Correlation, excitation, and relaxation of the antiferromagnetic nanoparticle

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.