Monte Carlo study of the superspin glass behavior of interacting ultrasmall ferrimagnetic nanoparticles

The magnetism of a dense assembly of ultrasmall ferrimagnetic nanoparticles exhibits unique features due to the combination of intraparticle and strong interparticle interactions. To model such system we need to account for the internal particle structure and the short- and long-range interparticle interactions. We have developed a mesoscopic model for the particle assembly that includes three spins (two for the surface and one for the core) for the description of each nanoparticle, interparticle dipolar interactions and the interparticle exchange interactions for the nanoparticles in contact. The temperature dependence of the observed exchange bias effect, due to exchange coupling at the interface between core/surface spins and the interparticle exchange coupling, and the zero-field-cooled–field-cooled magnetization vs temperature curves have been investigated using the Monte Carlo simulation technique with the implementation of the Metropolis algorithm. Our simulations reproduce well the experimental data of ultrasmall $\sim 2$-nm $\mathrm{Mn}{\mathrm{Fe}}_2{\mathrm{O}}_4$ nanoparticles, confirming the close relationship between the superspin glass state and the exchange-bias effect in dense nanoparticle systems, owing to the interplay between the intraparticle structure and the interparticle effects.

Figure 1

Schematic representation of the spin structure of a pair of nanoparticles and the intra- and interparticle interactions.

Figure 2

Experimental data (upper panel) and Monte Carlo simulations (lower panel) of the ZFC-FC magnetization curves at a low (a), (c) and a high (b), (d) applied field.

Figure 3

Monte Carlo simulations of the ZFC magnetization curves for applied field $H_{\mathrm{app}}=0.03$ for the simulated system (a); without including intraparticle characteristics $(j_{\mathrm{inter}}=0)$ (b); without including exchange-interparticle interactions $(j_{\mathrm{inter}}=0)$ (c); and without including dipolar interparticle interactions $(g=0)$ (d).

Figure 4

Monte Carlo simulations (a), (b) and experimental data (c), (d) for the temperature dependence of $H_C$ and $H_{ex}$ (a), (c) and the hysteresis loops (b), (d) after a field-cooling procedure (black line). The hysteresis loops after a cooling procedure without any applied field are also presented (red line) at $T=0.01$ (simulations) and $T=5\mathrm{K}$ (experiments).

Figure 5

Monte Carlo simulations of the hysteresis loops after a field-cooling procedure for the simulated system (a); for the case that we do not include (b) intraparticle interactions $(j_{\mathrm{inter}}=0)$; (c) exchange-interparticle $(j_{\mathrm{inter}}=0)$ and (d) interparticle dipolar interactions, at temperature $T=0.01$.