  We report muon-spin rotation, heat capacity, magnetization, and ac magnetic
susceptibility measurements of the layered spin-1/2 antiferromagnet NaNiO2.
These show the onset of long-range magnetic order below T_N = 19.5K. Rapid muon
depolarization persisting to about 5K above T_N is consistent with the presence
of short-range magnetic order. The temperature and frequency dependence of the
ac susceptibility suggests that magnetic clusters persist above 25K in the
paramagnetic state and that their volume fraction decreases with increasing
temperature. A frequency dependent peak in the ac magnetic susceptibility at
T_sf = 3K is observed, consistent with a slowing of spin fluctuations at this
temperature. A partial magnetic phase diagram is deduced.
