Spin-resonance modes (SRM) are taken as evidence for magnetically driven pairing in Fe-based superconductors, but their character remains poorly understood. The broadness, the splitting and the spin-space anisotropies of SRMs contrast with the mostly accepted interpretation as spin excitons. We study hole-doped Ba$_{1-x}$Na$_x$Fe$_2$As$_2$ that displays a spin reorientation transition. This reorientation has little impact on the overall appearance of the resonance excitations with a high-energy isotropic and a low-energy anisotropic mode. However, the strength of the anisotropic low-energy mode sharply peaks at the highest doping that still exhibits magnetic ordering resulting in the strongest SRM observed in any Fe-based superconductor so far. This remarkably strong SRM is accompanied by a loss of about half of the magnetic Bragg intensity upon entering the SC phase. Anisotropic SRMs thus can allow the system to compensate for the loss of exchange energy arising from the reduced antiferromagnetic correlations within the SC state.
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