A resonant inelastic x-ray scattering study of overdamped spin excitations in slightly underdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) with $x=0.12$ and 0.145 is presented. Three high-symmetry directions have been investigated: (1) the antinodal $(0,0)\to (\frac{1}{2},0)$, (2) the nodal $(0,0)\to (\frac{1}{4},\frac{1}{4})$, and (3) the zone-boundary direction $(\frac{1}{2},0)\to (\frac{1}{4},\frac{1}{4})$ connecting these two. The overdamped excitations exhibit strong dispersions along (1) and (3), whereas a much more modest dispersion is found along (2). This is in strong contrast to the undoped compound ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (LCO) for which the strongest dispersions are found along (1) and (2). The $t-t^{\prime }-t^{\prime \prime }-U$ Hubbard model used to explain the excitation spectrum of LCO predicts—for constant $U/t$—that the dispersion along (3) scales with ${(t^{\prime }/t)}^2$. However, the diagonal hopping $t^{\prime }$ extracted on LSCO using single-band models is low ($t^{\prime }/t\sim -0.16$) and decreasing with doping. We therefore invoked a two-orbital ($d_{x^2-y^2}$ and $d_{z^2}$) model which implies that $t^{\prime }$ is enhanced. This effect acts to enhance the zone-boundary dispersion within the Hubbard model. We thus conclude that hybridization of $d_{x^2-y^2}$ and $d_{z^2}$ states has a significant impact on the zone-boundary dispersion in LSCO.

• Received 8 February 2017
• Revised 2 May 2017

DOI:https://doi.org/10.1103/PhysRevB.95.214508