginal to pairing, while the influence of the low-energy excitations remains ambiguous.

Figure 1

(a) Doping phase diagram for LSCO. (b) RIXS geometry used for the experiment. (c) Plot of the cuprate Brillouin zone. Red squares represent $\mathit{Q}$ points measured for this report, and purple circles for previous work by this group [11]. The green semicircles represent the regions of reciprocal space accessible to Cu ${\mathrm{L}}_3$-edge RIXS. (d) RIXS spectra for each doping at $\mathit{Q}=(0.24,0.24)$ showing $dd$ excitation and paramagnon features. Data are offset vertically for clarity. The gray line denotes the zero-energy-loss position.

Figure 2

${\mathrm{La}}_2{\mathrm{CuO}}_4$ RIXS spectra. (a) An example spectrum at $\mathit{Q}=(0.24,0.24)$ showing the different components of the fit including magnon, multimagnon, phonon, and elastic as well as the total fit in gray. (b) Dispersion of the phonon, multimagnon, and single-magnon features.

Figure 3

Plots of the RIXS spectra dispersion for each doping represented as a two-dimensional color map. The broadening of the paramagnon feature with increased doping is readily apparent. All panels share the same intensity scale as shown on the top panel. The doping $x$ is noted in white in the top-left corner of every panel.

Figure 4

Individual RIXS spectra for each sample (horizontal) and every $\mathit{Q}$ point (vertical) with underlain fit. For all samples except the parent compound only the elastic (red), paramagnon (blue), and smooth background (dashed black) were used as components in the fit. The features of the spectra are displayed added to the background from the $dd$ excitations. The total fit is represented by a gray line. For the $x=0$ case, the multimagnon feature is shown in purple, which was not resolved for the doped samples. The detailed fitting procedure is discussed in the text.

Figure 5

(a) The paramagnon dispersion for each doping with applied fit. (b) Paramagnon peak width for each $\mathit{Q}$ point defined as a Lorentzian half-width at half-maximum (HWHM). (c) Paramagnon spectral weight for each sample and $\mathit{Q}$ point. (d) Maximum energy transfer for each doping. (e) $\mathit{Q}$-averaged widths with cumulative error. (f) $\mathit{Q}$-averaged intensities. The error bars represent the statistical error from the fitting procedure.

Figure 6

Comparison of the nodal and antinodal [10, 11] data for each doping. Dashed lines represent the spin-wave theory predictions for ${\mathrm{La}}_2{\mathrm{CuO}}_4$. $x=0.05$ was not previously measured.