Symmetries and their breaking mechanisms are fundamental in nuclear physics with spin symmetry (SS) and pseudospin symmetry (PSS) playing key roles in nucleon and antinucleon spectra. While PSS in nucleons has been extensively studied, the manifestation of SS in antinucleon resonances—critical for exotic nuclei, where resonant states dominate near drip lines—remains unexplored. Here, we present the first systematic investigation of SS in antineutron resonant states within nuclei using relativistic mean-field theory combined with the complex momentum representation method, focusing on ${}^{40}\mathrm{Ca}$ with Woods-Saxon potentials. Our results reveal pronounced near-degeneracy in energy and width for resonant spin doublets, confirming robust SS preservation in antineutron resonances. Dirac spinor analysis shows that upper components $f\left(r\right)$ exhibit near-perfect degeneracy. SS quality improves near the continuum threshold, aligning with threshold-driven symmetry restoration. Sensitivity analysis demonstrates that a shallower potential (reduced $|{\mathrm{\Sigma }}_0|$) enhances SS, while larger diffuseness ($a$) or radius ($R$) degrades it with $\mathrm{\Delta }\mathrm{\Gamma }$ exhibiting resonance-type-dependent trends. These results establish the first systematic evidence for SS in antineutron resonances, advancing our understanding of nuclear structure and providing benchmarks for future studies of antimatter-nucleus interactions at facilities like GSI-FAIR.

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• Nuclear forces
• Nuclear structure & decays
• 39 ≤ A ≤ 58
• Symmetries