  We use neutron powder diffraction to investigate the magnetic and crystalline
structure of Cr$_2$GaN. A magnetic phase transition is identified at $T \approx
170$ K, whereas no trace of structural transition is observed down to 6 K.
Combining Rietveld refinement with irreducible representations, the spin
configuration of Cr ions in Cr$_2$GaN is depicted as an incommensurate
sinusoidal modulated structure characterized by a propagating vector
${k}$=(0.365, 0.365, 0). Upon warming up to the paramagnetic state, the
magnetic order parameter closely resembles to the temperature dependence of
$c$-axis lattice parameter, suggesting strong magneto-elastic coupling in this
compound. Therefore, Cr$_2$GaN provides a potential platform for the
exploration of magnetically tuned properties such as magnetoelectric,
magnetostrictive and magnetocaloric effects, as well as their applications.
