T. Schrefl

Exchange spring media for perpendicular recording

A novel type of exchange spring media is proposed for magnetic recording systems consisting of a hard/soft bilayer. Finite element micromagnetic simulations show that the reversal modes induced by the external write field are significantly different from the thermally activated switching processes. Thus, the bilayers can be optimized in order to achieve a high thermal stability without increase of coercive field. In grains with identical size and coercivity an optimized bilayer reaches an energy barrier exceeding those of optimized single phase media by more than a factor of two. Additionally the lower angular dependence of coercivity of exchange spring media will improve the signal to noise ratio.

Micromagnetic modelling—the current state of the art

The increasing information density in magnetic recording, the miniaturization in magnetic sensor technology, the trend towards nanocrystalline magnetic materials and the improved availability of large-scale computer power are the main reasons why micromagnetic modelling has been developing extremely rapidly. Computational micromagnetism leads to a deeper understanding of hysteresis effects by visualization of the magnetization reversal process. Recent advances in numerical simulation techniques are reviewed. Higher order finite elements and adaptive meshing have been introduced, in order to reduce the discretization error. The use of a hybrid boundary/finite element method enables accurate stray field computation for arbitrary shaped particles and takes into account the granular microstructure of the material. A dynamic micromagnetic code based on the Gilbert equation of motion to study the time evolution of the magnetization has been developed. Finite element models for different materials and magnet shapes are obtained from a Voronoi construction and subsequent meshing of the polyhedral regions. Adaptive refinement and coarsening of the finite element mesh guarantees accurate solutions near magnetic inhomogeneities or domain walls, while keeping the number of elements small. The polycrystalline microstructure and assumed random magnetocrystalline anisotropy of elongated Co elements decreases the coercive field and the switching time compared to zero anisotropy elements, in which vortices form and move only after a certain waiting time after the application of a reversed field close to the coercive field. NiFe elements with flat, rounded and slanted ends show different hysteresis properties and switching dynamics. Micromagnetic simulations show that the magnetic properties of intergranular regions in nucleation-controlled Nd-Fe-B hard magnetic materials control the coercive field. Exchange interactions between neighbouring soft and hard grains lead to remanence enhancement of isotropically oriented grains in nanocrystalline composite magnets. Upper limits of the coercive field of pinning-controlled Sm-Co magnets for high-temperature applications are predicted from the micromagnetic calculations. Incorporating thermally activated magnetization reversal and micromagnetics we found complex magnetization reversal mechanisms for small spherical magnetic particles. The magnetocrystalline anisotropy and the external field strength determine the switching mechanism. Three different regimes have been identified. For fields, which are smaller than the anisotropy field, magnetization by coherent switching has been observed. Single droplet nucleation occurs, if the external field is comparable to the anisotropy field, and multi-droplet nucleation is the driving reversal process for higher fields.

GRAIN-SIZE DEPENDENCE OF REMANENCE AND COERCIVE FIELD OF ISOTROPIC NANOCRYSTALLINE COMPOSITE PERMANENT MAGNETS

Abstract Micromagnetic calculations using a finite element technique are useful to investigate magnetization processes in nanocrystalline ferromagnetic materials. In particular numerical calculations reveal the microstructural conditions required for high remanence and high coercivity isotropic permanent magnets. composite materials of Nd 2 Fe 14 B and α-Fe are excellent candidates for such high performance permanent magnets. The soft magnetic α-Fe grains cause a large spontaneous magnetization and the hard magnetic grains induce a large coercive field, provided that both phases are strongly exchange coupled. The numerical investigations on realistic three-dimensional grain arrangements suggest an optimal microstructure consisting of small soft magnetic grains ( D ≈ 10 nm, V soft ≈ 40%) embedded between hard magnetic grains with a mean grain diameter of about D ≈ 20 nm. Additionally, a microstructure with regular shaped grains improves the magnetic properties.

Scalable parallel micromagnetic solvers for magnetic nanostructures

A parallel finite element micromagnetics package has been implemented, that is highly scalable, easily portable and combines different solvers for the micromagnetic equations. The implementation is based on the standard Galerkin discretization on tetrahedral meshes with linear basis functions. A static energy minimization, a dynamic time integration, and the nudged elastic band method have been implemented. The details of the implementation and some aspects of the optimization are discussed and timing and speedup results are given. Nucleation and magnetization reversal processes in permalloy nanodots are investigated with this micromagnetics package.

Two‐ and three‐dimensional calculation of remanence enhancement of rare‐earth based composite magnets (invited)

Micromagnetic calculations using a finite element technique rigorously describe the magnetic properties of novel, isotropic rare‐earth‐based composite magnets. Numerical results obtained for a composite material of Nd2Fe14B, SmCo5 or Sm2(Fe0.8Co0.2)17N2.8 and α‐Fe particles show that remanence, coercivity, and coercive squareness sensitively depend on microstructural features. Interparticle exchange interactions enhance the remanence by about 60% with respect to noninteracting particles for a mean‐grain size approaching the exchange length of the soft magnetic phase and a significant percentage of α‐Fe. On the other hand, exchange interactions between the phases suppress the nucleation of reversed domains and thus preserve a high coercive field. Therefore, optimally structured, isotropic composite magnets show remarkably high energy products exceeding 400 kJ/m3.

Exchange hardening in nano-structured two-phase permanent magnets

Abstract The coercive field of a magnetically soft prismatic grain of irregular cross-section embedded in a hard magnetic matrix has been calculated as a function of the size of the soft magnetic grain. To solve the corresponding two-dimensional micromagnetic problem a finite element technique was used. In spite of large deviation of the spontaneous magnetic polarization in the soft magnetic phase at low external fields, the numerical calculations reveal remarkable high values of the coercive field, if the size of the soft magnetic grains is sufficiently small.

Current-driven vortex oscillations in metallic nanocontacts.

We present experimental evidence of subgigahertz spin-transfer oscillations in metallic nanocontacts that are due to the translational motion of a magnetic vortex. The vortex is shown to execute large-amplitude orbital motion outside the contact region. Good agreement with analytical theory and micromagnetics simulations is found.

Phase distribution and computed magnetic properties of high-remanent composite magnets

Abstract Numerical micromagnetic calculations using finite-element techniques allow a quantitative treatment of the correlation between the microstructure and the basic magnetic properties of two-phase permanent magnets such as the remanence, the coercive field and the maximum energy product. For the investigation of (A) the role of the amount of the soft magnetic phase, and (B) the effect of grain shape, realistic three-dimensional grain arrangements have been used. The numerical results show that both short-range exchange and long-range magnetostatic interactions determine the magnetic properties. The optimal microstructure of an isotropic nanocrystalline permanent magnet was found to consist of soft magnetic particles with a large spontaneous magnetization embedded between hard magnetic grains. Exchange interactions than enhance the remanence of isotropic, composite magnets of Nd 2 Fe 14 B and α-Fe by about 60%. Because of exchange hardening the soft magnetic phase can be increased up to 50% without a significant loss of coercivity. A uniform grain structure suppresses strong demagnetizing fields and this increases coercivity by 30% as compared with irregular shaped particles.

Overview of Nd-Fe-B magnets and coercivity (invited)

High performance Nd2Fe14B‐based permanent magnets are produced with different composition and various processing techniques. The composition and the processing route influence the complex, multiphase microstructure of the magnets, such as grain size, alignment, and distribution of phases. Grain sizes in the range between 10 and 500 nm are obtained by melt spinning, mechanical alloying, and the HDDR process. Sintered and hot worked magnets exhibit grain sizes above 1 μm. The coercive field is determined by the high uniaxial magnetocrystalline anisotropy as well as the magnetostatic and exchange interactions between neighboring hard magnetic grains. The dipolar interactions between misaligned grains are more pronounced in large‐grained magnets, whereas exchange coupling reduces the coercive field in small grained magnets. Transmission electron microscopy has been used to study the influence of substituent and dopant elements on microstructure, coercivity, and corrosion resistance of advanced (Nd,S1)–(Fe,S2)...

A path method for finding energy barriers and minimum energy paths in complex micromagnetic systems

Minimum energy paths and energy barriers are calculated for complex micromagnetic systems. The method is based on the nudged elastic band method and uses finite-element techniques to represent granular structures. The method was found to be robust and fast for both simple test problems as well as for large systems such as patterned granular media. The method is used to estimate the energy barriers in CoCr-based perpendicular recording media.