We study the dynamics
of spins in the canted antiferromagnetic hematite nanoparticles
$\alpha$-Fe$_2$O$_3$. The system includes an antiferromagnetic exchange ($J$)
between two sublattices as well as the potential dominated by a uniaxial
anisotropy and dissipates through the thermally triggered spin-phonon mechanism.
The exchange $J$ is found to reduce the superparamagnetic relaxation and drive
the incoherent relaxation of transverse spins in the low temperature.
Dynamical properties are semi-quantitatively understood within a role of the
exchange interaction $J$ and agree well with recent inelastic neutron scattering
experiments. As an outlook, if time is allowed, we introduce the further
interesting topics in the same system.