Dynamic susceptibility evidence of surface spin freezing in ultrafine NiFe₂O₄nanoparticles

Abstract

We investigated the dynamic behavior of ultrafine NiFe2O4 nanoparticles (average size D = 3.5 nm) that exhibit anomalous low temperature magnetic properties such as low saturation magnetization and high-field irreversibility in both M(H) and ZFC-FC processes. Besides the expected blocking of the superspin, observed at T1 approximately 45 K, the system undergoes a magnetic transition at T2 approximately 6 K. For the latter, frequency- and temperature-resolved dynamic susceptibility data reveal characteristics that are unambiguously related to collective spin freezing: the relative variation (per frequency decade) of the in-phase susceptibility peak temperature is approximately 0.025, critical dynamics analysis yields an exponent znu = 9.6 and a zero-field freezing temperature T(F) = 5.8 K, and, in a magnetic field, T(F)(H) is excellently described by the de Almeida-Thouless line delta T(F) = 1 - T(F)(H)/T(F) alpha H(2/3). Moreover, out-of-phase susceptibility versus temperature datasets collected at different frequencies collapse on a universal dynamic scaling curve. All these observations indicate the existence of a spin-glass-like surface layer that surrounds the superparamagnetic core and undergoes a transition to a frozen state upon cooling below 5.8 K.