  $^{75}$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.
