Christopher R. Pike

Characterizing interactions in fine magnetic particle systems using first order reversal curves

We demonstrate a powerful and practical method of characterizing interactions in fine magnetic particle systems utilizing a class of hysteresis curves known as first order reversal curves. This method is tested on samples of highly dispersed magnetic particles, where it leads to a more detailed understanding of interactions than has previously been possible. In a quantitative comparison between this method and the δM method, which is based on the Wohlfarth relation, our method provides a more precise measure of the strength of the interactions. Our method also has the advantage that it can be used to decouple the effects of the mean interaction field from the effects of local interaction field variance.

First‐order reversal curve diagrams: A new tool for characterizing the magnetic properties of natural samples

Paleomagnetic and environmental magnetic studies are commonly conducted on samples containing mixtures of magnetic minerals and/or grain sizes. Major hysteresis loops are routinely used to provide information about variations in magnetic mineralogy and grain size. Standard hysteresis parameters, however, provide a measure of the bulk magnetic properties, rather than enabling discrimination between the magnetic components that contribute to the magnetization of a sample. By contrast, first-order reversal curve (FORC) diagrams, which we describe here, can be used to identify and discriminate between the different components in a mixed magnetic mineral assemblage. We use magnetization data from a class of partial hysteresis curves known as first-order reversal curves (FORCs) and transform the data into contour plots (FORC diagrams) of a two-dimensional distribution function. The FORC distribution provides information about particle switching fields and local interaction fields for the assemblage of magnetic particles within a sample. Superparamagnetic, single-domain, and multidomain grains, as well as magnetostatic interactions, all produce characteristic and distinct manifestations on a FORC diagram. Our results indicate that FORC diagrams can be used to characterize a wide range of natural samples and that they provide more detailed information about the magnetic particles in a sample than standard interpretational schemes which employ hysteresis data. It will be necessary to further develop the technique to enable a more quantitative interpretation of magnetic assemblages; however, even qualitative interpretation of FORC diagrams removes many of the ambiguities that are inherent to hysteresis data.

An investigation of multi-domain hysteresis mechanisms using FORC diagrams

First-order reversal curve (FORC) diagrams provide a sensitive means of probing subtle variations in hysteresis behaviour, and can help advance our understanding of the mechanisms that give rise to hysteresis. In this paper, we use FORC diagrams to study hysteresis mechanisms in multi-domain (MD) particles. The classical domain wall (DW) pinning model due to Neel [Adv. Phys. 4 (1955) 191] is a phenomenological one-dimensional model in which a pinning function represents the interactions of a DW with the surrounding medium. Bertotti et al. [J. Appl. Phys. 85 (1999a) 4355] modelled this pinning function as a random Wiener–Levy (WL) process, where particle boundaries are neglected. The results of Bertotti et al. [J. Appl. Phys. 85 (1999a) 4355] predict a FORC diagram that consists of perfectly vertical contours, where the FORC distribution decreases with increasing microcoercivity. This prediction is consistent with our experimental results for transformer steel and for annealed MD magnetite grains, but it is not consistent with results for our MD grains that have not been annealed. Here, we extend the DW pinning model to include particle boundaries and an Ornstein–Uhlenbeck (OU) random process, which is more realistic that a WL process. However, this does not help to account for the hysteresis behaviour of the unannealed MD grains. We conclude that MD hysteresis is more complicated than the physical picture provided by the classical one-dimensional pinning model. It is not known what physical mechanism is responsible for the breakdown of the classical DW pinning model, but possibilities include DW interactions, DW nucleation and annihilation, and DW curvature.

Micromagnetic and Preisach analysis of the First Order Reversal Curves (FORC) diagram

The First Order Reversal Curve (FORC) diagrams of interacting single-domain ferromagnetic particle systems have been found experimentally to contain negative regions. In this paper, we use micromagnetic and phenomenological (Preisach-type) models to help explain the occurrence of these negative regions. In Preisach-type modeling, the position of the negative region is correlated with the sign of the mean-field interactions. In micromagnetic modeling, the position of the negative region is correlated with the spatial arrangement of the particles in the model.

An investigation of magnetic reversal in submicron-scale Co dots using first order reversal curve diagrams

First order reversal curve (FORC) diagrams are a powerful method of investigating the physical mechanisms giving rise to hysteresis in magnetic systems. We have acquired FORC diagrams for an array of submicron-scale Co dots fabricated by interference lithography. These dots reverse magnetization through the nucleation and annihilation of a single-vortex state. Using FORC diagrams, we are able to obtain precise values for the nucleation and annihilation fields involved in magnetic reversal. Our results indicate, however, that there are actually two distinct paths for vortex annihilation: When a complete magnetic reversal takes place, a vortex enters on one side of a dot and exits out the opposite side. But if the magnetization is returned to its original orientation before a complete reversal has occurred, then the vortex will exit on the same side from which it has entered. We are unable to obtain a precise field value for this later path of annihilation; however, it is shown that, statistically, the vort...

The effect of magnetic interactions on low temperature saturation remanence in fine magnetic particle systems

In studies of fine magnetic particle systems, saturation remanence is often measured during warming from liquid helium temperature in order to determine the distribution of blocking temperatures. These data have usually been treated as if they are unaffected by magnetic interactions. However, this treatment is often inconsistent with the experimental data. Furthermore, the thermal decay of saturation remanence often gives values for the mean blocking temperature that are inconsistent with other measurements, such as low temperature ac susceptibility and zero-field-cooled magnetization curves. As an alternative interpretation of these remanence data, we suggest that interactions destabilize the saturation remanence state and accelerate its decay with increasing temperature. As a result, the blocking temperatures associated with the thermal decay of remanence are effectively reduced. We have modeled the effects of interactions on low temperature saturation remanence data using a simple mean interaction fiel...

Hysteresis loops of Co?Pt perpendicular magnetic multilayers

We develop a phenomenological model to study magnetic hysteresis in two samples designed as possible perpendicular recording media. A stochastic cellular automaton model captures cooperative behaviour in the nucleation of magnetic domains. We show how this simple model turns broad hysteresis loops into loops with sharp drops like those observed in these samples, and explains their unusual features. We also present, and experimentally verify, predictions of this model, such as the temperature dependence of the hysteresis loop shape, and the existence and time dependence of drops in first-order reversal curves. We suggest how insights from this model may apply more generally.

Reversal-field memory in magnetic hysteresis

We report results demonstrating a singularity in the hysteresis of magnetic materials, the reversal-field memory effect. This effect creates a nonanalyticity in the magnetization curves at a particular point related to the history of the sample. The microscopic origin of the effect is associated with a local spin-reversal symmetry of the underlying Hamiltonian. We show that the presence or absence of reversal-field memory distinguishes two widely studied models of spin glasses (random magnets).