Fine Magnetic Particle Systems Research Articles

An Automatic Model Selection‐Based Machine Learning Framework to Estimate FORC Distributions

AbstractFirst‐order reversal curve (FORC) distributions are a powerful diagnostic tool for characterizing and quantifying magnetization processes in fine magnetic particle systems. Estimation of FORC distributions requires the computation of the second‐order mixed derivative of noisy magnetic hysteresis data. This operation amplifies measurement noise, and for weakly magnetic systems, it can compromise estimation of a FORC distribution. Previous processing schemes, which are based typically on local polynomial regression, have been developed to smooth FORC data to suppress detrimental noise. Importantly, the smoothed FORC distribution needs to be consistent with the measurement data from which it was estimated. This can be a challenging task even for expert users, who must adjust subjectively parameters that define the form and extent of smoothing until a “satisfactory” FORC distribution is obtained. For nonexpert users, estimation of FORC distributions using inappropriate smoothing parameters can produce distorted results corrupted by processing artifacts, which can lead to spurious inferences concerning the magnetic system under investigation. We have developed a statistical machine learning framework based on a probabilistic model comparison to guide the estimation of FORC distributions. An intuitive approach is presented that reveals regions of a FORC distribution that may have been smoothed inappropriately. An associated metric can also be used to compare data preparation and local regression schemes to assess their suitability for processing a given FORC data set. Ultimately, our approach selects FORC smoothing parameters in a probabilistic fashion, which automates the derivative estimation process regardless of user expertise.

Understanding fine magnetic particle systems through use of first-order reversal curve diagrams

Our research on FORC diagrams has been supported over the years by the U.S. National Science Foundation, the UK Natural Environment Research Council, the European Union, the Royal Society of London, and the Australian Research Council (grant DP120103952).

Non-equilibrium dynamics in fine magnetic particle systems

Extended dynamics (broader than Debye relaxation) occurs in fine magnetic particle systems because of the particle size distribution and the influence of interparticle interaction. In dilute negligibly interacting systems the broadening of the relaxation is governed by the effective anisotropy distribution of the particles. In dense systems, however, interparticle interaction alters the nature of the dynamics and phenomena due to correlation of the particle moments appear. The effects may at a glance only look like a change in the effective anisotropy of the individual particles. However, studies of the dynamics over several decades in observation time reveal that correlation related effects dominate the dynamics on long time scales and extend the maximum relaxation time well beyond the relaxation time of the individual particles. In addition, non-equilibrium dynamics, reminiscent of the ageing phenomenon of spin glasses, appears. Results and analyses of ac susceptibility and magnetic relaxation experiments on various fine magnetic particle systems, ranging from concentrated monodispersed ferrofluids to mechanically alloyed granular materials, are used to illustrate the cooperative nature of the dynamics.

Adaptation and performance of the fast multipole method for dipolar systems

We have developed a new specialized version of the fast multipole method (FMM) for dipolar systems. For this purpose we have derived general expressions of the multipole expansion coefficients (in spherical coordinates) for a system of point dipoles with the potential ϕ dip∼1/ r 2. Our version is especially useful for simulations of fine magnetic particle systems (magnetic nanocomposites, ferrofluids), molecular dipolar fluids or electric dipolar glasses.

Density of energy barriers in fine magnetic particle systems

Using a numerical method based on the minimization of the Onsager-Machlup functional, we have studied the energy barrier distributions in systems of fine magnetic particles with the uniaxial anisotropy and the dipolar interaction. In such systems, the interplay of the single particle anisotropy and the dipolar interaction strength (particle concentration) determines whether the single-particle or collective remagnetization dominates the system behavior (including barrier heights). Our main conclusion is that the influence of the dipolar interparticle interaction on the energy barrier density /spl rho/(E) depends qualitatively on the single particle anisotropy. For low anisotropies /spl rho/(E) shifts toward higher barriers when increasing interaction strength, whereby for moderate and high anisotropy values, the opposite shift takes place. We propose the explanation for this phenomenon.

The Langevin-dynamics simulation of interacting fine magnetic particle systems

Using Langevin dynamics simulations, we have calculated the AC-susceptibility χ= χ′+ iχ″ of disordered fine magnetic particle systems with the dipolar interparticle interaction. We have shown that the shift of the χ″( T)-peak with increasing particle concentration depends qualitatively on the single-particle anisotropy and quantitatively on the precession damping.

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 field model. This model produces remanence curves that have a steep slope at low temperatures, consistent with experimental curves frequently reported in the literature.

Deviation from the superparamagnetic behaviour of fine-particle systems

Studies concerning superparamagnetic behaviour of fine magnetic particle systems were performed using static and radiofrequency measurements, in the range 1–60 MHz. The samples were: a ferrofluid with magnetite particles dispersed in kerosene (sample A), magnetite powder (sample B) and the same magnetite powder dispersed in a polymer (sample C). Radiofrequency measurements indicated a maximum in the imaginary part of the complex magnetic susceptibility, for each of the samples, at frequencies with the magnitude order of tens of MHz, the origin of which was assigned to Néel-type relaxation processes. The static measurements showed a Langevin-type dependence of magnetisation M and of susceptibility χ, on the magnetic field for sample A. For samples B and C deviations from this type of dependence were found. These deviations were analysed qualitatively and explained in terms of the interparticle interactions, dispersion medium influence and surface effects.

Henkel plots of single-domain ferromagnetic particles

The use of Henkel plots as a tool to analyze the type and strength of interaction between particles in fine magnetic particle systems is wide spread. It is commonly accepted that noninteracting systems in general show linear Henkel plots, while interacting systems show curved plots. Using extensive Monte Carlo simulations Henkel plots for noninteracting and interacting systems of particles that show different anisotropies are studied. It is found that a direct relation between linearity and noninteraction exists only for systems of uniaxial particles at low temperatures, while particles with cubic anisotropy always show positive deviation of the Henkel plot in the whole range of temperatures. On the other hand, dipolar interaction always results in negative deviation. In the case of particles with cubic anisotropy and dipolar interaction, the deviation changes gradually from positive to negative with increasing strength of the interaction.

Erasing the glassy state in magnetic fine particles

BaFe10.4Co0.8Ti0.8O19 magnetic fine particles exhibit most of the features attributed to glassy behavior, e.g., irreversibility in the hysteresis loops and in the zero-field-cooling and field-cooling curves extends up to very high fields, and aging and magnetic training phenomena occur. However, the multivalley energy structure of the glassy state can be strongly modified by a field-cooling process at a moderate field. Slow relaxation experiments demonstrate that the intrinsic energy barriers of the individual particles dominate the behavior of the system at high cooling fields, while the energy states corresponding to collective glassy behavior play the dominant role at low cooling fields. @S0163-1829~99!05421-1# Fine magnetic particle systems show most of the features of glassy systems due to the random distribution of anisotropy axis, interparticle interactions, and surface effects. These main features 1 include the flattening of the field cooling susceptibility, 2 an increase in the magnetic viscosity, 3 the occurrence of aging effects, 4 the critical slowing down observed by ac susceptibility, 5 and the increase in the nonlinear susceptibility as the blocking temperature is approached from above. 3 These features do not seem to be associated with a true spin-glass transition. Nevertheless, some authors claim that they reveal the existence of some kind of collective state. 3,6 Although this state is mostly attributed to the frustration induced by magnetic interactions between randomly distributed particles, 6 some studies suggest the dominant role of surface spin disorder. 7 One of the facts that makes the behavior of these systems complex is the coexistence of the freezing associated with frustration and the intrinsic blocking of the particles. Consequently, depending on the time window of the experimental technique, one or both phenomena are observed. For example, blocking effects usu

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.

The anisotropy type effect on the field-cooled initial susceptibilities

We show that the Field-Cooled (FC) and Zero-Field-Cooled (ZFC) initial susceptibilities for fine magnetic particle systems are very sensitive to the particle intrinsic anisotropy type, allowing to distinguish between the cubic and uniaxial anisotropies. The effect of a Debye mean-field on the FC and ZFC initial susceptibilities for various particle anisotropy type is also discussed.

Ferromagnetic Resonance in Granular Co/Ag and NiFe/Ag Multilayers

This paper is concerned with the ways in which ferromagnetic resonance (FMR) may be used to study some properties of ferromagnetic particles in multilayered granular systems. The Co/Ag and NiFe/Ag multilayers have been investigated since the relation between their microstructure and magnetic/magnetotransport properties has already been well documented [1, 2] and, thus, these systems may be regarded as model materials for FMR investigations of fine magnetic particle systems. The samples were prepared by rf sputtering with a deposition rate of about 0.04 nm/s for each component. Two series of samples were made with variable Co or NiFe thickness 0.2 nm <d Co(NiFe) <1.5 nm and a constant Ag thickness of about 2 nm with the number of repetitions between 40 and 200. The structural characterisation were performed with the high- and low-angle X-ray diffraction and X-ray fluorescence. The high-angle X-ray diffraction shows that the multilayer films have coherent interfaces and a highly textured structure with [111] texture and a random orientation of crystallographic directions in the film plane. In low-angle XRD, the Bragg reflections up to the second order were observed. Ferromagnetic resonance spectra were taken at 9.4 GHz at the inplane and perpendicular to plane geometry in fields up to 1.2 T and at temperature range 300 - 600 K. The magnetic properties of our multilayers with ultrathin Co (NiFe) layers are very similar to those already reported in literature [1, 2]. For a nominal thickness of Co or NiFe below 0.6 - 0.7 nm, these multilayers consist of quasi two-dimensional arrays of flat particles embedded in a Ag matrix. With increasing the nominal thickness of Co or NiFe, the granular layers approach the behaviour of quasi-continuous magnetic films. However, a threshold between granular and quasi-continuous structure seems not to be very sharp and the transition region extends over 0.4 - 0.6 nm for the Co/Ag multilayers and even more (0.4 - 0.8 nm) for the NiFe/Ag system. For a very small nominal thickness (0.2 - 0.3 nm for Co/Ag and 0.2 - 0.6 nm for NiFe/Ag) the Co (NiFe) particles exhibit almost pure superparamagnetic behaviour since thermally activated magnetisation fluctuations diminish the apparent anisotropy field nearly to zero [4]. Important factors that determine the positions and shape of FMR spectra are anisotropies, particles size, their distribution [3, 4], a spatial variation of particles orientation around the film normal [5] and, for very fine particles, the influence of thermally activated magnetization reversal [3]. Due to limited space, we confine our discussion to the main points related to the anisotropy, the size effects, and thermally activated fluctuations in our granular Co/Ag multilayers.

Hyperfine field response to RF excitation in superparamagnetic particles

Small magnetic particles with uniaxial magnetic anisotropy are under investigation. A possible mechanism of amplification of the RF field acting on nuclei in fine magnetic particle systems is described. The calculations are based on the exact solution of the proper Fokker-Planck equation using the matrix continued fractions method. This more general approach expands and reaffirms results first obtained with the discrete orientation approximation.

Numerical simulations of quasistatic remagnetization processes in fine magnetic particle systems

Various numerical methods used for simulation of quasistatic remagnetization processes in interacting systems of fine single-domain magnetic particles are analyzed. Among them methods based on the sequential alignment of magnetic moments along the effective field are found to be the fastest, especially in the most interesting case of a small single particle anisotropy when cooperative remagnetization modes play a dominant role. Further it is shown, that the random field approximation (RFA) which is often used to take the interparticle interaction effects into account is valid for large particle anisotropies only. The distribution density of the interaction field is found to transform from the Lorentzian to the Gaussian form with the increasing particle volume fraction. Finally hysteresis loops for a wide range of single-particle anisotropy values and particle concentration are calculated and the crossover from the single particle to the collective behavior with decreasing single particle anisotropy is investigated.

The dependence of coercivity and remanence on dispersion concentration in fine particle systems

Fine magnetic particle systems of CrO 2, γ-Fe 2O 3 and BaFe, dispersed as films have been investigated with concentrations of particles between 5 and 55%. It was found that the coercivities showed minima at about 45% concentration, although remanence measurements, examined by “Henkel plots”, failed to indicate any major change in the interaction effects with concentration.