Connection between microstructure and magnetic properties of soft magnetic materials

The magnetic behavior of soft magnetic materials is discussed with some emphasis on the connection between macroscopic properties and underlying micromagnetic energy aspects. It is shown that important conceptual gaps still exist in the interpretation of macroscopic magnetic properties in terms of the micromagnetic formulation. Different aspects of hysteresis modeling, power loss prediction and magnetic non-destructive evaluation are discussed in this perspective.     

Magnetostatic interactions in dense nanowire arrays

We demonstrate the importance of magnetostatic interactions in dense arrays of ferromagnetic nanowires. Beginning from a simple micromagnetic model, we have calculated the interaction field for saturated magnetization in the plane of the array (perpendicular to the axes of the wires) and normal to the plane, using a hybrid (numerical and analytical) strategy. The slope of interaction field versus wire length changes dramatically at the transition between a dipolar regime (at very small lengths) and a monopolar regime (for longer nanowires). We present the interaction fields and the applied fields at saturation for large nanowire arrays. These results are compared with experiment for electrodeposited arrays, and very good agreement is obtained. This shows that the high field behavior of such arrays is dominated by magnetostatic effects and that a nanowire array behaves like a double-sided distribution of magnetic monopoles.     

Dipolar coupling effect in magnetic bilayer system

Equilibrium micromagnetic structures in a bilayer system composed of two thin cobalt films separated by a non magnetic spacer are systematically analysed. These 2D magnetization distributions are obtained by numerical computations according to different set of magnetic and geometric parameters. The coupling effect due to the dipolar long range interaction (or stray-field effect) between the two Co layers is studied through the evolution of the magnetic pattern in the stack with or without an applied field and compared to a continuous film of same thickness. Special attention is paid to the hysteresis process in a bilayer. Even though the general aspect of the magnetization distribution looks like a Landau-Lifshitz structure, the absence of any core in the vortex of the magnetic structure is analysed in relation to a possible disappearence of (topological) hysteresis. Received 12 December 2001     

Finite element analysis of the demagnetization effect and stress inhomogeneities in magnetic shape memory alloy samples

This paper is concerned with the finite element analysis of boundary value problems involving nonlinear magnetic shape memory behavior, as might be encountered in experimental testing or engineering applications of magnetic shape memory alloys (MSMAs). These investigations mainly focus on two aspects: first, nonlinear magnetostatic analysis, in which the nonlinear magnetic properties of the MSMA are predicted by the phenomenological internal variable model previously developed by Kiefer and Lagoudas, is utilized to investigate the influence of the demagnetization effect on the interpretation of experimental measurements. An iterative procedure is proposed to deduce the true constitutive behavior of MSMAs from experimental data that typically reflect the shape-dependent system response of a sample. Secondly, the common assumption of a homogeneous Cauchy stress distribution in the MSMA sample is tested. This is motivated by the expectation that the influence of magnetic body forces and body couples caused by field matter interactions may not be negligible in MSMAs that exhibit blocking stresses of well below 10?MPa. To this end, inhomogeneous Maxwell stress distributions are first computed in a post-processing step, based on the magnetic field and magnetization distributions obtained in the magnetostatic analysis. Since the computed Maxwell stress fields, though allowing a first estimation of the influence of the magnetic force and couple, do not satisfy equilibrium conditions, a finite element analysis of the coupled field equations is performed in a second step to complete the study. It is found that highly non-uniform Cauchy stress distributions result under the influence of magnetic body forces and couples, with magnitudes of the stress components comparable to externally applied bias stress levels.     

Micromagnetic simulation of thermally activated switching in fine particles

Effects of thermal activation are included in micromagnetic simulations by adding a random thermal field to the effective magnetic field. As a result, the Landau–Lifshitz equation is converted into a stochastic differential equation of Langevin type with multiplicative noise. The Stratonovich interpretation of the stochastic Landau–Lifshitz equation leads to the correct thermal equilibrium properties. The proper generalization of Taylor expansions to stochastic calculus gives suitable time integration schemes. For a single rigid magnetic moment the thermal equilibrium properties are investigated. It is found, that the Heun scheme is a good compromise between numerical stability and computational complexity. Small cubic and spherical ferromagnetic particles are studied.     

Magnetization reversal in granular thin films

The paper discusses the physics of magnetization reversal in granular magnetic films. It gives an overview of the key physical properties that determine the collective and macroscopically observable magnetization reversal behavior. In particular, the multitude of observable hysteresis loops is reduced to three key physical quantities, namely the single grain switching field distribution D(h_s), the inter-granular exchange coupling constant J_ex, and the magnetostatic interaction constant J_ms. By varying the relative influence of these quantities, many different shapes of hysteresis loops can occur, which is documented by experimental examples. The regime of partially and strongly correlated reversal is discussed in detail, and minor loop measurements are presented that show scaling behavior for strongly correlated magnetization reversal in the vicinity of hysteresis loop criticality.     

MuMax: A new high-performance micromagnetic simulation tool

We present MuMax, a general-purpose micromagnetic simulation tool running on graphical processing units (GPUs). MuMax is designed for high-performance computations and specifically targets large simulations. In that case speedups of over a factor 100 × can be obtained compared to the CPU-based OOMMF program developed at NIST. MuMax aims to be general and broadly applicable. It solves the classical Landau-Lifshitz equation taking into account the magnetostatic, exchange and anisotropy interactions, thermal effects and spin-transfer torque. Periodic boundary conditions can optionally be imposed. A spatial discretization using finite differences in two or three dimensions can be employed. MuMax is publicly available as open-source software. It can thus be freely used and extended by community. Due to its high computational performance, MuMax should open up the possibility of running extensive simulations that would be nearly inaccessible with typical CPU-based simulators.     

Micromagnetic calculation of magnetostatic oscillation modes of an orthogonally magnetized disk of yttrium iron garnet

The absorption spectrum of a normally magnetized disk of yttrium iron garnet, which is associated with resonances of magnetostatic oscillation modes excited by a homogeneous high-frequency magnetic field, has been investigated using a numerical analysis of the micromagnetic model developed for ferromagnetic objects. The distribution of magnetization oscillation amplitudes over the disk surface area has been obtained for the first four modes. A good agreement between the results of the micromagnetic simulation and the data of analytical calculations for special cases has proved the reliability and efficiency of the proposed approach in numerical experiments on the study of the magnetization dynamics in objects with different geometries and shapes, including multilayer magnetic film structures.     

On features of the magnetic structure of spherical iron nanoparticles

The results of research into the behavior of the magnetic structure inherent to spherical ferromagnetic nanoparticles with radii of 5–30 nm are presented. The behavioral features are investigated in an external magnetic field by means of computer modeling. The hysteresis loops and formation of the vortex structure of magnetization are analyzed using particles with different sizes. The size effect of changes in the magnetization symmetry, which is analogous to phase transitions of the second kind, is established. The magnetic moments of spherical iron nanoparticles with radii of 5–30 nm are calculated. Calculations are performed by means of the Nmag micromagnetic simulation package.     

Disordered domain structures and domain boundaries in thin magnetic films

The behavior of a disordered domain structure and domain boundaries with a change in temperature and magnetic field has been studied. The concept of magnetostatic pressure is used to explain the experimental results. It is shown that “the memory effect” and stability interval of a domain structure with a change in temperature or magnetic field depends on the degree of domain structure disorder and the domain boundary energy.     

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.     

Hysteresis magnetoresistance and micromagnetic modeling of Ni microbelts

Magnetization reversal process in a single nickel microbelt is investigated by measuring magnetoresistance (MR). A hysteresis MR curve is observed, which consists of a reversible bell-shaped curve under high magnetic field and an irreversible discontinuity under low magnetic field. A micromagnetic simulation is performed for understanding the underlying physics behind the MR curve. The hysteresis is ascribed to the competition of exchange energy and Zeeman energy, and the irreversible discontinuity is attributed to the formation of domain walls and vortices.     

Temperature dependence of the effective anisotropy in Ni nanowire arrays

Magnetic hysteresis in Ni nanowire arrays grown by electrodeposition inside the pores of anodic alumina templates is studied as a function of temperature in the range between 5 K and 300 K. Nanowires with different diameters, aspect ratios, inter-wire distance in the array and surface condition (smooth and rough) are synthesized. These microstructure parameters are linked to the different free magnetic energy contributions determining coercivity and the controlling magnetization reversal mechanisms. Coercivity increases with temperature in arrays of nanowires with rough surfaces and small diameters ─33 nm and 65 nm─ when measured without removing the alumina template and/or the Al substrate. For thicker wires ─200 nm in diameter and relatively smooth surfaces─ measured without the Al substrate, coercivity decreases as temperature rises. These temperature dependences of magnetic hysteresis are described in terms of an effective magnetic anisotropy K_a, resulting from the interplay of magnetocrystalline, magnetoelastic and shape anisotropies, together with the magnetostatic interaction energy density between nanowires in the array. The experimentally determined coercive fields are compared with results of micromagnetic calculations, performed considering the magnetization reversal mode acting in each studied array and microstructure parameters. A method is proposed to roughly estimate the value of K_a experimentally, from the hysteresis loops measured at different temperatures. These measured values are in agreement with theoretical calculations. The observed temperature dependence of coercivity does not arise from an intrinsic property of pure Ni but from the nanowires surface roughness and the way the array is measured, with or without the alumina template and/or the aluminum support.     

Thermo-magnetic history effects in the giant magnetostriction across the first-order transition and minor hysteresis loops modeling in Fe0.955Ni0.045Rh alloy

Results of temperature- and magnetic field-dependent strain measurements across the first-order antiferromagnetic to ferromagnetic phase transition in Fe(0.955)Ni(0.045)Rh are presented. Distinct thermal and magnetic field hystereses are observed in the measured strain across the phase transition. The minor hysteresis loops inside the hysteretic regime across the temperature-driven transition are modeled using the Preisach model of hysteresis. The applicability of the Preisach model to explain the general features of minor hysteresis loops is discussed for a disorder influenced first-order transition. The minor hysteresis loops show the property of retaining the memory of the starting or end point of the temperature cycle followed within the hysteretic region. A larger temperature excursion within the hysteretic region wipes out the memory of a smaller temperature cycle which contains one of the extrema of the larger cycle. The end-point memory and the wiping-out property of the minor hysteresis loops can be described quite well within the Preisach model, irrespective of the temperature history followed to reach a particular starting point. Thermo-magnetic history effects across the magnetic field-induced transition are explained, which will enable the choice of the starting point of an experimental cycle in the field-temperature phase space so as to achieve the desired functionality. Our results highlight the necessity to understand the influence of disorder on a first-order phase transition so as to achieve a repeatable performance of materials whose functionalities are based on such a transition.     

General magnetostatic shape-shape interaction forces and torques

Expressions for the magnetostatic interaction force and torque between two magnetic objects of arbitrary shape are derived within the shape amplitude formalism. A generalized force is derived as the gradient of the magnetometric tensor field, which is the convolution of the cross-correlation of the object shapes with the dipolar tensor field. Expressions for the mechanical and magnetic torques are also derived in terms of the magnetometric tensor field. Expressions suitable for numerical evaluation are given as finite Fourier summations. Example computations are given for the interactions between pairs of uniformly magnetized spheres (for which analytical results are compared to numerical results), cubes, octahedra, tetrahedra, and cuboctahedra. The accuracy of the derived numerical relations for energy, force, and torques is of the order of 0.1% for object spacings smaller than the object dimensions.     

Spin waves in nickel nanorings of large aspect ratio

The spin dynamics of high-aspect-ratio nickel nanorings in a longitudinal magnetic field have been investigated by Brillouin spectroscopy and the results are compared with a macroscopic theory and three-dimensional micromagnetic simulations. Good agreement is found between the measured and calculated magnetic field dependence of the spin wave frequency. Simulations show that as the field decreases from saturation, the rings switch from a "bamboo" to a novel "twisted bamboo" state at a certain critical field, and predict a corresponding dip in the dependence of the spin wave frequency on the magnetic field.     

低频弱场下超导铌球交流损耗的分析

本文根据Bean-London模型计算了超导铌球在迈斯纳态下由于表面穿透深度引起的磁滞损耗.在计算损耗的过程中,将准静态变化的外磁场引起的超导球表层的磁感应强度、感应电流的分布转化为静磁场问题求解,从而方便的计算出磁滞损耗的大小.     

Study on magnetization reversal of cobalt nanowire arrays by magnetic force microscopy

The magnetic properties of self-assembly cobalt nanowire arrays formed in anodic porous alumina template were investigated by nanosize imaging method and macroscopic magnetic measurement. We have successfully made a wire-by-wire observation of magnetization reversal of a cobalt nanowire array using magnetic force microscopy with a home-made FePt tip. The nanowires in this medium have uniaxial anisotropy with easy axis along the wire due to the large aspect ratio of the wires (30 nm in diameter and 300 nm in length). Considering the nanowires as single-domain structures, we can obtain the average DC demagnetization curve from nanosize images by calculating the number of wires in each magnetized direction, and the results agreed well with the DC demagnetization curve measured by macroscopic measurement. The magnetostatic field between wires was evaluated by a new nanosize imaging method. Macroscopic measurement shows that reversible magnetization occurs in this medium. Nanosize images of the remanent and saturated states prove that the reversible magnetization processes mainly take place inside individual wires and reversed wires induced by magnetostatic field just give a little contribution to the reversible magnetization.     

Micromagnetic study of magnetic domain structure and magnetization reversal in amorphous wires with circular anisotropy

In this work we present a detailed numerical investigation on the magnetic domain formation and magnetization reversal mechanism in sub-millimeter amorphous wires with negative magnetostriction by means of micromagnetic calculations. The formation of circular magnetic domains surrounding a multidomain axially oriented central nucleus was observed for the micromagnetic model representing the amorphous wire. The magnetization reversal explained by micromagnetic computations for the M-H curve is described in terms of a combined nucleation-propagation−rotational mechanism after the saturated state. Results are interpreted in terms of the effective magnetic anisotropy.     

Fe_3O_4单晶薄膜磁性电场调控的微磁学仿真研究

磁性薄膜磁学特性电场调控的相关研究对开发新型低功耗磁信息器件具有突出意义.本文基于电场调控磁性的基本理论,以OOMMF(Object Oriented Micro-Magnetic Frame)微磁学仿真软件为工具,研究了电场对生长于PZN-PT单晶衬底上Fe_3O_4单晶薄膜磁学特性的调控.研究结果显示:无外加电场时,薄膜表现出典型的软磁特性;沿衬底[001]方向施加的外加电场可以使得薄膜矫顽力、矩形比等磁学特性发生显著改变:当外加磁场沿[100]([010])时,施加正值(负值)电场强度可以显著增大薄膜的矫顽力与矩形比,当电场强度不小于0.6 MV/m时薄膜矩形比达到1.这是因为外加电场导致薄膜产生单轴应力各向异性,使得薄膜的等效磁各向异性发生了从无外电场下的面内四重磁晶各向异性向高电场下的近似单轴磁各向异性的过渡.外加1 MV/m与-1 MV/m的电场时等效易磁化轴分别沿[100]与[010]方向.另外,外加1 MV/m(-1 MV/m)的电场强度可以使得铁磁共振的频率增大(减小)接近1 GHz.