In cuprate superconductors, superconductivity appears below the CDW transition temperature TCDW. However, many-body electronic states under the CDW order are still far from understood. Here, we study the development of the spin fluctuations under the presence of d-wave bond order (BO) with wavevector q = (π/2, 0), (0, π/2), which is derived from the paramagnon interference mechanism in recent theoretical studies. Based on the 4 × 1 and 4 × 4 cluster Hubbard models, the feedback effects between spin susceptibility and self-energy are calculated self-consistently by using the fluctuation-exchange (FLEX) approximation. It is found that the d-wave BO leads to a sizable suppression of the nuclear magnetic relaxation rate 1/T₁. In contrast, the reduction in Tc is small, since the static susceptibility χs(Qs) is affected by the BO just slightly. It is verified that the d-wave BO scenario is consistent with the experimental electronic properties below TCDW.

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