Increasing stripe-type fluctuations in $A$Fe$_{2}$As$_{2}$ ($A$ = K, Rb, Cs) superconductors probed by $^{75}$As NMR spectroscopy

We report $^{75}$As nuclear magnetic resonance measurements on single crystals of RbFe$_{2}$As$_{2}$ and CsFe$_{2}$As$_{2}$. Taking previously reported results for KFe$_{2}$As$_{2}$ into account, we find that the anisotropic electronic correlations evolve towards a magnetic instability in the $A$Fe$_{2}$As$_{2}$ series (with $A$ = K, Rb, Cs). Upon isovalent substitution with larger alkali ions, a drastic enhancement of the anisotropic nuclear spin-lattice relaxation rate and decreasing Knight shift reveal the formation of pronounced spin fluctuations with stripe-type modulation. Furthermore, a decreasing power-law exponent of the nuclear spin-lattice relaxation rate $(1/T_{1})_{H\parallel{ab}}$, probing the in-plane spin fluctuations, evidences an emergent deviation from Fermi-liquid behavior. All these findings clearly indicate that the expansion of the lattice in the $A$Fe$_{2}$As$_{2}$ series tunes the electronic correlations towards a quantum critical point at the transition to a yet unobserved, ordered phase.