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We present a \asnmr Nuclear Magnetic Resonance (NMR) and resistivity study ofthe effect of 5.5 MeV proton irradiation on the optimal electron doped ($x=$0.068) and overdoped ($x=$ 0.107) Ba(Fe$_{1-x}$Rh$_x$)$_2$As$_2$ iron basedsuperconductors. While the proton induced defects only mildly suppress thecritical temperature and increase residual resistivity in both compositions,sizable broadening of the NMR spectra was observed in all the irradiatedsamples at low temperature. The effect is significantly stronger in theoptimally doped sample where the Curie Weiss temperature dependence of the linewidth suggests the onset of ferromagnetic correlations coexisting withsuperconductivity at the nanoscale. 1/T$_2$ measurements revealed that theenergy barrier characterizing the low energy spin fluctuations of thesecompounds is enhanced upon proton irradiation, suggesting that the defects arelikely slowing down the fluctuations between ($0,\pi)$ and ($\pi$,0) nematicground states.

Effect of proton irradiation on the normal state low-energy excitations of Ba(Fe$_{1-x}$Rh$_x$)$_2$As$_2$ superconductors