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

Abstract

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.

Spin‐Glass Irreversibility Temperature and Magnetic Stabilization in Ferromagnet/Spin‐Glass Bilayers

“…Interestingly, the peak width is not negligible and varies, while no size dispersion is considered. So it comes from the stochastic nature of thermally induced spin reversal in a finite temperature range, consistent with the conclusion drawn by Livesey et al when calculating T B SP in monodisperse samples . As a result, a large K SG deepens energy barriers and traps spins at higher temperatures, meanwhile the high temperature enhances uncertainty of spin reversal, resulting in a short and wide peak.…”

“…In noninteracting nanoparticles, T irr is obtained through measurements of magnetization made in the zero‐field‐cooled (ZFC) and field‐cooled (FC) regimes as a function of temperature . In this kind of experiment, a sample is cooled from a temperature where all particles show super paramagnetic behavior to a target low temperature, then a constant field is applied and the sample is heated to a temperature high enough to observe an initial growth and subsequent decrease of its magnetization.…”

“…Although ZFC/FC curves are easily measured, how to precisely determine phase‐transition‐like temperature between superparamagnetic and blocked states is controversial due to a finite width of transition temperature range . It is well‐known that the ZFC curve is given by net magnetization projection along field of randomly frozen magnetic moments and of polarized superparamagnetic ones.…”

Dynamics of interacting magnetic nanoparticles: effective behavior from competition between Brownian and Néel relaxation

“…Our model can also be used to study the blocking temperature in relation to the field-cooled and zero-field cooled magnetization, extending previous studies on non-interacting MNPs. 34 Some authors found it necessary to include distributions of magnetic anisotropy constants, representing the energy barriers of individual particles. 12 This could be incorporated in the present model by a distribution of L 0 values.…”

“…Let n denote the orientation of the ordering field. We assume that the magnetization remains parallel to n during the relaxation where the field has been switched off, hui = U B n. Assuming furthermore uniaxial symmetry, huui = S 2 nn + (1 À S 2 )I/3, where I denotes the threedimensional unit matrix, we can rewrite eqn (34) as…”