Damped spin excitations in a doped cuprate superconductor with orbital hybridization

Abstract

A resonant inelastic x-ray scattering (RIXS) study of overdamped spin-excitations in slightly underdoped La${}_{2-x}$Sr${}_x$CuO${}_4$ (LSCO) with $x=0.12$ and $0.145$ is presented. Three high-symmetry directions have been investigated: (1) the antinodal $(0,0)\to (1/2,0)$, (2) the nodal $(0,0)\to (1/4,1/4)$ and (3) the zone boundary direction $(1/2,0)\to (1/4,1/4)$ 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 La${}_2$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.

10 pages, 7 figures