  One of the fundamental interactions that is found in many functional
materials is the spin-phonon coupling (SPC), which is at the heart of many
novel functionalities. The simultaneous presence of multi-magnetic phases makes
SPC even more intriguing. We have used Raman spectroscopy as well as
first-principles methods to investigate the possibility of the appearance of
SPC in Gd-doped Y$_2$CoMnO$_6$ (YGCMO) double perovskite oxide and the
influence of anti-site disorder on the same. YGCMO is found to exhibit
anti-site disorder leading to both ferromagnetic (between Co and Mn) and
anti-ferromagnetic interactions (Co-Co, Mn-Mn, Gd-Co/Mn). An analysis of the
temperature-dependent phonon frequency for the stretching modes of YGCMO,
obtained using RAMAN spectroscopy, indicates that SPC is possibly emerging from
simultaneous presence of ferromagnetic and antiferromagnetic interactions. The
nature of the phonon linewidth and the insulating state of the material
eliminate the role of magnetostriction on the observed anomaly. The spin-phonon
coupling strength comes out to be 0.29 cm$^{-1}$. Our experimental findings are
corroborated by first-principles DFT calculations which indicate the presence
of SPC in ordered YGCMO getting enhanced in the presence of anti-site disorder.
This indicates a strong influence of B-site (Co/Mn) ordering on SPC in the bulk
double perovskite systems. An analysis of the cause behind the enhanced SPC in
the presence of anti-site disorder is also presented.
