  We investigated the paramagnetic resonance in single crystals of LiCuVO$_4$
with special attention to the angular variation of the absorption spectrum. To
explain the large resonance linewidth of the order of 1 kOe, we analyzed the
anisotropic exchange interaction in the chains of edge-sharing CuO$_6$
octahedra, taking into account the ring-exchange geometry of the
nearest-neighbor coupling via two symmetric rectangular Cu-O bonds. The
exchange parameters, which can be estimated from theoretical considerations,
nicely agree with the parameters obtained from the angular dependence of the
linewidth. The anisotropy of this magnetic ring exchange is found to be much
larger than it is usually expected from conventional estimations which neglect
the bonding geometry. Hence, the data yield the evidence that in copper oxides
with edge-sharing structures the role of the orbital degrees of freedom is
strongly enhanced. These findings establish LiCuVO$_4$ as one-dimensional
compound at high temperatures.
  PACS: 76.30.-v, 76.30.Fc, 75.30.Et
