Non-monotonic field-dependence of the ZFC magnetization peak in some systems of magnetic nanoparticles

We have performed magnetic measurements on a diluted system of gamma-Fe2O3 nanoparticles (~7nm), and on a ferritin sample. In both cases, the ZFC-peak presents a non-monotonic field dependence, as has already been reported in some experiments,and discussed as a possible evidence of resonant tunneling. Within simple assumptions, we derive expressions for the magnetization obtained in the usual ZFC, FC, TRM procedures. We point out that the ZFC-peak position is extremely sensitive to the width of the particle size distribution, and give some numerical estimates of this effect. We propose to combine the FC magnetization with a modified TRM measurement, a procedure which allows a more direct access to the barrier distribution in a field. The typical barrier values which are obtained with this method show a monotonic decrease for increasing fields, as expected from the simple effect of anisotropy barrier lowering, in contrast with the ZFC results. From our measurements on gamma-Fe2O3 particles, we show that the width of the effective barrier distribution is slightly increasing with the field, an effect which is sufficient for causing the observed initial increase of the ZFC-peak temperatures.Comment: LaTeX file 19 pages, 9 postscript figures. To appear in Phys. Rev. B (tentative schedule: Dec.97

Normalization factors for magnetic relaxation of small particle systems in non-zero magnetic field

We critically discuss relaxation experiments in magnetic systems that can be characterized in terms of an energy barrier distribution, showing that proper normalization of the relaxation data is needed whenever curves corresponding to different temperatures are to be compared. We show how these normalization factors can be obtained from experimental data by using the $T \ln(t/\tau_0)$ scaling method without making any assumptions about the nature of the energy barrier distribution. The validity of the procedure is tested using a ferrofluid of Fe_3O_4 particles.Comment: 5 pages, 6 eps figures added in April 22, to be published in Phys. Rev. B 55 (1 April 1997

The role of the alloy structure in the magnetic behavior of granular systems

The effect of grain size, easy magnetization axis and anisotropy constant distributions in the irreversible magnetic behavior of granular alloys is considered. A simulated granular alloy is used to provide a realistic grain structure for the Monte Carlo simulation of the ZFC-FC curves. The effect of annealing and external field is also studied. The simulation curves are in good agreement with the FC and ZFC magnetization curves measured on melt spun Cu-Co ribbons.Comment: 13 pages, 10 figures, submitted to PR

Magnetic relaxation in finite two-dimensional nanoparticle ensembles

We study the slow phase of thermally activated magnetic relaxation in finite two-dimensional ensembles of dipolar interacting ferromagnetic nanoparticles whose easy axes of magnetization are perpendicular to the distribution plane. We develop a method to numerically simulate the magnetic relaxation for the case that the smallest heights of the potential barriers between the equilibrium directions of the nanoparticle magnetic moments are much larger than the thermal energy. Within this framework, we analyze in detail the role that the correlations of the nanoparticle magnetic moments and the finite size of the nanoparticle ensemble play in magnetic relaxation.Comment: 21 pages, 4 figure

Beyond the blocking model to fit nanoparticle ZFC/FC magnetisation curves

We consider the probability of a magnetic nanoparticle to flip its magnetisation near the blocking temperature, and use this to develop quasi-analytic expressions for the zero-field-cooled and field-cooled magnetisation, which go beyond the usual critical energy barrier approach to the superparamagnetic transition. The particles in the assembly are assumed to have random alignment of easy axes, and to not interact. We consider all particles to be of the same size and then extend the theory to treat polydisperse systems of particles. In particular, we find that the mode blocking temperature is at a lower temperature than the peak in the zero-field-cooled magnetisation versus temperature curve, in agreement with experiment and previous rate-equation simulations, but in contrast to the assumption many researchers use to analyse experimental data. We show that the quasi-analytic expressions agree with Monte Carlo simulation results but have the advantage of being very quick to use to fit data. We also give an example of fitting experimental data and extracting the anisotropy energy density K

Magnetic Anisotropic Energy Gap and Strain Effect in Au Nanoparticles

We report on the observation of the size effect of thermal magnetization in Au nanoparticles. The thermal deviation of the saturation magnetization departs substantially from that predicted by the Bloch T3/2-law, indicating the existence of magnetic anisotropic energy. The results may be understood using the uniaxial anisotropy Heisenberg model, in which the surface atoms give rise to polarized moments while the magnetic anisotropic energy decreases as the size of the Au nanoparticles is reduced. There is a significant maximum magnetic anisotropic energy found for the 6 nm Au nanoparticles, which is associated with the deviation of the lattice constant due to magnetocrystalline anisotropy