We have studied the magnetic dynamics in nanocrystalline samples of alpha-F
e2O3 (hematite) and NiO by inelastic neutron scattering. By measuring aroun
d the structural and the antiferromagnetic reflections, we have probed unif
orm and staggered magnetic oscillations, respectively. In the hematite part
icles, we observed a clear double peak in the energy distribution of the an
tiferromagnetic signal, in addition to a quasi-elastic peak. We interpret t
he double peak to represent collective magnetic excitations. Broadening of
the central quasi-elastic peak with increasing temperature is interpreted a
s a sign of superparamagnetic relaxation. Studies of the antiferromagnetic
signal from NiO also show evidence of collective magnetic excitations, but
with a higher energy of the precession states than for hematite. The inelas
tic signal at the structural reflection of NiO presents evidence for unifor
m magnetic oscillations very similar to the antiferromagnetic signal, as is
expected for a simple antiferromagnet. The hematite sample did not show an
y signs of uniform oscillations, although these have been predicted theoret
ically.