3D and 1D micromagnetic calculation for hard/soft bilayers with in-plane easy axes

Macroscopic hysteresis loops and microscopic magnetic moment distributions have been determined by three-dimensional (3D) as well as one-dimensional (1D) micromagnetic models for exchange-coupled Nd₂Fe₁₄B/α–Fe bilayers and carefully compared with each other. It is found that the results obtained from the two methods are consistent with each other, where the nucleation and coercive fields decrease monotonically as the soft layer thickness L^s increases whilst the largest maximum energy products (roughly 600 kJ/m³) occur at L^s=5 nm. Moreover, the calculated angular distributions in the thickness direction for the magnetic moments are similar. Nevertheless, the calculated critical fields and energy products by 3D OOMMF are systematically smaller than those given by the 1D model, mainly due to the local demagnetization fields, which are taken into account in the 3D calculation and ignored in the 1D calculation. It is demonstrated by the 3D calculation that the large demagnetization fields in the corners of the soft layers reduce the nucleation fields and thus facilitate the magnetic reversal. Such an effect enhances as L^s increases. When L^s=20 nm, the differences between the coercivity is as large as 30%, while the nucleation fields obtained by the two methods have opposite signs.     

Magnetic reversal processes and critical thickness in FePt/α-Fe/FePt trilayers

Magnetic reversal processes of a FePt/α-Fe/FePt trilayer system with in-plane easy axes have been investigated within a micromagnetic approach. It is found that the magnetic reversal process consists of three steps: nucleation of a prototype of domain wall in the soft phase, the evolution as well as the motion of the domain wall from the soft to the hard phase and finally, the magnetic reversal of the hard phase. For small soft layer thickness L^s, the three steps are reduced to one single step, where the magnetizations in the two phases reverses simultaneously and the hysteresis loops are square with nucleation as the coercivity mechanism. As L^s increases, both nucleation and pinning fields decrease. In the meantime, the single-step reversal expands to a standard three-step one and the coercivity mechanism changes from nucleation to pinning. The critical thickness where the coercivity mechanism alters, could be derived analytically, which is found to be inversely proportional to the square root of the crystalline anisotropy of the hard phase. Such a scaling law might provide an easy way to test the present theory. Further increase of L^s leads to the change of the coercivity mechanism from pinning to nucleation.     

Three-and two-dimensional calculations for the interface anisotropy dependence of magnetic properties of exchange-spring Nd2Fe(14)B/α-Fe multilayers with out-of-plane easy axes

Hysteresis loops,energy products and magnetic moment distributions of perpendicularly oriented Nd2Fe(14)B/α-Fe exchange-spring multilayers are studied systematically based on both three-dimensional(3D)and one-dimensional(1D)micromagnetic methods,focused on the influence of the interface anisotropy.The calculated results are carefully compared with each other.The interface anisotropy effect is very palpable on the nucleation,pinning and coercive fields when the soft layer is very thin.However,as the soft layer thickness increases,the pinning and coercive fields are almost unchanged with the increment of interface anisotropy though the nucleation field still monotonically rises.Negative interface anisotropy decreases the maximum energy products and increases slightly the angles between the magnetization and applied field.The magnetic moment distributions in the thickness direction at various applied fields demonstrate a progress of three-step magnetic reversal,i.e.,nucleation,evolution and irreversible motion of the domain wall.The above results calculated by two models are in good agreement with each other.Moreover,the in-plane magnetic moment orientations based on two models are different.The 3D calculation shows a progress of generation and disappearance of vortex state,however,the magnetization orientations within the film plane calculated by the 1D model are coherent.Simulation results suggest that negative interface anisotropy is necessarily avoided experimentally.     

垂直取向Nd2Fe14B/α-Fe磁性三层膜的磁化反转

运用微磁学方法结合物质参数探究了垂直取向Nd₂Fe₁₄B/α-Fe磁性三层膜的磁化反转过程,计算出成核场、钉扎场以及磁滞回线随Ｌ^s（软磁相厚度）的变化,并与相关的实验和理论数据进行比较.由于考虑了退磁能量项,垂直取向的成核场比平行取向时低,在外磁场还没有反向时就发生了成核.随着软磁相厚度的增加,理论矫顽力从等于成核场（同时也等于钉扎场）,到等于钉扎场,再到小于钉扎场,矫顽力机理由成核变为钉扎. 关键词： 成核场 钉扎场 矫顽力 磁滞回线     

Magnetization reversal in submicron disks: exchange biased vortices

Submicron, circular, ferromagnetic-antiferromagnetic dots exhibit different magnetization reversal mechanisms depending on the direction of the magnetic applied field. Shifted, constricted hysteresis loops, typical for vortex formation, are observed for fields along the exchange bias direction. However, for fields applied close to perpendicular to the exchange bias direction, magnetization reversal occurs via coherent rotation. Magnetic force microscopy imaging together with micromagnetic simulations are used to further clarify the different magnetic switching behaviors.     

Effect of exchange coupling on magnetic property in Sm–Co/α-Fe layered system

The hysteresis loops as well as the spin distributions of Sm–Co/α-Fe bilayers have been investigated by both threedimensional(3D) and one-dimensional(1D) micromagnetic calculations, focusing on the effect of the interface exchange coupling under various soft layer thicknesses t~s. The exchange coupling coefficient Ahsbetween the hard and soft layers varies from 1.8 × 10~(-6)erg/cm to 0.45 × 10~(-6)erg/cm, while the soft layer thickness increases from 2 nm to 10 nm. As the exchange coupling decreases, the squareness of the loop gradually deteriorates, both pinning and coercive fields rise up monotonically, and the nucleation field goes down. On the other hand, an increment of the soft layer thickness leads to a significant drop of the nucleation field, the deterioration of the hysteresis loop squareness, and an increase of the remanence. The simulated loops based on the 3D and 1D methods are consistent with each other and in good agreement with the measured loops for Sm–Co/α-Fe multilayers.     

Nucleation field,reversal mechanism and coercivity paradox in two-phased magnetic nanosystem

The magnetic reversal mechanism has been determined within a micromagnetic model reliably for a two-phased magnetic nanosystem,with the formulae for nucleation fields derived analytically.It is found that the nucleation field HN decreases uniformly as the size of the soft phase Ls increases whereas it increases with the size of the hard phase Lh.The analysis shows that whilst the effect of Lh could be ignored in most cases,where the nucleation field is dominated by the Ls and the calculation could be signif...     

Hard–soft composite magnets

A thorough micromagnetic analysis of the exchange-spring problem is reported with special emphasis on multilayers constituted by hard–soft exchange-coupled phases. The developed one—dimensional micromagnetic model leads to a complete magnetic phase diagram in terms of layer thicknesses. Both perpendicular and parallel configurations are considered. The phase diagram provides information on the type of demagnetization processes and the critical fields at which nucleation and reversal take place, depending on the intrinsic properties of the chosen soft and hard materials. The model has been applied to a variety of hard magnetic phases (e.g., FePt, CoPt, SmCo and NdFeB), coupled to different soft materials (e.g., Fe, FeCo, FeRh or permalloy) both in the form of bilayers and multilayers. The most significant results will be highlighted.     

Sm2(TM)17合金的磁性(自旋再取向相变)研究

本文研究了Sm₂(FeNiCoM)₁₇合金(M为非磁性组元)的磁性。样品由六角结构无序型的2∶17主相及少量FeNi合金杂相组成。在六角结构的e轴方向(易磁化方向)观察到下述异常现象:低温(273K以下)时的磁化及反磁化曲线发生明显的跃变,跃变时相应的磁场H_r随温度下降而增大;磁滞迴线是蜂腰型的,温度愈低蜂腰愈明显;升温时磁化强度随温度变化(1.5K至居里点T_C)的曲线上出现极大值,其相应的温度T_t随磁场增大而降低;降温时观察到了热磁滞后现象。但在基面(难磁化方向)上及Co含量增多(>18at％)时,样品却表现了正常的铁磁行为。本文提出用磁矩非共线结构排列的自旋再取向相变来解释上述异常现象,并给出自旋倒向所需越过的能垒高度U=9.2×10^-15erg,用设想磁结构的模型得到的磁化强度的计算值与实验值也符合得较好。 关键词：     

Magnetization reversal measurements in mesoscopic amorphous magnets by magneto-optical Kerr effect

A magneto-optical setup based on the transverse Kerr effect has been designed to study the magnetization reversal processes by vector magnetometry in arrays of magnetic nanostructures with a reduced total volume. This system allows the measurement of both the parallel and perpendicular to the field components of the magnetization. It has been used to analyze the behavior of amorphous Co _x Si_1-x lines fabricated by electron beam lithography that present a very well defined shape induced uniaxial anisotropy. When the field is applied near to the hard direction, coherent rotation processes are found to occur with a collapse of this reversal mode at fields very close to the hard axis that allows to estimate the very low anisotropy dispersion of these samples. The analysis of the vector hysteresis loops reveals that the magnetization switches via an incoherent process that starts prior to the Stoner-Wohlfarth instability and that can be described in terms of a localized curling-like reversal mode.Received: 16 June 2004, Published online: 24 September 2004PACS: 75.75. + a Magnetic properties of nanostructures - 75.60.Jk Magnetization reversal mechanisms - 75.50.Kj Amorphous and quasicrystalline magnetic materials     

不同易轴取向下对Nd_2Fe_(14)B/Fe_(65)Co_(35)磁性双层膜的微磁学模拟

运用三维数值模拟计算方法,计算了膜面外不同易轴取向下Nd2Fe14B/Fe65Co35磁性双层膜的磁滞回线、角度分布、成核场、矫顽力和磁能积等,并与实验结果进行了细致比较.计算结果表明:只有当易轴与外场之间的夹角β=0?时,才有明显的成核现象,其成核场和矫顽力均随着软磁相厚度Ls的增加而降低;随着易轴偏角β的增大,剩磁逐渐减小,磁滞回线的方形度降低,从而磁能积减小,在Ls=1 nm,β=0?时磁能积(561.61 kJ/m3)最大.理论计算所得的磁滞回线与实验磁滞回线符合得很好,剩磁和矫顽力的理论值与实验值相差很小.     

Magnetization patterns simulations of Fe,Ni, Co,and permalloy individual nanomagnets

Hysteresis loop behaviours are studied in circular, triangular and Reuleaux's triangle (RT) of Fe, Co, Ni, and permalloy nanomagnets using micromagnetic simulations. The size and morphology of the nanomagnets are analyzed for three different thickness (10, 20, and 40 nm). For the triangle and RT shapes, our results reveal that for all magnetic material considered and in the low thickness (10 nm) the hysteresis prefer to be open, showing important coercive fields and remanence. However, when the thickness is increased (40 nm) almost all hysteresis loops are closed. Finally, the different mechanism of the magnetization reversal are investigated by monitoring the spin configuration as a function of the applied magnetic field.     

Monte Carlo study of magnetization reversal in the model of a hard/soft magnetic bilayer

Magnetization reversal in the model of a hard/soft magnetic bilayer under the action of an external magnetic field has been investigated by the Monte Carlo method. Calculations have been performed for three systems: (i) the model without a soft-magnetic layer (hard-magnetic layer), (ii) the model with a soft-magnetic layer of thickness 25 atomic layers (predominantly exchange-coupled system), and (iii) with 50 (weak exchange coupling) atomic layers. The effect of a soft-magnetic phase on the magnetization reversal of the magnetic bilayer and on the formation of a 1D spin spring in the magnetic bilayer has been demonstrated. An inf lection that has been detected on the arch of the hysteresis loop only for the system with weak exchange coupling is completely determined by the behavior of the soft layer in the external magnetic field. The critical fields of magnetization reversal decrease with increasing thickness of the soft phase.     

Domain reversal behavior in perpendicular magnetic nanothin films

We report domain reversal behavior in perpendicular ferromagnetic nanothin films investigated by means of a novel magneto-optical microscope magnetometer, capable of grabbing domain reversal patterns in real time under an applied field as well as simultaneous measurements of 8000 local hysteresis loops with 400-nm special resolution. Three contrasting domain reversal behaviors are found to exist: wall-motion dominant, dendritic-growth dominant, and nucleation dominant reversal. Quantitative analysis reveals that the contrasting reversal behavior is mainly caused by a sensitive change in wall-motion speed and that the reversal ratio of wall-motion speed over nucleation rate is a governing parameter for the contrasting domain reversal dynamics. The activation volumes of the wall-motion and nucleation processes are found generally unequal, and the inequality is closely related with the domain dynamics. The domain reversal pattern is truly coincident with submicron-scale local coercivity variation and local switching time of domain evolution is exponentially dependent on local coercivity governed by a thermal activation relaxation process. The observed domain reversal behavior could be well predicted by a Monte Carlo simulation of a micromagnetic model based on the uniaxial magnetic anisotropy of nanothin films.     

Magnetization reversal of micropattern Fe bar array: Combination of vector and Bragg magneto-optical Kerr effect measurements

We report on a magneto-optical Kerr effect (MOKE) investigation of alternating wide and narrow Fe bars, forming a two-dimensional periodic array. The magnetization reversal was studied by regular longitudinal Vector-MOKE in specular geometry as well as in Bragg-MOKE geometry, using the diffraction spots from the grating for hysteresis measurements. With Vector-MOKE a two-step switching process for the wide and narrow Fe bars is observed, indicative for a narrow switching field distribution in this array. In addition, hysteresis loops were determined as a function of the diffraction order for the hard and easy axis direction. The loops at different orders of diffraction can qualitatively and quantitatively be described by Fourier transformations of micromagnetic simulations.     

Micromagnetic modeling studies on the effects of stress on magnetization reversal and dynamic hysteresis

The complex behaviors of magnetic materials subjected to magneto-electro-mechanical coupled fields call for a better understanding of the mechanism of multi-fields coupling. In this paper, micromagnetic modeling is carried out to study the effect of stress on hysteresis loops and dynamic magnetization reversal. The time-dependent Landau–Lifshitz–Gilbert equation which governs the evolution of magnetization is solved using the fast Fourier transform technique in reciprocal space. The simulation results show that the stress changes the distribution of easy directions and, therefore, leads to the change of magnetic properties. Moreover, the positive product of the stress and saturation magnetostriction coefficients increases the coercivity, hence, increases the area enclosed by the hysteresis loop. A stress-induced magnetization reversal is investigated.     

易轴取向对Nd2Fe14B/α-Fe双层膜退磁过程影响的微磁学分析

运用一维和三维微磁学模拟探究了易轴与外场存在偏角β情况下Nd₂Fe₁₄B/α-Fe 双层膜的磁矩反转过程, 计算了磁矩反转过程中磁滞回线和磁能积, 并与实验结果进行了对比. 计算结果表明, 在膜面内的易轴偏角β严重影响磁矩反转过程. 当β≠0°时, 磁矩反转过程中无明显成核现象, 随着易轴偏角β的增大, 剩磁显著减小, 磁滞回线方形度变差, 导致磁能积急剧减小. 对于Nd₂Fe₁₄B(10 nm)/α-Fe(8 nm)双层膜, β=10°时, 最大磁能积下降30.3%. 在磁矩反转过程中, 总能量最大时对应的外磁场能随易轴偏角的增大而减小, 交换作用能先增大后减小, 磁晶各向异性能则随着易轴偏角的增大而增大. 软磁相厚度越大, 双层膜的磁能积受易轴偏角影响越大. 在膜面外的易轴偏角对磁矩反转过程也有类似的影响. 关键词： 微磁学模拟 磁晶易轴 磁能积 能量     

Magnetization Reversal in Magnetic Bilayer Systems

Magnetization reversal in magnetic soft/hard bilayer systems is studied analytically by means of a variational method for magnetic energies in a continuum model. The demagnetization curve is involved with nonlinear equations,and the solution is given implicitly in the form of Jacobi functions,which is valid for the total reversal process. Based on the non-trivial solutions, hysteresis loops, as well as the maximum energy product(BH)_(max) versus thicknesses of soft/hard layers are obtained. With regard to(BH)_(max), improvement of the remanence competes with loss of coercive force. As a result, an optimum condition exists. For a given thickness of the hard layer, the optimum condition at which the largest(BH)_(max) could be achieved is discussed, which is slightly different from previous works.     

Study of the magnetic interaction in nanocrystalline Pr-Fe-Co-Nb-B permanent magnets

The magnetic properties of an isotropic, epoxy resin bonded magnets made from Pr-Fe-Co-Nb-B powder were investigated. The magnetization reversal process and magnetic parameters were examined by measurements of the initial magnetization curve, major and minor hysteresis loops and sets of recoil curves. From the initial magnetization curve and the field dependencies of the reversible and irreversible magnetization components derived from the recoil loops it was found that the magnetization reversal process is the combination of the nucleation of reversed domains and pinning of domain walls at the grain boundaries and the reversible rotation of magnetization vector in single domain grains. The interactions between grains were studied by means of δM plots. The nonlinear behavior of δM curve approve that the short range intergrain exchange coupling interactions are dominant in a field up to the sample coercivity.The interaction domains and fine magnetic structure were revealed as the evidence of exchange coupling between soft α-Fe and hard magnetic Nd₂Fe₁₄B grains.     

Micromagnetic simulations of 200-nm-diameter cobalt nanorings using a Reuleaux triangular geometry

Using micromagnetic simulations, we investigated the magnetic states and switching processes of Co nanorings with lateral dimensions of 200 nm. We propose a special geometry of nanorings that adopts different Reuleaux triangular shapes. Reuleaux's triangles (RT) combine both the equilateral triangle and circular geometries. We studied the magnetic spin configurations of individual nanorings by varying the thickness and geometry of the nanomagnets. Our results demonstrated that in most nanomagnets exhibiting a thickness of less than 4 nm, there exists an onion-type state, which precedes either a twisted, double twisted, or cardioid state, when studying the magnetization reversal process. The hysteresis loops and magnetic states found in these RTs are compared with circular nanorings.