High-Tc superconductivity and antiferromagnetism on self-doped high-Tc cuprate Ba$_{2}$Ca$_{3}$Cu$_{4}$O$_{8}$F$_{2}$

We report on the antiferromagnetism and high-Tc superconductivity in a F-substituted four-layered cuprate, composed of two outer and inner CuO$_{2 }$planes in a unit cell, Ba$_{2}$Ca$_{3}$Cu$_{4}$O$_{8}$F$_{2}$. Although a formal Cu valence is expected to be just +2.0 in the nominal composition, this is not a half-filled Mott insulator but a superconductor with Tc = 55K. Recently, it has been suggested that the origin of the superconductivity in this compound is self-doping by ARPES measurement [1] and band calculation [2], which means either outer or inner CuO$_{2}$ planes are hole-doped, and the others are electron-doped. From F-NMR study, we have confirmed magnetic order with T$_{N}$ = 100K, concluding the uniform mixing of superconductivity and magnetic order in a single CuO$_{2}$ plane. In addition, we have compared a three-layered compound Ba$_{2}$Ca$_{2}$Cu$_{3}$O$_{6}$F$_{2}$, which is also superconductor with Tc = 76K. We will introduce the unique magntic and superconducting phenomena in F-substituted cuprates from microscopic points of view. [1]Y. Chen, \textit{et al}., cond-mat/0611291 (2006) [2] W. Xie, et al., cond-mat/0607198 (2006)