  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 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 approximation. Although
the non-interacting 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 Bogoliubov Fermi
surface, resulting in robust upturns when the interaction is strong. Our
results suggest that in addition to the presence of Bogoliubov Fermi surfaces,
correlation and multiband physics also play important roles in the system's low
energy excitations.
