Evidence of superspin-glass behavior in Zn0.5Ni0.5Fe2O4 nanoparticles.

We have used dc-magnetization and ac-susceptibility to investigate the superspin dynamics in 9 nm average size Zn(0.5)Ni(0.5)Fe(2)O(4) magnetic particles at temperatures (T) between 3 and 300 K. Dc-magnetization M versus T data collected in a H = 50 Oe magnetic field using a field-cooled-zero-field-cooled protocol indicate that the onset of irreversibility occurs in the vicinity of 190 K. This is confirmed by M versus H|(T) hysteresis loops, as well as by frequency- and temperature-resolved ac-susceptibility data. We demonstrate that this magnetic event is not due to the blocking of individual superspins, but can be unequivocally ascribed to their collective freezing in a spin-glass-like fashion. Indeed, the relative variation (per frequency decade) of the in-phase susceptibility peak temperature is ∼0.032, critical dynamics analysis of this peak shift yields an exponent zν = 10.0 and a zero-field freezing temperature T(g) = 190 K, and, in a magnetic field, Tg(H) is excellently described by the de Almeida-Thouless line δT(g) = 1 - T(g)(H)/T(g) ∝ H(2/3). In addition, out-of-phase susceptibility versus temperature datasets collected at different frequencies collapse on a universal dynamic scaling curve. Finally, memory imprinting during a stop-and-wait magnetization protocol confirms the collective freezing nature of the state below 190 K.