  La$_{1.5}$Sr$_{0.5}$NiO$_4$ is well known to have a colossal dielectric
constant ($\varepsilon_R>10^7$). The La$_{1.5}$Sr$_{0.5}$NiO$_4$ nanoparticle
powder was prepared by a combinational method of solid state reaction and
high-energy ball milling. Magnetic measurements show that the material has a
very small magnetic moment and paramagnetic characteristic at room temperature.
The mixture of the nanoparticle powder (40% vol.) and paraffin (60% vol.)
coated in the form of flat layers of different thicknesses ($t$) exhibits
strong microwave absorption resonances in the 4-18 GHz range. The reflection
loss ($RL$) decreases with $t$ and reaches down to -36.7 dB for $t=3.0$ mm. The
impedance matching ($|Z|=Z_0=377$ $\Omega$), rather than the phase matching
mechanism, is found responsible for the resonance observed in the samples with
$1<t\leq3.0$ mm. Further increase of the thickness leads to $|Z|>Z_0$ at all
frequencies and a reduced absorption. The influence of non-metal backing is
also discussed. Our observation suggests that La$_{1.5}$Sr$_{0.5}$NiO$_4$
nanoparticles could be used as good fillers for high performance radar
absorbing material.
