  We show that LiVCuO4 should be described by strongly ferromagnetically
coupled Heisenberg antiferromagnetic chains (HAC) in sharp contrast with the
effective exchange integrals Ji given in Enderle et al., Phys. Rev. Lett. vol.
104, 237207 (2010), and the main issues of that work, namely, (i) LiVCuO4 is
well described by two weakly ferromagnetically coupled interpenetrating
Heisenberg antiferromagnetic spin-1/2 chains, (ii) the extracted exchange
integrals J1, J2 agree with a previous spin-wave description (Enderle et al.,
Euphys. Lett. vol. 70, 237 (2005)), (iii) the spectral density of inelastic
neutron scattering (INS) above 10 meV is ascribed to a 4-spinon continuum.
Applying exact diagonalization and DMRG methods to fit their INS and
magnetization M(H) data, supported by two independent microscopic methods
(5-band Hubbard model and LSDA+U calculations), we demonstrate that LiCuVO4
exhibits strong inchain frustration with alpha =-J2/J1 < 1, i.e. strong
coupling of the HAC at odds with (i). An alternative phenomenological set in
accord with various experimental results is proposed. In view of the recent
possible discovery of quantum-spin nematics and Bose condensation of two-magnon
bound states (M. Zhitomirsky et al. arXiv:1003.4096v2 (2010), L. Svistov et al.
ibid. 1005.5668v2 (2010)) in LiCuVO4 precise knowledge of the main J-values is
of key importance.
