The aging and memory effects of Fe3O4 nanoparticles have been studied using a series of zero-field cooled (ZFC) and field-cooled (FC) magnetization measurements at various aging protocols. The genuine ZFC magnetization after the ZFC procedure with a single stop and wait process shows an aging dip at the stop temperature on reheating. The depth of the aging dip is dependent on the wait time. The frequency dependence of the AC magnetic susceptibility is indicative of critical slowing down at a freezing temperature T f (= 30.6 ± 1.6 K). The relaxation time τ is described by a power law form with a dynamic critical exponent x (= 8.2 ± 1.0) and a microscopic relaxation time τ0 [= (1.33 ± 0.05) × 10 −9 sec]. The ZFC-peak temperature decreases with increasing magnetic field (H), forming a critical line with an exponent p = 1.78 ± 0.26, close to the de Almeida-Thouless exponent (p = 3/2). These results indicate that the superspin glass phase occurs below T f .

a b s t r a c tThe scaling form of the normalized ZFC and FC susceptibility of superparamagnets (SPMs) is presented as a function of the normalized temperature yð ¼ k B T=K u /VSÞ, normalized magnetic field h (¼H/H K ), and the width s of the log-normal distribution of the volumes of nanoparticles, based on the superparamagnetic blocking model with no interaction between the nanoparticles. Here /VS is the average volume, K u is the anisotropy energy, and H K is the anisotropy field. Main features of the experimental results reported in many SPMs can be well explained in terms of the present model. The normalized FC susceptibility monotonically increases as the normalized temperature y decreases. The normalized ZFC susceptibility exhibits a peak at the normalized blocking temperature y b ð ¼ k B T b =K u /VSÞ, forming the y b vs h diagram. For large s ðs 4 0:4Þ, y b starts to increase with increasing h, showing a peak at h¼ h b , and decreases with further increasing h. The maximum of y b at h ¼h b is due to the nonlinearity of the Langevin function. For small s, y b monotonically decreases with increasing h. The derivative of the normalized FC magnetization with respect to h shows a peak at h¼ 0 for small y. This is closely related to the pinched form of M FC vs H curve around H¼0 observed in SPMs.