Memory effects in a nanoparticle system: Low-field magnetization and ac susceptibility measurements

Abstract

A dilute magnetic liquid with Co nanoparticles with an average diameter of 5 nm in hexane has been studied systematically following the experimental approach proposed recently for observing memory effects in magnetic nanoparticles. All phenomena reported previously have been observed, which were earlier ascribed to the memory effect. However, the standard experiments for observing memory effects ͑low frequency as susceptibility and low field dc magnetization measurements͒ do not show the memory effect. To understand those observations, very detailed physical pictures, based on the relaxation of the individual particle, are proposed here.

Memory effect and spin-glass-like behavior in Co-Ag granular films

“…In a typical dc memory experiment, one should follow a stop-and-wait protocol consisting of three steps: 14,24 ͑a͒ cool the sample in a zero-field at a constant rate from a temperature, T H , which is much higher than T p , the peak temperature of ZFC curves; ͑b͒ stop the cooling process at a temperature, T w , below T p and wait for t w ͑=6 h, in our experiments͒ and then resume the cooling process down to T base ͑=5 K in our experiments͒; ͑c͒ apply a small field at T base and measure the magnetization with increasing temperature up to T H . The difference between the stop-and-wait ZFC curve and a reference ZFC curve ͑without stopping at T w ͒ at the temperature T w can be attributed to the memory effect.…”

“…We observed that ⌬M depends strongly on the waiting time because of the logarithmic relaxation. 14,41 In addition, it also varies with T w . To reduce the complexity caused by the waiting time and T w , we fix the waiting time to be 2.16ϫ 10 4 seconds ͑i.e., 6 h͒ and the ratio of T w / T p ͑or T w / T F ͒ to be about 0.7, where the magnetic relaxation is neither too slow nor too fast to observe the memory effect.…”

“…12 In a very diluted system, i.e., where interparticle dipole-dipole interactions are negligibly small in comparison with anisotropy energy, the dynamics of particles are well described by the superparamagnetism framework of the Néel-Brown model. 13,14 That is, the flipping rate ͑⌫͒ of the magnetic moment of an individual magnetic particle is only governed by its own anisotropy energy at a given temperature ͑T͒, ⌫͑T͒ = ⌫ 0 exp͑−KV / k B T͒, where ⌫ 0 is the attempt frequency in the order of 10 9 -10 13 ; k B is the Boltzmann constant; K and V are the anisotropy constant and the volume of particle respectively. 15 ⌫͑T͒ decreases exponentially with decreasing temperature.…”

“…Most studies on how dipole-dipole interactions lead to SGL phase in particles systems were carried out by changing the concentration of particles ͑particle-particle distance͒ in the liquid carrier. [1][2][3][4][5][6][7][8][9][10][11]14 Here, we studied the same issue by changing the particle ͑or cluster͒ size and the concentration of solute Co atoms in Ag matrix. We focused on the study of memory effect because it is usually considered as typical characteristics of the spinglass dynamics and has been clearly observed in different ͑canonical͒ spin-glass systems.…”

Non-equilibrium effects in the magnetic behavior of Co3O4 nanoparticles

“…28,33 Absence of aging and memory effects in ZFC protocol confirms that the behavior of Co 3 O 4 nanoparticles is not spin glass like. 6,8,17,18 Thus below T P , observation of a bifurcation in FC and ZFC magnetization and a slow magnetic relaxation seems to correspond to a blocked state as observed in superparamagnetic particles. Presence of memory effects in FC protocol also support this inference.…”