Uniform mixing of antiferromagnetism and high-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math>superconductivity in multilayer copper oxides<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Ba</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>Ca</mml:mtext></mml:mrow><mml:mrow><mml:mi>n</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:msub><mml:mrow><mml:mtext>Cu</mml:mtext></mml:mrow><mml:mi>n</mml:mi></mml:msub><mml:msub><mml:mtext>O</mml:mtext><mml:mrow><mml:mn>2</mml:mn><mml:mi>n</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mtext>F</mml:mtext><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mi>n</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>,</mml:mo><mml:mn>3</mml:mn><mml:mo>,</mml:mo><mml:mn>4</mml:mn></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>with apical fluorines:<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mtext>C</mml:mtext><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>63</mml:mn></mml:mrow></mml:mmultiscripts><mml:mtext>u-NMR</mml:mtext><mml:mo>/</mml:mo><mml:mtext>NQR</mml:mtext></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mtext>F</mml:mtext><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>19</mml:mn></mml:mrow></mml:mmultiscripts><mml:mtext>-NMR</mml:mtext></mml:mrow></mml:math>studies (2009)

We report $^{63}\text{C}\text{u-NMR}/\text{NQR}$ and $^{19}\text{F}\text{-NMR}$ studies on the multilayered high-${T}_{c}$ copper oxides ${\text{Ba}}_{2}{\text{Ca}}_{n\ensuremath{-}1}{\text{Cu}}_{n}{\text{O}}_{2n}{\text{F}}_{2}$ with $n=2,3,4$, where $n$ is the number of ${\text{CuO}}_{2}$ planes. It is revealed that bilayered ${\text{Ba}}_{2}{\text{CaCu}}_{2}{\text{O}}_{4}{\text{F}}_{2}$ is an underdoped superconductor with hole carriers, which are introduced into ${\text{CuO}}_{2}$ planes by an unexpected deviation from the nominal content of apical fluorines. In a previous paper, we proposed a self-doping mechanism as the origin of carrier doping in $n=3$ and $n=4$; in the mechanism, electrons are transferred from the inner ${\text{CuO}}_{2}$ plane (IP) to the outer one (OP). However, since it has been found that the bilayered compound is hole doped, we have re-examined the superconducting and magnetic properties in $n=3$ and $n=4$ by $^{63}\text{C}\text{u-NMR}/\text{NQR}$ and $^{19}\text{F}\text{-NMR}$. The extensive NMR studies have confirmed that the apical-fluorine compounds are not self-doped but hole doped and that antiferromagnetism (AFM) and superconductivity (SC) coexist in a single ${\text{CuO}}_{2}$ plane. In $n=4$, the AFM ordering occurs at ${T}_{N}=80\text{ }\text{K}$ well above ${T}_{c}=55\text{ }\text{K}$, where the respective AFM moments are ${M}_{\text{AFM}}=0.11{\ensuremath{\mu}}_{B}$ and $0.18{\ensuremath{\mu}}_{B}$ at the OP and the IP. In $n=3$, on the other hand, the underdoped single IP exhibits a spontaneous moment ${M}_{\text{AFM}}=0.12{\ensuremath{\mu}}_{B}$ at low temperatures and a peak in the nuclear-spin-lattice relaxation rate $1/{T}_{1}$ of $^{19}\text{F}$ at ${T}_{N}=23\text{ }\text{K}$ much lower than ${T}_{c}=76\text{ }\text{K}$. We note that the increase in the number of IPs from one to two results in the strengthening of the interlayer coupling; ${T}_{N}$ increases as the interlayer coupling becomes stronger, although the doping levels for both compounds are comparable. Consequently, we conclude that the uniform mixing of AFM and SC is a general property inherent to a single ${\text{CuO}}_{2}$ plane in an underdoped regime for hole doping. This conclusion incorporates the angle-resolved photoemission spectroscopy results on the $n=4$ compound [Chen et al., Phys. Rev. Lett. 97, 236401 (2006)]; it was found that the two Fermi sheets of the IP and OP are observed and that the SC gap opens at the IP and OP below ${T}_{c}=55\text{ }\text{K}$.