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The perovskite nickelates RNiO$_3$ (R: rare-earth) have been studied aspotential multiferroic compounds. A certain degree of charge disproportionationin the Ni ions has been confirmed by high resolution synchrotron powerdiffraction: instead of the nominal Ni$^{3+}$ valence, they can have themixed-valence state Ni$^{(3-\delta)+}$ and Ni$^{(3+\delta)+}$, though agreementhas 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 stateis not yet clear: collinear and non-collinear Ni-O magnetic structures havebeen proposed to explain neutron diffraction and soft X-ray resonantsccattering results in these compounds, and more recently a cantedantiferromagnetic spin arrangement was proposed on the basis of magneticsusceptibility measurements. This scenario is reminiscent of the situation inthe half-doped manganites.  In order to gain insight into the ground state of these compounds, we studiedthe magnetic excitations of some of the different phases proposed, using alocalized spin model for a simplified spin chain which could describe thesecompounds. We first analize the stability of the collinear, orthogonal, andintermediate phases in the classical case. We then explore the quantum groundstate indirectly, calculating the spin excitations obtained for each phase,using the Holstein-Primakoff transformation and the linear spin-waveapproximation. For the collinear and orthogonal ($\theta=\pi/2$) phases, wepredict differences in the magnon spectrum which would allow to distinguishbetween them in future inelastic neutron scattering experiments.

Magnetic excitations of perovskite rare-earth nickelates: RNiO$_3$