We use inelastic neutron scattering (INS) to study the spin excitations in partially detwinned NaFe$_{0.985}$Co$_{0.015}$As which has coexisting static antiferromagnetic (AF) order and superconductivity ($T_c=15$ K, $T_N=30$ K). In previous INS work on a twinned sample, spin excitations form a dispersive sharp resonance near $E_{r1}=3.25$ meV and a broad dispersionless mode at $E_{r1}=6$ meV at the AF ordering wave vector ${bf Q}_{rm AF}={bf Q}_1=(1,0)$ and its twinned domain ${bf Q}_2=(0,1)$. For partially detwinned NaFe$_{0.985}$Co$_{0.015}$As with the static AF order mostly occurring at ${bf Q}_{rm AF}=(1,0)$, we still find a double resonance at both wave vectors with similar intensity. Since ${bf Q}_1=(1,0)$ characterizes the explicit breaking of the spin rotational symmetry associated with the AF order, these results indicate that the double resonance cannot be due to the static and fluctuating AF orders, but originate from the superconducting gap anisotropy.
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