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Here, by conducting a systematic $^{89}$Y NMR study, we explore the nature ofthe magnetic ground state in a newly discovered iron-based superconductorYFe$_2$Ge$_2$. An incoherent-to-coherent crossover due to the Hund's couplinginduced electronic correlation is revealed below the crossover temperature$T^*\sim 75\pm15\,\mathrm{K}$. During the electronic crossover, both the Knightshift ($K$) and the bulk magnetic susceptibility ($\chi$) exhibit a similarnonmonotonic temperature dependence, and a so-called Knight shift anomaly isalso revealed by a careful $K$-$\chi$ analysis. Such an electronic crossoverhas been also observed in heavily hole-doped pnictide superconductors\emph{A}Fe$_2$As$_2$ (\emph{A} = K, Rb, and Cs), which is ascribed to theHund's coupling induced electronic correlation. Below $T^*$, the spin-latticerelaxation rate divided by temperature $(1/T_1T)$ shows a similar suppressionas the Knight shift, suggesting the absence of critical spin fluctuations. Thisseems to be in conflict with a predicted magnetic quantum critical point (QCP)near this system. However, considering a $\mathbf{q}$-dependent "filter" effecton the transferred hyperfine field, a predominant spin fluctuation with A-typecorrelation would be perfectly filtered out at $^{89}$Y sites, which isconsistent with the recent inelastic neutron scattering results. Therefore, ourresults confirm that, through a Hund's coupling induced electronic crossover,the magnetic ground state of YFe$_2$Ge$_2$ becomes close to an itinerantmagnetic QCP with A-type spin fluctuations. In addition, the possiblesuperconducting pairing due to spin fluctuations is also discussed.

Approaching itinerant magnetic quantum criticality through a Hund's coupling induced electronic crossover in the YFe$_2$Ge$_2$ superconductor