We use inelastic neutron scattering to study the fate of the two spin resonance modes in underdoped superconducting NaFe$_{1-x}$Co$_x$As ($x=0.0175$) under applied magnetic fields. While an applied in-plane magnetic field of $B=12$ T only modestly suppresses superconductivity and enhances static antiferromagnetic order, the two spin resonance modes display disparate responses. The spin resonance mode at higher energy is mildly suppressed, consistent with the field effect in other unconventional superconductors. The spin resonance mode at lower energy, on the other hand, is almost completely suppressed. Such dramatically different responses to applied magnetic field indicate distinct origins of the two spin resonance modes, resulting from the strongly orbital-selective nature of spin excitations and Cooper-pairing in iron-based superconductors.
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