Oxygen on-site Coulomb energy in Pr${}_{1.3-x}$La${}_{0.7}$Ce${}_x$CuO${}_4$ and Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ and its relation with Heisenberg exchange

Abstract

We study the electronic structure of electron-doped Pr${}_{1.3-x}$La${}_{0.7}$Ce${}_x$CuO${}_4$ (PLCCO ; $T_c$ = 27 K, x = 0.1) and hole-doped Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta }$ (Bi2212 ; $T_c$ = 90 K) cuprate superconductors using x-ray absorption spectroscopy (XAS) and resonant photoemission spectroscopy (Res-PES). From Res-PES across the O K-edge and Cu L-edge, we identify the O 2p and Cu 3d partial density of states (PDOS) and their correlation satellites which originate in two-hole Auger final states. Using the Cini-Sawatzky method, analysis of the experimental O 2p PDOS shows an oxygen on-site Coulomb energy for PLCCO to be $U_p$ = 3.3$\pm$0.5 eV and for Bi2212, $U_p$ = 5.6$\pm$0.5 eV, while the copper on-site Coulomb correlation energy, $U_d$ = 6.5$\pm$0.5 eV for Bi2212. The expression for the Heisenberg exchange interaction $J$ in terms of the electronic parameters $U_d$, $U_p$, charge-transfer energy $\Delta$ and Cu-O hopping $t_{pd}$ obtained from a simple Cu${}_2$O cluster model is used to carry out an optimization analysis consistent with $J$ known from scattering experiments. The analysis also provides the effective one band on-site Coulomb correlation energy $\tilde{U}$ and the effective hopping $\tilde{t}$. PLCCO and Bi2212 are shown to exhibit very similar values of $\tilde{U}$/$\tilde{t}$ $\sim$9-10, confirming the strongly correlated nature of the singlet ground state in the effective one-band model for both the materials.

arXiv comment13, pages, 11 figures

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