Magnetostatic Interaction Fields Research Articles

FORC signatures and switching-field distributions of dipolar coupled nanowire-based hysterons

Analysis of first-order reversal curves (FORCs) is a powerful tool to probe irreversible switching events in nanomagnet assemblies. As in essence switching events are related to the intrinsic properties of the constituents and their interactions, the resulting FORC diagrams contain much information that can be cross-linked and complex to deconvolute. In order to quantify the relevant parameters that drive the FORC diagrams of arrays of perpendicularly magnetized nanomagnets, we present step-by-step simulations of assemblies of hysterons to determine the specific signatures related to different known inputs. While we explored the consequences of dipolar interactions using either mean field or magnetostatic approaches, we completed by taking the hysteron switching field distribution (SFD) as either normal or lognormal. We demonstrated that the transition between FORC diagrams composed of an isolated interaction field distribution (IFD) and a wishbone shape operates via the SFD deviation, σHsw, in the presence of a weakly dispersed interaction field. In the presence of a magnetostatic interaction field, the IFD profile is peaked and a coercive field distribution (CFD) sums to the IFD as σHsw increases. A transition between IFD + CFD and wishbone shapes is clearly demonstrated as a function of the interaction field deviation σHint. In addition, we demonstrate that whatever the considered cases, σHswcan be quantitatively extracted from the FORC diagrams within an error inferior to 10%. These findings are of interest for dipolar coupled perpendicularly magnetized nanomagnets, as in assemblies of magnetic nanowires and nanopillars, as well as bit patterned media.

Micromagnetic simulation of dynamic magnetic susceptibility and magnetostatic interaction fields of conical-shaped barium ferrite nanodot arrays

In this paper, the dynamic susceptibility spectra and magnetostatic interaction fields of conical-shaped barium ferrite nanodot arrays were systematically simulated based on the 3D object-oriented micromagnetic framework (OOMMF). This unique structure exhibits multi-resonance peaks and the stratified resonance model due to the non-uniform distribution of the demagnetizing field. Furthermore, the calculated the interaction fields of the conical-shaped nanodot arrays illustrate the dependence of the resonance frequency on the distance and size. Consequently, this conical-shaped nanodots array has potential to be applied in microwave-absorbing materials due to the multi-resonance peaks formation and requires precise control of the size and distance, which determine the resonance frequency.

Periodic Boundary Conditions for Finite-Differentiation-Method Fast-Fourier-Transform Micromagnetics**Supported by the National Natural Science Foundation of China under Grant Nos 51171086 and 51371101.

We describe an accurate periodic boundary condition (PBC) called the symmetric PBC in the calculation of the magnetostatic interaction field in the finite-differentiation-method fast-Fourier-transform (FDM-FFT) micromagnetics. The micromagnetic cells in the regular mesh used by the FDM-FFT method are finite-sized elements, but not geometrical points. Therefore, the key PBC operations for FDM-FFT methods are splitting and relocating the micromagnetic cell surfaces to stay symmetrically inside the box of half-total sizes with respect to the origin. The properties of the demagnetizing matrix of the split micromagnetic cells are discussed, and the sum rules of demagnetizing matrix are fulfilled by the symmetric PBC.

Tunable magnetic anisotropy in two-dimensional arrays of Ni80Fe20 elements

Tunable two-fold magnetic anisotropy in two-dimensional arrays of Ni80Fe20 (permalloy) elliptical elements arranged along their long (LA) or short axis (SA) are demonstrated from the measurement of time-resolved magnetization dynamics. The anisotropy field is maximum (minimum) when the elements are closely packed along their LA (SA) and take an intermediate value when they are well separated. Micromagnetic simulations reveal that the centre mode of the ellipse shows the two-fold anisotropy and that the variation in the anisotropy field stems from the strong competition between the shape anisotropy of the constituent elements and the inter-element magnetostatic interaction fields within the arrays.

Nonbinary LDPC Coding and Iterative Decoding System With 2-D Equalizer for TDMR R/W Channel Using Discrete Voronoi Model

A 2-D magnetic recording (TDMR) by shingled magnetic recording (SMR) is one of the most promising technologies for realizing ultra-high areal densities. We have developed the discretized granular medium model with nonmagnetic grain boundaries and the simple writing process considering intergranular exchange fields and magnetostatic interaction fields between grains on the discrete Voronoi model for TDMR. In this paper, the bit-error rate (BER) performance of the iterative decoding system using a nonbinary low-density parity-check (LDPC) code over Galois field GF(q) with the 2-D finite-impulse-response equalizer (2D-FIRE) is obtained via computer simulation using an R/W channel model employing the writing process under TDMR specifications of 4.12 Tb/in2, and it is compared to that with the 1-D FIRE (1D-FIRE). The results show that the BER performance of the nonbinary LDPC coding and iterative decoding system with the 2D-FIRE is better than that with the 1D-FIRE.

Magnetostatic interactions in various magnetosome clusters

Hysteretic properties of dilute assemblies of various types of magnetosome clusters, i.e., linear chains, closed rings, and random three-dimensional (3D) configurations are studied by means of numerical simulation. It is shown that after averaging over random particle positions and random orientations of the particle easy anisotropy axes, there remain only several physical parameters that determine the shape of the assembly hysteresis loop: the cluster topology, the characteristic value of the magnetostatic interaction field, and the number of the nanoparticles within the cluster. The strong magnetostatic interaction between the particles increases significantly the coercive force of an assembly of linear chains or circular rings. On the other hand, for these assemblies, the type of the random anisotropy assumed as well as the number of the particles within the cluster has only minor effect on the hysteresis loop shape. For an assembly of 3D magnetosome clusters, the remanent magnetization shows strong dependence on the volume fractions of magnetic nanoparticles, contrary to the coercive force behavior.

Modeling of Writing Process for Two-Dimensional Magnetic Recording and Performance Evaluation of Two-Dimensional Neural Network Equalizer

Modeling of a simple writing process considering intergranular exchange fields and magnetostatic interaction fields between grains is studied for two-dimensional magnetic recording (TDMR). A new designing method of a two-dimensional neural network equalizer with a mis-equalization suppression function (2D-NNEMS) for TDMR is also proposed. The bit-error rate (BER) performance of a low-density parity-check coding and iterative decoding system with the designed 2D-NNEMS is obtained via computer simulation using a read/write channel model employing the proposed writing process under TDMR specifications of 4 Tb/in <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , and it is compared with those for one- and two-dimensional finite impulse response equalizers (FIREs). It is clarified that the BER performance for the designed 2D-NNEMS is far superior to those for the FIREs.

Influence of magnetic interactions on the anisotropy of magnetic susceptibility: the case of single domain particles packed in globule aggregates

The influence of magnetic interactions on the anisotropy of magnetic susceptibility (AMS) have been largely studied by several theoretical models or experiments. Numerical models have shown that when magnetostatic interactions occur, the distributions of particles over the volume rather than their individual orientations control the AMS. We have shown recently from a comprehensive rock magnetic study and from a theoretical 2-dimensional (2-D) model that single domain particles closely packed in globule aggregates could produce strong local random interaction magnetic fields which could influence the magnetic susceptibility and decrease the degree of anisotropy. In this paper, we first present in detail this 2-D theoretical model and then we extend it to the 3-D case. The possible distribution function of the magnetostatic interaction fields comprises two extreme states: it is either isotropic or ordered. The former case corresponds to the thermal-demagnetized state while the second case corresponds to the alternating field (AF) demagnetized state. We show that when easy axes of magnetization are not uniformly distributed, the degree of anisotropy decreases as the interaction field increases in both AF- and thermal-demagnetized states in 2-D and 3-D geometry. Thus we conclude that random magnetic fields generated by a random arrangement of magnetic particles over the sample volume decrease the degree of anisotropy of AMS and may alter the magnetic fabric.

Size effect of Fe nanoparticles on the high-frequency dynamics of highly dense self-organized assemblies

Molded Fe nanoparticle (NP) assemblies 4 mm × 8 mm × 0.3 mmt in size were fabricated by a uniaxial press from Fe NPs 3 nm to 22 nm in diameter, and their high-frequency dynamics and static properties were investigated. The freezing temperature of the magnetic moment of the assemblies increased from 25 K to over 400 K with an increasing Fe NP diameter, and for particles larger than 8.1 nm, the Fe NP assemblies showed ferromagnetic behavior even at room temperature. For particles smaller than 8.1 nm, on the contrary, the assemblies showed superparamagnetism at room temperature. From the complex magnetic susceptibility spectra of the assemblies normalized by the volume of the Fe NPs, χ′Fe, and χ″Fe, the minimum ferromagnetic resonance frequency, fr (106 MHz), and maximum χ′Fe at 1 MHz (123) were obtained at 8.1 nm. The fr of the Fe NP assembly increased because of an enhanced magnetostatic interaction field between NPs larger than 8.1 nm. For NPs smaller than 8.1 nm, in the superparamagnetic phase, the thermal magnetic field increasingly dominated the effective magnetic field with a decreasing NP diameter. This indicates the existence of a critical diameter for the thermal fluctuation of the moment, which competes with the magnetostatic interactions between the Fe nanoparticles.

Hysteresis and relaxation in granular permanent magnets

Some nontrivial aspects of the magnetic and structural characterization of hard-magnetic nanoparticles are investigated. Dilute ensembles are well-described by mean-field theory, although there is an asymmetry between exchange and magnetostatic interaction fields. Corrections to the mean-field approximation are caused by cooperative effects and have the character of Onsager reaction fields, which are much stronger in micromagnetism than in atomic-scale magnetism. The slow dynamics of zero-field-cooled (ZFC) magnetization curves is strongly affected by the particles′ magnetic anisotropy, which reduces the corresponding energy-barrier height from 25 to 19.1 kBT.

Magnetite magnetosome and fragmental chain formation ofMagnetospirillum magneticumAMB-1: transmission electron microscopy and magnetic observations

SUMMARY Stable single-domain (SD) magnetite formed intracellularly by magnetotactic bacteria is of fundamental interest in sedimentary and environmental magnetism. In this study, we studied the time course of magnetosome growth and magnetosome chain formation (0–96 hr) in Magnetospirillum magneticum AMB-1 by transmission electron microscopy (TEM) observation and rock magnetism. The initial non-magnetic cells were microaerobically batch cultured at 26 ◦ C in a modified magnetic spirillum growth medium. TEM observations indicated that between 20 and 24 hr magnetosome crystals began to mineralize simultaneously at multiple sites within the cell body, followed by a phase of rapid growth lasting up to 48 hr cultivation. The synthesized magnetosomes were found to be assembled into 3–5 subchains, which were linearly aligned along the long axis of the cell, supporting the idea that magnetosome vesicles were linearly anchored to the inner membrane of cell. By 96 hr cultivation, 14 cubo-octahedral magnetosome crystals in average with a mean grain size of ∼44.5 nm were formed in a cell. Low-temperature (10–300 K) thermal demagnetization, room-temperature hysteresis loops and first-order reversal curves (FORCs) were conducted on whole cell samples. Both coercivity (4.7–18.1 mT) and Verwey transition temperature (100–106 K) increase with increasing cultivation time length, which can be explained by increasing grain size and decreasing nonstoichiometry of magnetite, respectively. Shapes of hysteresis loops and FORCs indicated each subchain behaving as an ‘ideal’ uniaxial SD particle and extremely weak magnetostatic interaction fields between subchains. Low-temperature thermal demagnetization of remanence demonstrated that the Moskowitz test is valid for such linear subchain configurations (e.g. δ FC/δ ZFC > 2.0), implying that the test is applicable to ancient sediments where magnetosome chains might have been broken up into short chains due to disintegration of the organic scaffold structures after cell death. These findings provide new insights into magnetosome biomineralization of magnetotactic bacteria and contribute to better understanding the magnetism of magnetofossils in natural environments.

Magnetostatic interaction fields in first-order-reversal-curve diagrams

The contribution of magnetostatic interaction fields in magnetic systems during first-order-reversal-curve (FORC) simulations has been systematically addressed using a dynamic micromagnetic algorithm. The interaction field distributions (IFD) display a nonlinear dependency on the field history and intergrain spacing, and are commonly asymmetric. The IFDs tend to be more Gaussian on average than Cauchian as predicted analytically for disordered systems, due to ordering during FORC diagram determination. The spreading of the FORC distribution in the vertical direction of the FORC diagram is shown to be directly related to the mean standard deviation of the IFD during the FORC measurement, with a small offset related to the smoothing factor.

Effects of magnetic layer thickness and of head-to-medium spacing on noise in advanced particulate recording media

The effects of magnetic layer thickness on the noise characteristics of advanced metal particle tape have been observed using a dc demagnetization process generated with a uniform in-plane magnetizer. The three-dimensional (3D) surface maps of spectral noise power plotted as a function of remanent magnetization state showed a change in behavior as the recording layer became thinner. The thickest magnetic coating of 310 nm showed “trough-like” characteristics associated with conventional thick particulate media. The thinnest sample with a 165 nm magnetic coating showed a “peak-like” response that is observed in continuous thin-film media, with a graduated trend from one to the other for the two intermediate samples. A simulation of these results has been made with an 8000 spherical particle micromagnetic model of the media remanent states and a simulated magnetoresistive read head. Noise maps produced from the simulation compared well with experiment. Spatial isolation of the noise contributions was achieved by dividing the modeled magnetic layer into sublayers. This revealed that particles at the surface were the source of the “peak-like” response, and their contributions became more dominant as the magnetic coating got thinner. Further model investigations showed an association of the different sublayer characteristics with a change in the mean magnetostatic interaction field. The interaction field of particles at the surface had characteristics similar to those of 2D granular thin films and hence generated “thin film-like” noise. A further effect was associated with the spacing between the head and various regions of particles. As this was increased, not only was the amplitude of the noise reduced, but the increased region of integration meant that longer range correlations were incorporated into the observed characteristics, resulting in noise maps more like those of conventional thick particulate media.

Direct imaging of nanoscale magnetic interactions in minerals.

The magnetic microstructure of a natural, finely exsolved intergrowth of submicron magnetite blocks in an ulvöspinel matrix is characterized by using off-axis electron holography in the transmission electron microscope. Single-domain and vortex states in individual blocks, as well as magnetostatic interaction fields between them, are imaged at a spatial resolution approaching the nanometer scale. The images reveal an extremely complicated magnetic structure dominated by the shapes of the blocks and magnetostatic interactions. Magnetic superstates, in which clusters of magnetite blocks act collectively to form vortex and multidomain states that have zero net magnetization, are observed directly.

Computational model of the magnetic and transport properties of interacting fine particles

A computational model is applied to the study of the hysteresis properties of a system of interacting single domain particles. The model is based on Monte Carlo techniques and takes into account both magnetostatic and exchange interactions. The results presented concentrate on a detailed study of the behavior of Co particles, with the interaction strength varied by variations in the packing density. It is found that the magnetic properties are strongly dependent on the parameter $\ensuremath{\beta}=KV/kT,$ with K the anisotropy constant and $V$ the mean particle volume. For small \ensuremath{\beta}---i.e., close to superparamagnetic systems---the microstructure is dominated by a tendency to flux closure. However, the interactions lead to an increase in the local energy barriers, resulting in an increase in ${H}_{c}$ with packing density \ensuremath{\epsilon}. For large \ensuremath{\beta} the anisotropy and magnetostatic interaction fields become comparable and the competition leads to a decrease in the coercivity ${H}_{c}$ with \ensuremath{\epsilon}. For intermediate values of \ensuremath{\beta} a maximum in the variation of ${H}_{c}$ with \ensuremath{\epsilon} is predicted. The irreversible susceptibility is shown to have a complex dependence on interactions, especially in small fields where frustration effects arising from the competition between exchange and magnetostatic interactions are apparent. Exchange and magnetostatic interactions give rise to local magnetic order which is strongly dependent on the relative strength of the exchange interactions. The magnetic order has a strong bearing on the magnetic properties. A link is also made to the transport properties of the system, which are dependent on a spin-spin correlation function. It is shown that exchange interactions give rise to a significant deviation from the quadratic dependence of the giant magnetoresistance on ${M}^{2}.$

Micromagnetic model of perpendicular head and double-layer media for 100 Gb/in/sup 2/

A system including a perpendicular recording head, a soft underlayer, and a recording layer has been studied using a micromagnetic simulation. The model uses Voronoi cells to represent the recording layer and cubic cells for the soft underlayer and head. The total field consists of the magnetostatic interaction field, the demagnetization field, the exchange field, the anisotropy field, and the field generated by the nontip region of the head. The geometrical configuration of the pole tips and soft underlayer was optimized for. performance at 100 Gb/in/sup 2/. It is demonstrated that high anisotropy fields in the soft underlayer have only small effects on peak fields and gradients. This suggests that low permeability underlayers are an effective way of combating stray field effects. Simulations of the recording layer show the effects of increasing anisotropy on reducing trackwidth. We find a large increase in the perpendicular recording field caused by the permeability of the recording layer exceeding that of free space. This should greatly aid the achievement of adequate recording fields at high density.

Magnetostatic interactions between sub-micrometer patterned magnetic elements

We have investigated the effect of the magnetostatic interaction field between submicrometer patterned magnetic elements in arrays (/spl sim/10/sup 8/ elements) using Alternating Gradient Force Magnetometry. Single layer NiFe elements were studied over a range of width (0.12 to 0.48 /spl mu/m), length to width aspect ratio (1.5 to 4) and thickness (30 /spl Aring/ to 60 /spl Aring/). The arrays were patterned using e-beam lithography in a rectangular lattice with bit separation equal to element width. Effective interaction fields were obtained using a novel application of /spl Delta/M plots to these patterned arrays. The /spl Delta/M plot is derived by subtracting remanent magnetization curves that had initial states of full magnetization from those that were initially demagnetized. Interaction fields were quantified using H/sub int/=/spl Delta/M//spl chi//sub irr/, where /spl Delta/M is the difference in these remanent loops and /spl chi//sub irr/ is the derivative of the remanent magnetization with respect to field. We found H/sub int/ to increase with element aspect ratio, thickness and inverse width. For structures with the largest aspect ratio, thickness and smallest width, H/sub int//spl ap/6 Oe. We calculated the actual dipolar interaction fields using micromagnetic simulation and used these fields in a simple 2-d Ising model to simulate the experiment. We found H/sub int/ that is a good measure of the difference in interaction fields tending to magnetize or demagnetize the sample.

Micromagnetic model of perpendicular recording head with soft underlayer

A system including a perpendicular recording head and soft underlayer has been studied using micromagnetic simulation. The model uses cubic cells in the underlayer and pole tips. In our model the total field consists of the magnetostatic interaction field, exchange field, anisotropy field and applied field from the nontip region of the head. A closed form result was used to calculate interaction fields in the soft underlayer and pole tips. The equation of motion for the magnetization is taken to be the Landau-Lifshitz-Gilbert equation. The geometrical configuration of the head and underlayer was varied to optimize for a high perpendicular field component and a high gradient at the media.

Micromagnetic evaluation of statistical and mean-field interactions in particulate ferromagnetic media

Samples with Stoner–Wohlfarth ferromagnetic particles interacting only through dipolar magnetostatic fields were computer generated and the effects of the interactions on the magnetisation processes have been analysed. In some geometrical configurations of the particles, magnetostatic mean-field interaction field was also obtained, in agreement with the usual assumption in the moving Preisach model. A micromagnetic analysis of the magnetostatic mean interaction field is made. Classical Δ M and integral generalised Δ M curves have been calculated and the results have been analysed.

Size effects on characteristic magnetic fields of a spin-valve multilayer by computer simulation

The change in characteristic magnetic fields of a spin-valve multilayer is investigated as a function of the size by computer simulation. The spin-valve modeled in this work is IrMn (9 nm)/CoFe (4 nm)/Cu (2.6 nm)/CoFe (2 nm)/NiFe (6 nm). The spin-valve dimensions are varied widely from 20 mm×10 mm to 0.5 μm×0.25 μm, but the aspect ratio defined by the ratio of the length to the width is fixed at 2.0. The magnetostatic interactions begin to affect the magnetic properties substantially at a spin-valve length of 5 μm, and, at a length of 1 μm, they become even more dominant. The main consequences of the magnetostatic interactions are a significant increase of the coercivity and a very large shift of the bias field in both the pinned and free layers. It is shown that these changes can be explained by two separate contributions to the total magnetostatic interactions: the coercivity change by the self-demagnetizing field and the change of the bias field by the interlayer magnetostatic interaction field.