Nonmagnetic impurity effects on spectrum of antiferromagnetic spin fluctuations and nuclear spin-lattice relaxation rate in high-T_c superconductivity

We theoretically investigate antiferromagnetic (AF) spin fluctuations in impurity-doped high-T_c superconductivity. We assume a d_x2-y2-wave superconductor with strong AF spin fluctuations, and take into account nonmagnetic impurities within the t-matrix approximation. In the clean system, the imaginary part of the AF spin susceptibility (Imχ(Q,ω)) is suppressed far below the excitation gap E_g = 2 × Max[Δp] (Δp: superconducting order parameter), while it has a peak slightly below E_g. On the other hand, in the presence of unitarity scatterers, it is shown that Imχ(Q,ω) far below E_g increases with decreasing temperature even in the superconducting state. As a result, at low temperatures, Imχ(Q,ω) has two peaks far and slightly below E_g as observed in Zn-doped YBa₂Cu₃O_6.97. In addition, because of the enhancement of the low-energy AF spin fluctuations, the nuclear spin-lattice relaxation rate on Cu ((1/T₁T)_Cu) also increases at low temperatures in contrast to the case of the clean superconductivity. This result can explain the recent experiment on (1/T₁T)_Cu in Zn-doped YBa₂Cu₄O₈.