  The perovskite nickelates RNiO$_3$ (R: rare-earth) have been studied as
potential multiferroic compounds. A certain degree of charge disproportionation
in the Ni ions has been confirmed by high resolution synchrotron power
diffraction: instead of the nominal Ni$^{3+}$ valence, they can have the
mixed-valence state Ni$^{(3-\delta)+}$ and Ni$^{(3+\delta)+}$, though agreement
has not been reached on the precise value of $\delta$ (e.g. for NdNiO$_3$,
$\delta=0.0$ and $\delta=0.29$ were reported). Also, the magnetic ground state
is not yet clear: collinear and non-collinear Ni-O magnetic structures have
been proposed to explain neutron diffraction and soft X-ray resonant
sccattering results in these compounds, and more recently a canted
antiferromagnetic spin arrangement was proposed on the basis of magnetic
susceptibility measurements. This scenario is reminiscent of the situation in
the half-doped manganites.
  In order to gain insight into the ground state of these compounds, we studied
the magnetic excitations of some of the different phases proposed, using a
localized spin model for a simplified spin chain which could describe these
compounds. We first analize the stability of the collinear, orthogonal, and
intermediate phases in the classical case. We then explore the quantum ground
state indirectly, calculating the spin excitations obtained for each phase,
using the Holstein-Primakoff transformation and the linear spin-wave
approximation. For the collinear and orthogonal ($\theta=\pi/2$) phases, we
predict differences in the magnon spectrum which would allow to distinguish
between them in future inelastic neutron scattering experiments.
