Competing effects of Mn and Y doping on the low-energy excitations and phase diagram of La$_{1-y}$Y$_{y}$Fe$_{1-x}$Mn$_x$AsO$_{0.89}$F$_{0.11}$ iron-based superconductors

Muon Spin Rotation ($mu$SR) and $^{19}$F Nuclear Magnetic Resonance (NMR) measurements were performed to investigate the effect of Mn for Fe substitutions in La$_{1-y}$Y$_{y}$Fe$_{1-x}$Mn$_x$AsO$_{0.89}$F$_{0.11}$ superconductors. While for $y = 0$ a very low critical concentration of Mn ($x = 0.2$%) is needed to quench superconductivity, as $y$ increases the negative chemical pressure introduced by Y for La substitution stabilizes superconductivity and for $y= 20$% it is suppressed at Mn contents an order of magnitude larger. A magnetic phase arises once superconductivity is suppressed both for $y$=0 and for $y= 20$%. Low-energy spin fluctuations give rise to a peak in $^{19}$F NMR $1/T_1$ with an onset well above the superconducting transition temperature and whose magnitude increases with $x$. Also the static magnetic correlations probed by $^{19}$F NMR linewidth measurements show a marked increase with Mn content. The disruption of superconductivity and the onset of the magnetic ground-state are discussed in the light of the proximity of LaFeAsO$_{0.89}$F$_{0.11}$ to a quantum critical point.