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Electron doping evolution of the neutron spin resonance in NaFe$_{1-x}$Co$_{x}$As

Neutron spin resonance, a collective magnetic excitation coupled to superconductivity, is one of the most prominent features shared by a broad family of unconventional superconductors including copper oxides, iron pnictides, and heavy fermions. In this work, we study the doping evolution of the resonances in NaFe$_{1-x}$Co$_x$As covering the entire superconducting dome. For the underdoped compositions, two resonance modes coexist. As doping increases, the low-energy resonance gradually loses its spectral weight to the high-energy one but remains at the same energy. By contrast, in the overdoped regime we only find one single resonance, which acquires a broader width in both energy and momentum, but retains approximately the same peak position even when $T_c$ drops by nearly a half compared to optimal doping. These results suggest that the energy of the resonance in electron overdoped NaFe$_{1-x}$Co$_x$As is neither simply proportional to $T_c$ nor the superconducting gap, but is controlled by the multi-orbital character of the system and doped impurity scattering effect.