Magnetic Excitations and Phase Separation in the Underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ Superconductor Measured by Resonant Inelastic X-Ray Scattering

We probe the collective magnetic modes of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ and underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) by momentum resolved resonant inelastic x-ray scattering (RIXS) at the Cu $L_3$ edge. For the undoped antiferromagnetic sample, we show that the single magnon dispersion measured with RIXS coincides with the one determined by inelastic neutron scattering, thus demonstrating that x rays are an alternative to neutrons in this field. In the spin dynamics of LSCO, we find a branch dispersing up to $\sim 400\mathrm{meV}$ coexisting with one at lower energy. The high-energy branch has never been seen before. It indicates that underdoped LSCO is in a dynamic inhomogeneous spin state.

Figure 1

Panel (a) layout of the experimental setup and indication of the reciprocal space region [red thick line] spanned inside the first Brillouin zone. Panel (b) decomposition of the LCO spectrum at $q_{\parallel }=1.85$: elastic ($A$) and single magnon peaks ($B$); multiple magnon ($C$) and optical phonons ($D$) spectral features. In the inset the $L_3$ absorption spectrum, the red arrow indicates excitation energy. Panel (c) single magnon dispersion determined by RIXS (this work, blue dots) and by inelastic neutron scattering (Ref. 12, dashed purple line).

Figure 2

Overview of the RIXS results for LSCO at $T=15\mathrm{K}$. Panel (a) 3D representation of the whole dataset, where the intensity (normalized to the integral of the $dd$ excitations) is plotted as function of the energy loss and of the transferred momentum $q_{\parallel }$. Panel (b) example of one spectrum including the $dd$ excitations ($q_{\parallel }=-2.29$), Panel (c) selected spectra in the low energy spectral region.

Figure 3

Panel (a) example of RIXS spectrum decomposition for underdoped LSCO in the low energy region: elastic peak (grey dashed line), phonon peak (purple dotted line), and magnetic excitations (blue solid line). Panel (b) temperature effects for $q_{\parallel }=-2.29$ and $-1.85$: the single peak structure at room $T$ splits into two peaks at low $T$. Panel (c) comparison between LCO and LSCO for $q_{\parallel }=-1.26$ at low temperature.

Figure 4

Panel (a) dispersion of the two magnetic excitations in underdoped LSCO at $T=15\mathrm{K}$: one higher-energy LCO-like branch (open blue squares) and one lower energy branch (full blue circles). At small $q_{\parallel }$ (black squares), the separation into subcomponents, if any, is not resolvable. In the shaded area, phonon scattering influences the data analysis. The dotted blue line is the LCO dispersion taken from Fig. 1c and multiplied by 1.09. The solid blue line is a guide to the eye. Panel (b) dispersion at room $T$ (red diamonds) and low $T$ (blue circles and squares). Panel (c) low energy branch measured with RIXS near (0, 0) (blue circles) and with neutrons close to ($\pi$, $\pi$) (thin black line for $p=0.05$, green dashed line for $p=0.085$, brown thick line for $p=0.16$).