  Elastic and inelastic neutron scattering studies of
Li(Ni$_{1-x}$Fe$_{x}$)PO$_4$ single crystals reveal anomalous spin-wave
dispersions along the crystallographic direction parallel to the characteristic
wave vector of the magnetic incommensurate phase. The anomalous spin-wave
dispersion ({\it magnetic soft mode}) indicates the instability of the
Ising-like ground state that eventually evolves into the incommensurate phase
as the temperature is raised. The pure LiNiPO$_4$ system ($x=0$), undergoes a
first-order magnetic phase transition from a long-range incommensurate phase to
an antiferromagnetic ground state at {\it T}$_N$ = 20.8 K. At 20% Fe
concentrations, although the AFM ground state is to a large extent preserved as
that of the pure system, the phase transition is second-order, and the
incommensurate phase is completely suppressed. Analysis of the dispersion
curves using a Heisenberg spin Hamiltonian that includes inter- and in-plane
nearest and next-nearest neighbor couplings reveals frustration due to strong
competing interactions between nearest- and a next-nearest neighbor site,
consistent with the observed incommensurate structure. The Fe substitution only
slightly lowers the extent of the frustration, sufficient to suppress the IC
phase. An energy gap in the dispersion curves gradually decreases with the
increase of Fe content from $\sim$2 meV for the pure system ($x=0$) to
$\sim$0.9 meV for $x=0.2$.

Strongly Correlated Electrons