Atomic-scale magnetic modeling of oxide nanoparticles

We present a method for atomic-scale modeling of the magnetic behavior of ionic magnetic solids. Spin distributions and net magnetic moments are calculated for nanoparticles of ferrimagnetic ${\mathrm{NiFe}}_2{\mathrm{O}}_4$ and $\gamma -{\mathrm{Fe}}_2{\mathrm{O}}_3,$ and antiferromagnetic NiO as a function of applied field. Calculations incorporate crystal structures and exchange parameters determined from bulk data, bulk anisotropy for core spins, reasonable estimates for the anisotropy of surface spins, and finite temperatures simulated by random perturbations of spins. Surface spin disorder was found in the case of ferrimagnetic spinel nanoparticles, due to broken exchange bonds at the surface. The calculations also demonstrate that surface anisotropy enhances the coercivity of such particles only when surface spin disorder is present. Simulated thermal perturbations were used to characterize the distribution of energy barriers between surface spin states of such particles. The distribution of barriers can explain the macroscopic quantum tunneling like magnetic relaxation at low temperatures found experimentally. Calculations on NiO nanoparticles predict eight, six, or four-sublattice spin configurations in contrast to the two-sublattice configuration accepted for bulk NiO. Relatively weak coupling between the multiple sublattices allows a variety of reversal paths for the spins upon cycling the applied field, resulting in large coercivities and loop shifts, in qualitative agreement with experiment.