  The magnetic ordering of the hexagonal multiferroic compound YbMnO$_3$ has
been studied between 100 K and 1.5 K by combining neutron powder diffraction,
$^{170}$Yb M\"ossbauer spectroscopy and magnetization measurements. The Yb
moments of the two crystallographic sites order at two different temperatures,
the $4b$ site together with the Mn moments (at $T_N \simeq$85 K) and the $2a$
site well below (at 3.5 K). The temperature dependences of the Mn and Yb
moments are explained within a molecular field model, showing that the $4b$ and
$2a$ sites order via Yb-Mn and Yb-Yb interactions respectively. A simple
picture taking into account the local Mn environment of the Rare earth R ($4b$)
ion is proposed to couple R and Mn orders in hexagonal RMnO$_3$ manganites. The
nature and symmetry of the R-Mn interactions yielding the R order are
discussed.
