  Resonant-magnetic x-ray scattering (RMXS) near the vanadium
$L_{2,3}$-absorption edges has been used to investigate the low temperature
magnetic structure of high quality \bvs\ single crystals. Below $T_N$ = 31 K,
the strong resonance revealed a triple-incommensurate magnetic ordering at wave
vector (0.226 0.226 $\xi$) in the hexagonal notation, with $\xi$ = 0.033. The
simulations of the experimental RMXS spectra with a time-dependent density
functional theory indicate an antiferromagnetic order with the spins polarized
along $a$ in the monoclinic structure.
