We report ${}^{63,65}\mathrm{Cu}$- and ${}^{19}\mathrm{F}$-NMR studies on a four-layered high-temperature superconductor ${\mathrm{Ba}}_2{\mathrm{Ca}}_3{\mathrm{Cu}}_4{\mathrm{O}}_8{\mathrm{F}}_2\mathbf{(}(0234F(2.0)\mathbf{)}$ with apical fluorine (${\mathrm{F}}^{-1}$), an undoped 55 K superconductor with a nominal ${\mathrm{Cu}}^{2+}$ valence on average. We reveal that this compound exhibits the antiferromagnetism (AFM) with a Néel temperature $T_N=100\mathrm{K}$ despite being a $T_c=55$ $K$ superconductor. Through a comparison with a related trilayered cuprate ${\mathrm{Ba}}_2{\mathrm{Ca}}_2{\mathrm{Cu}}_3{\mathrm{O}}_6{\mathrm{F}}_2\mathbf{(}0233F(2.0)\mathbf{)}$, it is demonstrated that electrons are transferred from the inner plane (IP) to the outer plane (OP) in 0234F(2.0) and 0223F(2.0), confirming the self-doped high-temperature superconductivity (HTSC) having electron and hole doping in a single compound. Remarkably, uniform mixing of AFM and HTSC takes place in both the electron-doped OPs and the hole-doped IPs in 0234F(2.0).

• Received 20 August 2006

DOI:https://doi.org/10.1103/PhysRevLett.98.257002