  Recently, the NANOGrav, PPTA, EPTA and CPTA collaborations reported
compelling evidence of the existence of the Stochastic Gravitational-Wave
Background (SGWB). The amplitude and spectrum of this inferred
gravitational-wave background align closely with the astrophysical predictions
for a signal originating from the population of supermassive black-hole
binaries. In light of these findings, we explore the possibility to detect dark
matter spikes surrounding massive black holes, which could potentially impact
the gravitational-wave waveform and modulate the SGWB. We demonstrate that the
SMBH binary evolution induced by the combined effects of GW radiation and the
dynamical friction of the dark matter spike exhibits detectable manifestations
within the nHz frequency range of the SGWB.
