Local Hole Distribution in the CuO₂ Plane of High-T_c Cu-Oxides Studied by Cu and Oxygen NQR/NMR

Abstract

The hole numbers at Cu and oxygen sites in the CuO₂ plane in a wide variety of high-T_c materials have been extracted from the measured nuclear quadrupole frequency, ν _Q. The hole number in the Cu-3d_x²_-y² orbit, n_x²_-y², is found to be more than 0.85 in La_2-xSr_xCuO₄ (x=0.075-- 0.24), while decreases to 0.74 in Tl₂Ba₂Ca₂Cu₃O₁₀. Thus estimated n_x²_-y² is supported by the result that the orbital Knight shift along the c-axis, K^c_orb, increases in proportion to n_x²_-y². In contrast to the decrease of n_x²_-y², the hole number in the O-2p_σ orbit, n_p_σ, increases in going from the La- to the Tl-systems. It has been found that T_c is determined by two parameters about holes, i.e., n_x²_-y²+2n_p_σ and n_x²_-y²/2n_p_σ . The former tells the microscopic “ doping level'' of the CuO₂ plane, while a smaller n_x²_-y²/2n_p_σ results in a weaker antiferromagnetic spin fluctuations of low energy. It has been found that not only a proper n_x²_-y²+2n_p_σ but also a sufficiently small n_x²_-y²/2n_p_σ (~= 1) are needed to obtain a high value of T_c.