Static and dynamic magnetic properties of spherical magnetite nanoparticles

Abstract

We present a detailed study of static and dynamic magnetic behavior of ${\mathrm{Fe}}_3{\mathrm{O}}_4$ nanoparticles with average particle sizes 〈d〉 ranging from 5 to 150 nm. Bulk-like properties such as saturation magnetization, hyperfine parameters, coercive field, and Verwey transition are observed in 150 nm particles. For decreasing particle size, the Verwey temperature, $T_V,$ shifts down to ∼20 K for $\text{〈d〉=50\hspace{0.17em}}\mathrm{nm}$ and is no longer observable for smaller particles. The smallest particles $\text{(〈d〉=5\hspace{0.17em}}\mathrm{nm})$ display superparamagnetic behavior at room temperature, with transition to a blocked state at $T_B\text{∼45\hspace{0.17em}}\mathrm{K},$ which depends on the applied field. The existence of surface spin disorder can be inferred from the decrease of saturation magnetization $M_S$ at low temperatures, as the average particle size is reduced. This disordered surface did not show effects of exchange coupling to the particle core, as observed from hysteresis loops after field cooling in a 7 T magnetic field. For particles with $\text{〈d〉=5\hspace{0.17em}}\mathrm{nm},$ dynamic ac susceptibility measurements show a thermally activated Arrhenius–Néel dependence of the blocking temperature with applied frequency. The interparticle interactions are found to influence the energy barriers yielding an enhancement of the estimated magnetic anisotropy. From the calculus of the magnetic anisotropy, it is inferred that there is no structural transition from cubic to triclinic symmetry for $\text{〈d〉=5\hspace{0.17em}}\mathrm{nm},$ in agreement with the absence of the Verwey transition. A value $K_1{\text{=4.68×10}}^5\hspace{0.17em}{\mathrm{erg/cm}}^3$ is obtained for the magnetocrystalline anisotropy constant of the cubic phase.