The magnetic properties of LixN1-xO compounds with x ranging between 0.4 an
d 0.49 are investigated. Magnetization and ac susceptibility measured at te
mperatures between 2 K and 300 K reveal a high sensitivity to x, the excess
lithium concentration. We introduce a percolation model describing the for
mation of Ni clusters and use an Ising model to simulate their magnetic pro
perties. Numerical results, obtained by a Monte Carlo technique, are compar
ed to the experimental data. We show the existence of a critical concentrat
ion, x(c) = 0.432, locating the Ni percolation threshold. The system is sup
erparamagnetic for x > x(c), while it is ferrimagnetic for x < x(c). The 18
0 degrees Ni-O-Ni interplane superexchange coupling J(perpendicular to) sim
ilar or equal to -110 K is confirmed to be the predominant magnetic interac
tion. From the low-temperature behavior, we find a clear indication of a 90
degrees Ni-O-Ni intraplane antiferromagnetic interaction J(parallel to) si
milar or equal to -1.5 K, which implies magnetic frustration.