${}^{75}$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${}_{8\ensuremath{-}y}$ (${T}_{c}^{\text{onset}}=47$ K) and Ca${}_{5}$(Sc,Ti)${}_{4}$Fe${}_{2}$As${}_{2}$O${}_{11\ensuremath{-}y}$ (${T}_{c}^{\text{onset}}=41$ K). In Ca${}_{5}$(Sc,Ti)${}_{4}$Fe${}_{2}$As${}_{2}$O${}_{11\ensuremath{-}y}$, the nuclear spin relaxation rate $1/{T}_{1}$ shows pseudogap behavior below $\ensuremath{\sim}$80 K, suggesting that the electronic state is similar to that of the LaFeAs(O,F) system with moderate electron doping. The presence of the pseudogap behavior gives an interpretation that the holelike band (so-called $\ensuremath{\gamma}$ pocket) is located just below the Fermi level from the analogy to the LaFeAs(O,F) system and the disappearance of the $\ensuremath{\gamma}$ 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${}_{8\ensuremath{-}y}$, 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 $1/{T}_{1}T$; however, the moderate temperature dependence of $1/{T}_{1}T$ appears by its suppression under high magnetic field. In both systems, the high ${T}_{c}$ of $\ensuremath{\sim}$40 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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