  Neutron scattering studies of single-crystal LiNiPO$_4$ reveal a spontaneous
first-order commensurate-incommensurate magnetic phase transition. Short- and
long-range incommensurate phases are intermediate between the high temperature
paramagnetic and the low temperature antiferromagnetic phases. The modulated
structure has a predominant antiferromagnetic component, giving rise to
satellite peaks in the vicinity of the fundamental antiferromagnetic Bragg
reflection, and a ferromagnetic component giving rise to peaks at small
momentum-transfers around the origin at $(0,\pm Q,0)$. The wavelength of the
modulated magnetic structure varies continuously with temperature. It is argued
that the incommensurate short- and long-range phases are due to
spin-dimensionality crossover from a continuous to the discrete Ising state.
These observations explain the anomalous first-order transition seen in the
magnetoelectric effect of this system.
