We report systematic Cu- and F-NMR measurements of five-layered high-Tc cuprates Ba2Ca4Cu5O10(F,O)2. It is revealed that antiferromagnetism (AFM) uniformly coexists with superconductivity (SC) in underdoped regions, and that the critical hole density
pc for AFM is ~ 0.11 in the five-layered compound. We present the layer-number dependence of AFM and SC phase diagrams in hole-doped cuprates, where pc for n-layered compounds, pc(n), increases from pc(1) ~ 0.02 in LSCO or pc(2) ~ 0.05 in YBCO to pc(5) ~ 0.11. The variation of pc(n) is attributed to interlayer magnetic coupling, which becomes stronger with increasing n. In addition, we focus on the ground-state phase diagram of CuO2 planes, where AFM metallic states in slightly doped Mott insulators change into the uniformly mixed phase of AFM and SC and into simple d-wave SC states. The maximum Tc exists just outside the quantum critical hole density, at which AFM moments on a CuO2 plane collapse at the ground state, indicating an intimate relationship between AFM and SC. These characteristics of the ground state are accounted for by the Mott physics based on the t-J model; the attractive interaction of high-Tc SC, which raises Tc as high as 160 K, is an in-plane superexchange interaction Jin (~ 0.12 eV), and the large Jin binds electrons of opposite spins between neighboring sites. It is the Coulomb repulsive interaction U ~ (> 6 eV) between Cu-3d electrons that plays a central role in the physics behind high-Tc phenomena.
We report on the phase diagram of antiferromagnetism (AFM) and superconductivity (SC) in three-layered Ba_2Ca_2Cu_3O_6(F,O)_2 by means of Cu-NMR measurements. It is demonstrated that AFM and SC uniformly coexist in three-layered compounds as well as
in four- and five-layered ones. The critical hole density p_c for the long range AFM order is determined as p_c ~ 0.075, which is larger than p_c ~ 0.02 and 0.055 in single- and bi-layered compounds, and smaller than p_c ~ 0.08-0.09 and 0.10-0.11 in four- and five-layered compounds, respectively. This variation of p_c is attributed to the magnetic interlayer coupling which becomes stronger as the stacking number of CuO_2 layers increases; that is, the uniform coexistence of AFM and SC is a universal phenomenon in underdoped regions when a magnetic interlayer coupling is strong enough to stabilize an AFM ordering. In addition, we highlight an unusual pseudogap behavior in three-layered compounds -- the gap behavior in low-energy magnetic excitations collapses in an underdoped region where the ground state is the AFM-SC mixed phase.
We report that planar CuO_2 hole densities in high-T_c cuprates are consistently determined by the Cu-NMR Knight shift. In single- and bi-layered cuprates, it is demonstrated that the spin part of the Knight shift K_s(300 K) at room temperature monot
onically increases with the hole density $p$ from underdoped to overdoped regions, suggesting that the relationship of K_s(300 K) vs. p is a reliable measure to determine p. The validity of this K_s(300 K)-p relationship is confirmed by the investigation of the p-dependencies of hyperfine magnetic fields and of spin susceptibility for single- and bi-layered cuprates with tetragonal symmetry. Moreover, the analyses are compared with the NMR data on three-layered Ba_2Ca_2Cu_3O_6(F,O)_2, HgBa_2Ca_2Cu_3O_{8+delta}, and five-layered HgBa_2Ca_4Cu_5O_{12+delta}, which suggests the general applicability of the K_s(300 K)-p relationship to multilayered compounds with more than three CuO_2 planes. We remark that the measurement of K_s(300 K) enables us to separately estimate p for each CuO_2 plane in multilayered compounds, where doped hole carriers are inequivalent between outer CuO_2 planes and inner CuO_2 planes.
