Calculation of the four-spin cyclic exchange in cuprates

Abstract

Starting from the three-band Hubbard model for the cuprates, we calculate analytically the four-spin cyclic exchange in the limit of infinite on-site Coulomb repulsion and zero O-O hopping $t_{pp}$ using two methods: i) perturbation theory in $t_{pd}/\Delta$, where $t_{pd}$ is the Cu-O hopping and $\Delta$ the Cu-O charge transfer energy and ii) exact solution of a Cu${}_4$O${}_4$ plaquette. The latter method coincides with the first to order eight in $t_{pd}$ and permits to extend the results to $t_{pd}/\Delta$ of order one. The results are relevant to recent experimental and theoretical research that relate the splitting of certain spin excitations with $\Delta$ and the superconducting critical temperature.

6 pages, 2 figures, some typos corrected and references added

References in corpus (3)

• Influence of apical oxygen on the extent of in-plane exchange interaction in cuprate superconductors
• Generalized one-band model based on Zhang-Rice singlets for Tetragonal CuO
• Magnon Splitting Induced by Charge Transfer in the Three-Orbital Hubbard Model

Cited by in corpus (3)

• Magnon Spectra of Cuprates beyond Spin Wave Theory
• Systematic determination of coupling constants in spin clusters from broken-symmetry mean-field solutions
• Multimagnon and multispinon $L_3$-edge RIXS spectra of an effective ${\tilde{J}}_1-{\tilde{J}}_2-{\tilde{J}}_3$ square lattice Heisenberg model