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$^{31}$P NMR studies of an iron-based superconductor Ba$_{0.5}$Sr$_{0.5}$Fe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ with $T_\mathrm{c}$ = 29 K

We report $^{31}$P NMR studies of an oriented polycrystalline superconductor of Ba$_{0.5}$Sr$_{0.5}$Fe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ with $x\sim$ 0.4 ($T_\mathrm{c}$ = 29 K) at $T$ = 14$-$325 K and $B_{0}$ = 1 and 5 T. The $^{31}$P Knight shift $K_{ab}$ at $B_{0}\perp c$ shows a nearly $T$-independent uniform spin susceptibility above $T_\mathrm{c}$ and a spin singlet decrease below $T_\mathrm{c}$. The $^{31}$P nuclear spin-lattice relaxation rate 1/$T_{1}$ shows an asymptotic behavior of $a+bT$ ($a$ and $b$ are constants) at $T >$ 100 K and the minimum at 40 K with an upturn toward $T_\mathrm{c}$. The $a$ term in 1/$T_{1}$ indicates the presence of two-dimensional antiferromagnetic spin fluctuations. The negative $θ$ = $-$15 K of the Curie-Weiss-type antiferromagnetic spin susceptibility $χ$($Q$) $\propto$ 1/($T$+$θ$) in the analysis of 1/$T_{1}T$ suggests antiferromagnetic instability in the superconducting state. Discussions are made from the self-consistent renormalization (SCR) theory for the spin fluctuations with interlayer correlation.