Micromagnetic Finite Element Method Research Articles

Magnetic properties and reverse magnetization process of anisotropic nanocomposite permanent magnet

Abstract The effects of microstructure parameter upon the magnetic properties of anisotropic nanocomposite permanent magnet (ANPM) Pr2Fe14B/α-Fe were investigated by Micromagnetic finite-element method. The results show that soft magnetic phase filling in the intergranular layer between the hard magnetic phase grains is more favorable for obtaining excellent ANPM Pr2Fe14B/α-Fe. The maximum energy product ((BH)max) of ANPM Pr2Fe14B/α-Fe can reach 762 kJ/m3 for the ideally oriented magnet with the mean grain size of 5 nm and the intergranular layer thickness of 2 nm. The larger (BH)max mainly derives from the contribution of higher remanence which is ascribed to the intergranular exchange coupling between soft and hard magnetic phase. In addition, the reverse magnetization process of ANPM Pr2Fe14B/α-Fe has been studied. It is found that the magnetic moments coherently reverse in reversal magnetization process for ANPM Pr2Fe14B/α-Fe. The study takes the specific composition Pr2Fe14B/α-Fe as an example, however, the results about reasonable microstructure and demagnetization mechanism are still applicable to ANPM with other different hard and soft magnetic phase materials.

Modelling External Magnetic Fields of Magnetite Particles: From Micro- to Macro-Scale

We determine the role of particle shape in the type of magnetic extraction processes used in mining. We use a micromagnetic finite element method (FEM) to analyze the effect of external magnetic fields on the magnetic structures of sub-micron magnetite particles. In non-saturating fields, the magnetite particles contain multiple possible non-uniform magnetization states. The non-uniformity was found to gradually disappear with increasing applied field strength; at 100 mT the domain structure became near uniform; at 300 mT the magnetic structure saturates and the magnetization direction aligned with the field. In magnetic separation techniques, we suggest that 100 mT is the optimal field for magnetite to maximize the magnetic field with the lowest energy transfer; larger particles, i.e., >1 µm, will likely saturate in smaller fields than this. We also examined the effect of external magnetic fields on a much larger irregular particle (L × W × H = 179.5 × 113 × 103 μm) that was too large to be examined using micromagnetics. To do this we used COMSOL. The results show the relative difference between the magnitude of magnetic flux density of the particle and that of a corresponding sphere of the same volume is <5% when the distance to the particle geometry center is more than five times the sphere radius. The ideas developed in this paper have the potential to improve magnetic mineral extraction yield.

Notice of Removal: Micromagnetic Study for Magnetic Properties of Exchange-Coupled Nanocomposite Magnetic Systems With $\alpha$ -Fe Grains Embedded in Nd2Fe14B Matrix

In this paper, the relationship between the magnetic properties and microstructures of nanocomposite isotropic exchange-coupled systems with the structure of α-Fe crystalline grains embedded in Nd 2 Fe 14 B matrices has been estimated by micromagnetic finite-element method. And then, the results have been analyzed by means of the effectiveness of exchange coupling between the magnetically hard Nd 2 Fe 14 B and soft α-Fe phase of the exchange-coupled Nd 2 Fe 14 B/α-Fe magnetic systems. The effectiveness of interphase exchange coupling has been estimated by the volume fractions of exchange coupling area near phase boundaries between α-Fe grains and Nd 2 Fe 14 B matrix. The results have shown the micromagnetic mechanism of the advanced magnetic properties of the exchange coupled magnetic systems with the structure of α-Fe grains embedded in Nd 2 Fe 14 B matrix. In addition, the optimal magnetic properties can be expected in the case of comparatively the large grain sizes of α-Fe and Nd 2 Fe 14 B phase due to the characteristic structure of those magnetic systems.

Micromagnetic study for magnetic properties of exchange coupled nanocomposite magnetic systems with Nd2Fe14B grains embedded in α-Fe matrix

Developing high efficiency rare earth alloy magnets at low cost is an economically hopeful way to expand their application area. In this study, magnetic properties of nanocomposite isotropic exchange coupled systems with the structure of Nd2Fe14B crystalline grains embedded in α-Fe matrices have been simulated by micromagnetic finite element method (FEM). The results have been analyzed by means of the effect of volume fraction of nanosized exchange coupling area between the magnetically hard Nd2Fe14B and soft α-Fe phase on magnetic properties of the exchange coupled Nd2Fe14B/α-Fe magnetic systems. The results show that the magnetic systems with the structure of Nd2Fe14B grains embedded in α-Fe matrices can have comparatively advanced magnetic properties with small amount of Nd2Fe14B components, because of efficient inter-phase exchange coupling between magnetically hard Nd2Fe14B grains and soft α-Fe matrix.

Micromagnetic finite element study for magnetic properties of nanocomposite exchange coupled Nd2Fe14B/α-Fe multilayer systems

In this study, magnetic properties of exchange coupled nanocomposite multilayer thin films constructed alternately with magnetic hard Nd2Fe14B layers and soft α-Fe layers have been studied by micromagnetic finite element method (FEM). According to the results, effects of the thicknesses of layers and the magneto-crystalline anisotropy on the magnetic properties of the Nd2Fe14B/α-Fe multilayer systems have been estimated. On the other hand, the results have been analyzed by means of efficiency of interphase exchange coupling, which can be estimated by volume ratios of exchange coupled areas between magnetically hard Nd2Fe14B and soft α-Fe phase layers. The results show that the magnetic properties of exchange coupled Nd2Fe14B/α-Fe multilayer systems can be enhanced by efficient interphase exchange coupling between magnetically hard Nd2Fe14B layers and soft α-Fe layers.

Investigation of magnetic properties of MnBi/Co and MnBi/Fe65Co35 nanocomposite permanent magnets by micro-magnetic simulation

Demagnetization curves of anisotropic nanocomposite MnBi/Co and MnBi/Fe65Co35 permanent magnets were investigated by micro-magnetic finite element method. Effects of volume ratio, deviation degree of orientation and intrinsic magnetic properties of the soft magnetic phase on the magnetic properties of the magnets were investigated. From the viewpoint of practical applications, to meet the requirement of hardness parameters, ĸ=K/(μ0MS2)1/2>1, the calculation maximum (BH)max of MnBi/Co and MnBi/Fe65Co35 magnets are about 199kJ/m3 (V(Co)=22vol%) and 196kJ/m3 (V(FeCo)=14vol%), respectively, indicating their good potential in application. Compared with single phase MnBi magnet, the (BH)max of nanocomposite MnBi/Co and MnBi/Fe65Co35 magnets increases by 66% and 63%, respectively. The remanence and coercivity of MnBi/Co nanocomposite magnets reduce as appearing a deviation degree of orientation, result of greatly decrease of the magnetic energy product.

Investigation of Magnetic Properties of MnBi/$\alpha$-Fe Nanocomposite Permanent Magnets by Micro-Magnetic Simulation

In the present study, the demagnetization curves of MnBi/α-Fe nanocomposite permanent magnets were calculated by the micromagnetic finite element method. The effect of volume ratio between magnetically soft α-Fe phase and MnBi hard phase on the magnetic properties of magnets was investigated. The sample used in the present simulation was consisted of 91 spherical fourteen faces units of hard phase grains with diameter of 20 nm, and the soft matrix phase with the thickness (t) ranging from 1 to 6 nm. For the isotropic MnBi/α-Fe magnets, as increases, the remanence (B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> )increases first, peaks at 0.855 T for t = 3 nm, then decreases again, while the coercivity (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ci</sub> ) drops monotonically from 691 kA/m for t = 1 nm to 94 kA/m for t = 6 nm. The sample with t = 2 nm has the optimal maximum energy product (BH) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> = 55.15 kJ/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . For the anisotropic magnets, the B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ci</sub> exhibit their t-dependent behavior similar to that of the isotropic ones. The optimal values of B <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> , H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ci</sub> and (BH) <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">max</sub> are 1.47 T, 3200 kA/m, and 322 kJ/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> when t = 5,1, and 3 nm, respectively, indicating a good potential of the anisotropic MnBi/α-Fe nanocomposite as practical permanent magnets.

Investigation on magnetic properties of orientated nanocomposite Pr2Fe14B/α-Fe permanent magnets by micromagnetic finite-element method

Demagnetization curves for nanocomposite Pr2Fe14B/α-Fe permanent magnets with different hard grain alignment are calculated by a micromagnetic finite-element method. The results show that both remanence and coercivity increase with improving hard grains alignment. The demagnetization curves show a single-phase demagnetization behavior for the samples with grain size d of 10nm and two-phase behavior for the samples with d of 20 and 30nm. Hex (reflecting the magnetic hardening of α-Fe) and Hirr (expressing the irreversible reversal of hard phase) are both enhanced with improving the hard grain alignment. The magnetic reversal in orientated nanocomposite permanent magnets is mainly controlled by inhomogeneous pinning of the nucleated type.

Simulation of magnetization behaviours of Sm(Co, Fe, Cu, Zr)z magnet with low Cu content

The effects of microstructure, cell orientation and temperature on magnetic properties and the coercivity mechanism in Sm(Co, Fe, Cu, Zr)z with low Cu content are studied by using the micromagnetic finite element method in this paper. The simulations of the demagnetization behaviours indicate that the pinning effect weakens gradually with the thickness of cell boundary decreasing and strengthens gradually with the cell size decreasing. Because of the intergrain exchange coupling, the coercivity mechanism is determined by the difference in magnetocrystalline anisotropy between the cell phase and the cell boundary phase. And the coercivity mechanism is related to not only the cells alignment but also temperature. With temperature increasing, a transformation of the demagnetization mechanism occurs from the domain pinning to the uniform magnetization reversal mode and the transformation temperature is about 650 K.

Grain boundary contribution to recoil loop openness of exchange-coupled nanocrystalline magnets

It has been well known that recoil loop openness is related to soft-phase presence in exchange-coupled hard-soft nanocomposite magnets. Our study on recoil loop openness of exchange-coupled nanocrystalline magnets (both single-phase and composite) using a micromagnetic finite-element method has revealed that the recoil loop openness is also due to decreased grain size. Open recoil loops exist in single-phase magnets as well. Simulation of magnetization distribution in both nanocrystalline single-phase magnets and nanocomposite magnets shows that the openness of the recoil loops is correlated with unstable magnetization behavior in grain boundary and soft-phase regions, which is attributed to high energy state caused by exchange coupling in these regions. The simulation results are supported by experimental data.

Investigation on mechanism of magnetization reversal for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element methods

Magnetization configurations were calculated under various magnetic fields for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element method. According to the configurations during demagnetization process, the mechanism of magnetization reversal was analyzed. For the Pr 2Fe 14B with 10 nm grains or its composite with 10vol.% a-Fe, the coercivity was determined by nucleation of reversed domain that took place at grain boundaries. However, for Pr 2Fe 14B with 30 nm grains, coercivity was controlled by pinning of the nucleated domain. For Pr 2Fe 14B/a-Fe with 30vol.% a-Fe, the demagnetization behavior was characterized by continuous reversal of a-Fe moment.

The physical origin of open recoil loops in nanocrystalline permanent magnets

The numerical simulation of the open recoil loops has been carried out using micromagnetic finite element method. By giving an example for this issue, the magnetization behaviors during the recoil processes of nanocomposite Pr2Fe14B∕α-Fe magnets have been analyzed. It is the strong intergrain exchange coupling that results in the magnetization reversal in some hard grains during the recoil processes, which leads to the large opening of recoil loops. The magnetization reversal of α-Fe grain follows that of its neighboring hard grains. Consequently, the opening of recoil loops is enhanced due to the presence of α-Fe grains.

Numerical investigation of spin-torque using the Heisenberg model

We present numerical calculations of the spin transfer torque resulting in current-induced domain wall motion. Rather than the conventional micromagnetic finite difference or finite element method, we use an atomistic/classical Heisenberg spin model approach, which is well suited to study geometrically confined domain walls. We compute the behaviour of domain walls in a one dimensional chain when currents are injected using adiabatic and non-adiabatic spin torque terms. Our results are compared to analytical calculations and are found to agree very well for small current densities. At larger current densities deviations are observed, which can be attributed to the approximations used in the analytical calculations.

Studies on the magnetic properties for single-phase nanocrystalline FePt magnets with different orientation degrees

The single-phase nanocrystalline FePt magnets composed of 343 irregular-shaped grains are built. The demagnetization curves are simulated by micromagnetic finite element method. The remanence, coercivity and maximum energy product of the magnets decrease with deteriorating grain alignment. The characteristics of variation of magnetic properties with the degree of orientation are closely related to the average grain size of nanocrystalline magnets. The contribution of intergrain exchange coupling (IGEC) to remanence enhancement is associated to the degree of orientation, and decreases with improved grain alignment. With decreasing grain size, coercivity increases for anisotropic nanocrystalline magnets, which is completely different from that of isotropic nanocrystalline magnets.

Micromagnetic simulation of angular dependence of coercivity in Sm(Co,Fe,Cu,Zr)z magnets

The angular dependence of coercivity in Sm(Co,Fe,Cu,Zr)z magnets is investigated with the micromagnetic finite element method. The results show that the mechanism of the magnetization reversal changes from the domain wall pinning to magnetization uniform reversal with the increase of the angle between the easy axes and the applied field. According to the results of calculation, the microstructural parameter αφ is determined.

Temperature dependence of the magnetization reversal in [formula omitted] magnets

The magnetization reversal for traditional cell-structured Sm ( Co , Fe , Cu , Zr ) z magnets has been investigated using micromagnetic finite element method. The variation of coercivity mechanism with temperature is observed. With the increase of temperature, the transition of coercivity mechanism from domain-wall pinning to reversed-domain nucleation happens at about 700 K. At the temperature below 700 K, the nucleation of reversed domain in the cell wall with weak anisotropy and strong stray field cannot propagate until the magnetic field is large enough to overcome the pinning in cell phase. In contrast, at 700 K or above, the coercivity is controlled by the nucleation of reversed domain. Furthermore, it is found that the nucleation field of cell wall is larger than the corresponding anisotropy field, which is due to the strong exchange-coupled hardening by the cell phase.

Micromagnetic Analysis on Demagnetization Process of Single-Phase Nanocrystalline Permanent Magnets with Different Degrees of Orientation

A three-dimentional finite element micromagnetic algorithm was developed to study the magnetization reversal of Pr 2Fe 14B single-phase nanocrystalline permanent magnets. A single-phase nanocrystalline Pr 2Fe 14B magnets composed of 216 irregular shaped grains was built. The magnetic hysteresis loops were simulated by micromagnetic finite element method. The contribution of intergrain exchange coupling (IGEC) to remanence enhancement is considered related to the alignment degree in oriented magnets, and decreased with improved grain alignment. For the magnets with perfectly crystallo-graphic alignment of grains, the contribution of IGEC to remanence enhancement is nearly zero. The shape of demagnetization curve is not only dependent on grain alignment degree but also on the strength of IGEC in magnets.

Write head analysis by using a parallel micromagnetic FEM

We develop a parallel micromagnetic finite-element method (micromagnetic-FEM) to handle a large number of micromagnetic elements and utilize it to analyze full head and media models. When the calculation domain decomposition and the one-one node communication are applied, the program shows four times faster calculation in eight CPU operation, as compared with one CPU calculation. We study head field and media magnetization reversal on the frequency of 714 MHz, using different yoke length heads of 6, 10, and 15/spl mu/m. The shorter yoke head shows faster head field reversal and stronger head field strength, and the recorded media magnetization is also larger. The small damping parameter of the head causes not only smaller head field but also the disorder of the media transition.

Effects of grain size distribution on remanence and coercivity of Pr 2 Fe 14 B nanocrystalline magnet

The demagnetization curves of Pr2Fe14B nanocrystalline magnets are calculated using micromagnetic finite-element method. Samples with three different distributions of grain size are simulated. We find that the remanence enhancement does not depend on grain size distribution but on the mean diameter of grains, and the influence of grain size distribution on coercivity is affected by the strength of intergrain exchange coupling.

Micromagnetic-FEM models of a perpendicular writer and reader

We have developed a micromagnetic finite element method (micromagnetic-FEM) to analyze perpendicular magnetic recording (PMR) writers and readers. The head field reversal time is 0.55-0.76 ns including the 0.2-ns current rise, and it is dependent on the current amplitude. The main pole has a faster reversal time, but the yoke and media soft-magnetic underlayer (SUL) show a slower response. In the media recording layer, the trailing region shows a faster reversal due to the longitudinal head field component of the trailing write shield. After writing, the media state affects the remanent field behavior. Since the moving media changes the head-media coupling, the remanent field can be relieved with a long relaxation time within 10 ns. To suppress the remanent field, a good anisotropy control of the main pole and yoke is required. A TMR reader with a flat top shield shows less side-reading, especially when the physical track width is below 0.1 /spl mu/m. The PMR media plays a role in read width reduction over a wide range of physical track widths.