$^{75}$As and $^{45}$Sc NMR measurements unravel the electronic state for Fe-based superconductors with perovskite-type blocking layers Ca$_4$(Mg,Ti)$_3$Fe$_2$As$_2$O$_{8-y}$ ($T_c^{onset}=47$ K) and Ca$_5$(Sc,Ti)$_4$Fe$_2$As$_2$O$_{11-y}$ ($T_c^{onset}=41$ K). In Ca$_5$(Sc,Ti)$_4$Fe$_2$As$_2$O$_{11-y}$, the nuclear spin relaxation rate $1/T_1$ shows pseudogap behavior below $sim80$ K, suggesting that the electronic state is similar to that of LaFeAs(O,F) system with moderate electron doping. The presence of the pseudogap behavior gives an interpretation that the hole-like band (so-called $gamma$ pocket) is located just below the Fermi level from the analogy to LaFeAs(O,F) system and the disappearance of the $gamma$ pocket yields the suppression of the low-energy spin fluctuations. On the other hand, in Ca$_4$(Mg,Ti)$_3$Fe$_2$As$_2$O$_{8-y}$ satisfying the structural optimal condition for higher $T_c$ among the perovskite systems, the extrinsic contribution, which presumably originates in the Ti moment, is observed in $1/T_1T$; however, the moderate temperature dependence of $1/T_1T$ appears by its suppression under high magnetic field. In both systems, the high $T_c$ of $sim40$ K is realized in the absence of the strong development of the low-energy spin fluctuations. The present results reveal that the structural optimization does not induce the strong development of the low-energy spin fluctuations. If we consider that superconductivity is mediated by spin fluctuations, the structural optimization is conjectured to provide a benefit to the development of the high-energy spin fluctuations irrespective to the low-energy part.
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