Oxygen on-site Coulomb energy in Pr1.3−xLa0.7CexCuO4 and Bi2Sr2CaCu2O8+δ and its relation with Heisenberg exchange

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We study the electronic structure of electron-doped ${\mathrm{Pr}}_{1.3\ensuremath{-}x}{\mathrm{La}}_{0.7}{\mathrm{Ce}}_{x}{\mathrm{CuO}}_{4}$ (PLCCO; ${T}_{c}=27\phantom{\rule{0.16em}{0ex}}\mathrm{K}, x=0.1$) and hole-doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (Bi2212; ${T}_{c}=90\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) cuprate superconductors using x-ray absorption spectroscopy 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 ${U}_{p}$ = $3.3\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, and for Bi2212, ${U}_{p}=5.6\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, while the copper on-site Coulomb correlation energy is ${U}_{d}$ = $6.5\ifmmode\pm\else\textpm\fi{}0.5\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ for Bi2212. The expression for the Heisenberg exchange interaction $J$ in terms of the electronic parameters ${U}_{d}, {U}_{p}$, charge-transfer energy $\mathrm{\ensuremath{\Delta}}$, and Cu-O hopping ${t}_{pd}$ obtained from a simple ${\mathrm{Cu}}_{2}\mathrm{O}$ 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 $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}$ and the effective hopping $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}$. PLCCO and Bi2212 are shown to exhibit very similar values of $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{U}/\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{t}\ensuremath{\sim}9--10$, confirming the strongly correlated nature of the singlet ground state in the effective one-band model for both materials.

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