  We investigate ferromagnetic resonance (FMR) modulation in $d$-wave
superconductor (SC)/ferromagnetic insulator (FI) bilayer systems theoretically.
The modulation of the Gilbert damping in these systems reflects the existence
of nodes in the $d$-wave SC and shows power-law decay characteristics within
the low-temperature and low-frequency limit. Our results indicate the
effectiveness of use of spin pumping as a probe technique to determine the
symmetry of unconventional SCs with high sensitivity for nanoscale thin films.
