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Due to their non-toxicity and their ability to be functionalized, magnetite (Fe3O4) nanoparticles (NPs) are good candidates for a variety of biomedical applications. To better implement their applications, it is crucial to well understand the basic structural and magnetic properties of the NPs in correlation with their synthesis method. Here, we show interesting properties of Fe3O4 NPs of various sizes ranging from 5 to 100 nm and the dependence of these properties on particle size and preparation method. One synthetic method based on heating Fe(acac)3 with oleic acid consistently gives 5 ± 1 nm NPs. A second method using the thermal decomposition of Fe(oleate)3 in oleic acid led to larger NPs, greater than 8 nm in size. Increasing the amount of oleic acid caused the average NP size to slightly increase from 8 to 10 nm. Increasing both the reaction temperature and the reaction time caused the NP size to drastically increase from 10 to 100 nm. Powder X-ray diffraction and electron-microscopy imaging show a pure single crystalline Fe3O4 phase for all NPs smaller than 50 nm and spherical in shape. When the NPs get larger than 50 nm, they notably tend to form faceted, FeO core–Fe3O4 shell structures. Magnetometry data collected in various field-cooling conditions show a pure superparamagnetic (SPM) behavior for all NPs smaller than 20 nm. The observed blocking temperature, $T_{B}$ , gradually increases with NP size from about 25–150 K. In addition, the Verwey transition is observed with the emergence of a strong narrow peak at 125 K in the magnetization curves when larger NPs are present. Our data confirm the vanishing of the Verwey transition in smaller NPs. Magnetization loops indicate that the saturating field drastically decreases with NP size. While larger NPs show some coercivity ( $H_{c}$ ) up to 30 mT at 400 K, NPs smaller than 20 nm show no coercivity ( $H_{c} = 0$ ), confirming their pure SPM behavior at high temperature. Upon cooling below $T_{B}$ , some of the SPM NPs gradually show some coercivity, with $H_{c}$ reaching 45 mT at 5 K for the 10 nm NPs, indicating emergent interparticle couplings in the blocked state.

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 $\ensuremath{\mu}\mathrm{S}\mathrm{R}$.

Magnetic frustration can produce exotic spin configurations and dynamics. Here, the authors explore the seemingly simple competition between ferromagnetic nearest- and antiferromagnetic next-nearest neighbor interactions along Ising spin chains, as realized in the magnetoelectric compound Lu${}_{2}$CoMnO${}_{6}$. Commonly, this situation is described by the axial next-nearest-neighbor Ising model. For the first time, the authors measure and calculate its correlated magnetic dynamics, resulting from a characteristic fractal set of first-order phase boundaries. Experiments and Monte Carlo simulations reveal a dynamics slowdown while approaching the phase transition regime.