Itinerant effects and enhanced magnetic interactions in Bi-based multilayer cuprates

Abstract

The cuprate high temperature superconductors exhibit a pronounced trend in which the superconducting transition temperature ${T}_{\mathrm{c}}$ increases with the number of ${\mathrm{CuO}}_{2}$ planes $n$ in the crystal structure. We compare the magnetic excitation spectrum of ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2\ensuremath{-}x}{\mathrm{CuO}}_{6+\ensuremath{\delta}}$ (Bi-2201) and ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{Ca}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{10+\ensuremath{\delta}}$ (Bi-2223), with $n=1$ and 3, respectively, using Cu ${L}_{3}$-edge resonant inelastic x-ray scattering. Near the antinodal zone boundary we find the paramagnon energy in Bi-2223 is substantially higher than that in Bi-2201, indicating that multilayer cuprates host stronger effective magnetic exchange interactions, providing a possible explanation for the ${T}_{\mathrm{c}}$ vs $n$ scaling. In contrast, the nodal direction exhibits very strongly damped, almost nondispersive excitations. We argue that this implies that the magnetism in the doped cuprates is partially itinerant in nature.