Training effect of exchange bias in the $\gamma \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ coated $\mathrm{Fe}$ nanoparticles were studied. The experimental results indicate that the frozen spins in $\gamma \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ shells are responsible for both the horizontal and vertical shifts of the field-cooling hysteresis loops. To understand exchange bias and training effect in the nanoparticles, we modified the Stoner-Wohlfarth model by adding the unidirectional anisotropy energy term to the total energy. It is found that the exchange bias and training effect in the nanoparticles can be well interpreted within the modified model. Since the configuration of the frozen spins was gradually varying as the applied field cycled for the hysteresis loop measurements, the number of the spins frozen along the cooling-field direction decreased, consequently, the exchange bias field $H_E$ became smaller.

• Received 11 January 2004

DOI:https://doi.org/10.1103/PhysRevB.69.214431