The iron-based superconductor FeSe isovalently substituted with S displays an abundance of remarkable phenomena that have not been fully understood, at the center of which are apparent zero-energy excitations in the superconducting state in the tetragonal phase. The phenomenology has been generally consistent with the proposal of the so-called ultranodal states where Bogoliubov Fermi surfaces (BFSs) are present. Recently, nuclear magnetic resonance measurements have seen unusually large upturns in the relaxation rate as temperature decreases to nearly zero in these systems, calling for theoretical investigations. In this paper, we calculate the spin susceptibility of an ultranodal superconductor including correlation effects within the random phase ap- proximation. Although the noninteracting mean-field calculation rarely gives an upturn in the low-temperature relaxation rate within our model, we found that correlation strongly enhances scattering between coherent parts of the BFS, resulting in robust upturns when the interaction is strong. Our results suggest that, in addition to the presence of BFSs, correlation and multiband physics also play important roles in the low-energy excitations of the system.

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• Multiband superconductivity
• Iron-based superconductors
• Random phase approximation