Superparamagnetic dynamics and blocking transition in Fe 3 O 4 nanoparticles probed by vibrating sample magnetometry and muon spin relaxation

The magnetic properties of ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ nanoparticle assemblies have been investigated in detail through a combination of vibrating sample magnetometry (VSM) and muon spin relaxation ($\ensuremath{\mu}\mathrm{S}\mathrm{R}$) techniques. Two samples with average particle sizes of 5 and 20 nm, respectively, were studied. For both samples, the VSM and $\ensuremath{\mu}\mathrm{S}\mathrm{R}$ results exhibit clear signatures of superparamagnetism at high temperature and magnetic blocking at low temperature. The $\ensuremath{\mu}\mathrm{S}\mathrm{R}$ data demonstrate that the transition from the superparamagnetic to the blocked state occurs gradually throughout the sample volume over an extended temperature range due to the finite particle size distribution of each nanoparticle batch. The transition occurs between approximately 3 and 45 K for the 5-nm nanoparticles and 150 and 300 K for the 20-nm nanoparticles. The VSM and $\ensuremath{\mu}\mathrm{S}\mathrm{R}$ data are further analyzed to yield estimates of microscopic magnetic parameters including the nanoparticle spin-flip activation energy ${E}_{A}$, magnetic anisotropy $K$, and intrinsic nanoparticle spin reversal attempt time ${\ensuremath{\tau}}_{0}$. These results highlight the complementary information about magnetic nanoparticles that can be obtained by bulk magnetic probes such as magnetometry and local magnetic probes such as $\ensuremath{\mu}\mathrm{S}\mathrm{R}$.