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Density functional theory calculations have been carried out for the hard magnetic compound Y C o 5 and its related phases. The calculations provide a straightforward but accurate method, as reflected in good agreement obtained with experimental results in terms of saturation magnetization and magnetocrystalline anisotropy energy (MAE). For the calculations we used the projector augmented wave method with GGA-PBE approximation and included spin-orbit coupling and ( U , J ) potentials, which are calculated to convergence. It is shown that these properties are influenced by the crystal structure and atomic distances, hence the crystal structures have been optimized and relaxed. The influence of changes in symmetry, distances and lattice parameters are studied, as well as the effect of substituting one C o - atom by F e or C u as examples for a magnetic and a non-magnetic impurity. The comparison between Y C o 5 and hcp - C o shows the importance of atomic environments and lattice symmetry for a large MAE. The calculations predict that F e and C u both reduce MAE, but F e increases magnetization. Despite lacking 4 f - orbitals as compared to S m C o 5 , Y C o 5 exhibits a large anisotropy, originating from the contribution of the C o - atoms. We have also shortly studied the influence of 4 f - electrons for rare earths R = P r and S m on MAE for comparison. Y C o 4 F e , Y C o 4 C u , S m C o 4 F e and S m C o 4 C u are calculated to have MAE values of 2.1 M J / m 3 , 2.7 M J / m 3 , 19.2 M J / m 3 and 8 . 2 M J / m 3 at 0 K respectively.

Micromagnetic calculations using the finite element technique describe semi-quantitatively the coercivity of novel rare earth permanent magnets in dependence on grain size, grain shape, grain alignment and composition of grain boundaries and grain boundary junctions and allow the quantitative prediction of magnetic hysteretic properties of rare earth free magnets based on densely packed elongated Fe and Co nanoparticles, which depend on crystal anisotropy, aspect ratio and packing density. The nucleation of reversed domains preferentially takes place at grain boundary junctions in granular sintered and melt-spun magnets independently on the grain size. The microstructure and the nanocompostion of the intergranular regions are inhomogeneous and too complex in order to make an exact model for micromagnetic simulations and to allow a quantitative prediction. The incoherent magnetization reversal processes near the end surfaces reduce and determine the coercive field values of Co- and Fe-based nanoparticles.

In the framework of the ongoing research for novel rare earth free permanent magnet materials, the alloy Fe–Co–C has attracted interest from theorists, since carbon could induce a magneto-crystalline anisotropy. In this work structural and magnetic properties of strongly doped magnetron sputtered thin films were investigated. Au–Cu buffers on MgO (100) substrates were used in order to promote epitaxial FeCo with 001 orientation. By adding carbon as a third element a tetragonal distortion was observed, according to structural measurements. An anisotropic behavior was induced in the magnetic properties of the system, where the magneto-crystalline anisotropy constant Ku value was estimated in the order of 0.8×106 J/m3f or 3 nm thick Fe–Co(C) magnetic layer.

The promising high magnetocrystalline anisotropy of about K 1 > 0.4 MJ/m 3 has been derived for (Fe,Co) 2–3 B melt-spun ribbons leading to a potential candidate for novel hard magnetic applications. We present the microstructural and magnetic analysis of the phase relations in various microcrystalline alloys with a nominal composition of (Fe 1− x Co x ) 71 B 29 (0 ⩽ x ⩽ 1) by means of SEM and TEM investigations. The melt-spun ribbons were prepared at different wheel speeds (18–38 m/s) and annealed at 500 °C for one hour. The optimum hard magnetic properties were obtained for (Fe 0.7 Co 0.3 ) 71 B 29 at 26.7 m/s. The crystal anisotropy and saturation polarisation have been confirmed by DFT calculations.

The objective of the rare-earth free permanent magnets (REFREEPM) project is to develop a new generation of high-performance permanent magnets (PMs) without rare earths. Our approach is based on modeling using a combinatorial approach together with micromagnetic modeling and the realization of the modeled systems (I) by using a novel production of high-aspect-ratio (>5) nanostructrures (nanowires, nanorods, and nanoflakes) by exploiting the magnetic shape anisotropy of the constituents that can be produced via chemical nanosynthesis polyol process or electrodeposition, which can be consolidated with novel processes for a new generation of rare-earth free PMs with energy product in the range of 60 kJ/m3 < (BH)max < 160 kJ/m3 at room temperature, and (II) by using a high-throughput thin-film synthesis and high-throughput characterization approach to identify promising candidate materials that can be stabilized in a tetragonal or hexagonal structure by epitaxial growth on selected substrates, under various conditions of pressure, stoichiometry, and temperature. In this article, we report the progress so far in selected phases., This work is supported by European Commission (REFREEPERMAG project) grant number GA-NMP3-SL-2012-280670.

Hard magnetic nanostructures have several applications such as magnetic recording media, sensors, and microelectromechanical systems applications containing permanent magnets. In this paper, we performed micromagnetic simulations on Co nanorods on a regular grid and in an irregular packing. Both types of models describe structures which can be produced experimentally: regular grids of nanorods can be created by electro deposition in an alumina template and irregularly packed structures can be obtained by compacting nanorods synthesized in a polyol process. In addition, we also studied the increase of coercivity of capped Fe nanorods with an antiferromagnetic layer. The packed structures have been generated by a packing algorithm on the basis of gravity and collision forces and have a packing density of up to 58%. The simulations on the regular hexagonal grid of nanorods show that energy density products (BH) $_{\rm max}$ of up to 200 kJ/m $^{3}$ can be reached with this packing density, but the calculations on irregularly packed structures exhibit only energy density products of up to 85 kJ/m $^{3}$ . The discrepancy can be explained by the misalignment of nanorods which reduces both coercive field and remanence of the structure. The antiferromagnetic caps on Fe nanorods suppress the formation of nucleation centers at the tips and increase the coercivity of the nanorod by 11% in the case of asymmetric hysteresis loops with hard caps ( $K_{1, {\rm cap}}= 4.6$ MJ/m $^{3}$ ) and 25% in the case of symmetric hysteresis with softer caps ( $K_{1, {\rm cap}}= 460$ kJ/m $^{3}$ ).

Fine-grained, heavy rare earth free Nd-Fe-B sintered magnets were prepared from He jet milled powders with an average particle size of 1.5 µm by low temperature sintering at 920 °C or 980 °C. A coercivity of >1600 kA/m was achieved for an average grain size of 1.68 µm. Transmission electron microscopy showed that the distribution and composition of intergranular and grain boundary junction phases was similar to that in conventionally processed magnets. Microstructural analysis on different length scales revealed the occurrence of abnormal grain growth, which is unexpected for sintering temperatures below 1000 °C. A larger area fraction of abnormal grains was observed in the sample sintered at 920 °C compared to that sintered at 980 °C. Microtexture investigation showed a better crystallographic alignment of the abnormal grains compared to the fine-grained matrix, which is explained by a size dependent alignment of the powder particles during magnetic field alignment prior to sintering. Slightly larger particles in the initial powder show a better alignment and will act as nucleation sites for abnormal grain growth. Magneto-optical Kerr investigations confirmed the lower switching field of the abnormal grains compared to the fine-grained matrix. The demagnetisation curve of the sample sintered at 920 °C showed reduced rectangularity and this was attributed to a cooperative effect of the larger fraction of abnormal grains with low switching field and, as a minor effect, a reduced degree of crystallographic texture in this sample compared to the material sintered at 980 °C, which did not show the reduced rectangularity of the demagnetisation curve.

We have prepared FePt L10/A1 exchange spring graded media by controlling deposition temperature. The performance of the media was determined by the deposition conditions, particularly the cooling rate. By varying the deposition conditions a coercivity of 4.0 kOe was achieved without loss in remanent magnetization, the value corresponds to 88% reduction compared with that of FePt L10 single phase (32.2 kOe). High-resolution transmission electron microscopy (HRTEM) investigations have revealed that this drastic coercivity reduction originates from the unique microstructure of the specimens: coexistence of the L10 and A1 phases at the interphase boundary. In this region the two phases are dispersed one into another like inclusions in a matrix. Finally, the role of the complicated phase boundary on switching field reduction was discussed using micromagnetic simulations.

In this study, the signal-to-noise ratio (SNR) performances of longitudinally, randomly, and perpendicularly oriented particles, based on hexagonal barium ferrite (h-BaFe) platelets with an average volume of 2400 nm 3 have been studied as a function of the recording head to media distance by numerical micromagnetic simulations. The distances from the write head to media and from the read head to media were varied independently. For a fixed read distance and varied writing distances, the SNR was decreasing in larger write distance. An optimum write distance of 40 and 50 nm was found for the longitudinally oriented media and the perpendicularly oriented media, respectively. The optimum write distance for longitudinally oriented media, 40 nm, resulted in the local minimum SNR for the perpendicularly oriented media. In most write distances the perpendicularly oriented media show the outstanding best performance, but near the write distance of 40 nm the longitudinally oriented media work as good as the perpendicularly oriented media. In a fixed write distance with various read distances, the SNR was almost constant in each media whereas the average signal amplitude was exponentially decayed in larger read head to media distance. The best SNR was found in the perpendicularly oriented media at write head to media distance d write =20 nm and read head to media distance d read =40 nm. The best SNR value is 11.9 and 24.4 dB in time domain and frequency domain, respectively.

In this work, we have studied the switching of single phase material and exchange spring bit patterned islands under the influence of a microwave field. Micromagnetic simulations shows that the reduction of the switching field owing to a microwave assist field is most effective for an optimal value of the Gilbert damping constant of 0.05. The microwave assist field changes the angle dependence of the switching field. With increasing field angle the switching field can be reduced to 25% of the switching field at zero field angle.

Finite element micromagnetic studies on the magnetic behaviors of granular structures are performed to investigate the magnetostatic contributions of the curved surfaces of grains with various film thicknesses. From the result, it is found that the magnetization reversal process in one grain is much faster when the grains have convex surfaces. The magnetization vectors of all convex models are stabilized in shorter time by factor of 10 compared to those of flat models. And, the reversals of each grain are carried out by nucleation and domain wall propagation in the entire granular structure, whereas the grains in flat model are individually reversed. Moreover, the magnetization behaviors of the convex models are closer to the experimental results. Since the geometric and magnetic conditions are same for the two models, the only origin of the more realistic magnetic behavior is the magnetostatic interaction between the grains, enhanced by introducing the convex surfaces. From the further analysis, it is found that the convex surface induces pinning field that suppress other parts' reversal.

We performed micromagnetic simulations in order to investigate the effect of intergranular exchange coupling on the magnetic properties of advanced magnetic recording structures. We found that the coercive field of granular recording media decreases with increasing intergrain exchange coupling (A int). We observed this decay even for perfect films without switching field distributions and soft magnetic inclusions. A mean field exchange field of about mu0 H ex = 0.34 T leads to the same thermal stability of the grains at the transition and in the center of a bit. A larger value of A int lowers the thermal stability of the grains close to the transitions. Micromagnetic simulations of coupled granular continuous (CGC) media indicate that the top layer in CGC media is not continuous. The simulations suggest that the top layer is granular with a relatively weak intergrain exchange coupling, A int.

Micromagnetic simulations are used to study magnetic recording processes of ion-irradiated bit-patterned media. The media is composed of several hundred grains. It is assumed that the ion irradiation affects the magnetic anisotropy but keeps the magnetization unchanged. The recording simulations were performed using a fully integrated micromagnetic simulation package. The background region that is regarded to be irradiated triggers the magnetic switching of the bits. Thus some degree of intergrain exchange between bits and background is needed to reduce the write field. However, the intergrain exchange leads to spin waves. It is found that the spin waves may cause adjacent tracks erasure.

Isotropic Nd-Fe-B thick film magnets were prepared by a high-speed pulsed laser deposition method followed by a post annealing. The deposition rate of 90 μm/h could be successfully achieved, and a pulse annealing was adopted as the post annealing process in order to enhance coercivity. Use of a substrate heating system under the high deposition rate enabled us to obtain anisotropic thick films with (BH)max of approximately 120 kJ/m3, which show the potential for an improvement in the properties of the micromachines. Novel micromachines comprising the Isotropic films were introduced., IEEE Transactions on Magnetics, 43(6), pp.2672-2676; 2007

We have explored, computationally and experimentally, the magnetic properties of (Fe1-xCox)(2)B alloys. Calculations provide a good agreement with experiment in terms of the saturation magnetizatio ...

We have analysed the influence of the microstructural features, such as intergranular grain boundary (GB) phases and misalignment of the hard magnetic grains, on the optimization of magnetization reversal processes in order to improve the coercive field of Nd-Fe-B magnets. The microstructural model of the grains and intergranular phases, which is used for theoretical simulations, has been derived from a detailed nanoanalytical TEM/STEM study of a Dy/Tb free magnet and a high coercive (Nd,Tb)-Fe-B magnet. Special attention is laid on the EELS analysis of GB with a thickness ranging from 2 - 30 nm. This analysis identified the majority of the GB phases to have about 50 -70 at.% of iron and only a few GBs, which are connecting two nearby grain boundary junctions (GBj), possess a similar chemical composition as the adjacent GBj with a low iron content (< 10 at. %) and a high rare earth and oxygen content. Finite element micromagnetic simulations have been carried out in order to study the influence of internal demagnetizing fields determined by the microstructure on the magnetization switching behaviour. Special emphasis was put on the influence of the GB and their magnetic properties, due to their substantial influence on the nucleation of reverse magnetic domains and the pinning of domain walls. The strongest reduction of the coercive field is caused by GB with soft ferromagnetic properties. Shielding the Nd-Fe-B grains from the nucleation sites at the GBj with Dy or Tb shells, leads to an increase of the coercivity from 2.5 to 3.6 T and 2.5 to 4.3 T, respectively., 8 pages, 5 figures, 1 table; conference: International Conference on Magnetism (ICM) 2015 in Barcelona/Spain, paper accepted for publication

3d transition metal-based magnetic nanowires (NWs) are currently considered as potential candidates for alternative rare-earth-free alloys as novel permanent magnets. Here, we report on the magnetic hardening of FeConanowires in anodic aluminium oxide templates with diameters of 20 nm and 40 nm (length 6 μm and 7.5 μm, respectively) by means of magnetic pinning at the tips of the NWs. We observe that a 3-4 nm naturally formed ferrimagnetic FeCo oxide layer covering the tip of the FeCo NW increases the coercive field by 20%, indicating that domain wall nucleation starts at the tip of the magnetic NW. Ferromagnetic resonance (FMR) measurements were used to quantify the magnetic uniaxial anisotropy energy of the samples. Micromagnetic simulations support our experimental findings, showing that the increase of the coercive field can be achieved by controlling domain wall nucleation using magnetic materials with antiferromagnetic exchange coupling, i.e. antiferromagnets or ferrimagnets, as a capping layer at the nanowire tips., We acknowledge funding from the European Community's Seventh Framework Programme (FP7-NMP) under grant agreement no. 280670 (REFREEPERMAG).

We have studied the hard magnetic properties of the low-temperature phase of MnBi with first principle calculations based on the density functional theory. The calculations have been carried out on two distinct unit cell configurations MnBi and BiMn with the element in the unit cell origin named first. Our results show that these configurations are not equivalent and that MnBi describes the system better near T = 0K and the BiMn configuration describes the system better for T > 300K. The magnetic moments of both configurations agree well with experimental measurements considering both spin and orbital contributions. At high temperatures the magneto-crystalline anisotropy energy increases with increasing unit cell volume and reaches a maximum of 2:3MJ=m3 and a c=a ratio of 1:375., Presented at 20th International Conference on Magnetism (ICM2015) in Barcelona, accepted for publication. 5 pages, 2 figures, 4 tables

A Fe-Co-Nb thin film materials library was deposited by combinatorial magnetron sputtering and investigated by high-throughput methods to identify new noncubic ferromagnetic phases, indicating that combinatorial experimentation is an efficient method to discover new ferromagnetic phases adequate for permanent magnet applications. Structural analysis indicated the formation of a new magnetic ternary compound (Fe,Co)(3)Nb with a hexagonal crystal structure (C36) embedded in an Fe Co-based matrix. This nanocomposite exhibits characteristics of a two-phase ferromagnetic system, the so-called hard-soft nanocomposites, indicating that the new phase (Fe,Co)3Nb is ferromagnetic. Magnetic hysteresis loops at various angles revealed that the magnetization reversal process is governed by a domain wall pinning mechanism.

Nanocrystalline zinc-substituted cobalt ferrite powders, Co 1− x Zn x Fe 2 O 4 ( x =0, 0.2, 0.4), were for the first time prepared by forced hydrolysis method. Magnetic and structural properties in these specimens were investigated. The average crystallite size is about 3.0 nm. When the zinc substitution increases from x =0 to x =0.4, at 4.2 K, the saturation magnetization increases from 72.1 to 99.7 emu/g and the coercive field decreases from 1.22 to 0.71 T. All samples are superparamagnetic at room temperature and ferrimagnetic at temperatures below the blocking temperature. The high value of the saturation magnetization and the very thin thickness of the disorder surface layer of all samples suggests that this forced hydrolysis method is suitable not only for preparing two metal element systems but also for three or more ones.

In nonzero-temperature micromagnetics the intrinsic magnetic parameters depend on the computational cell size. For large cells the experimentally measured, only temperature dependent intrinsic properties can be used. For simulations on an atomistic level the experimentally measured zero-temperature values can be applied. In between, the intrinsic magnetic properties follow scaling laws which can be derived from Metropolis Monte Carlo simulations. Equilibrium magnetization states and thermally activated switching processes of small ferromagnetic cubes were calculated. With proper scaling of the material parameters the numerical results were found to be almost independent of the computational cell size.

Hard magnetic properties and microstructure of PLD-made Nd–Fe–B thick film magnets were studied. The films were mainly composed of Nd2Fe14B grains, and the average grain size was approximately 150 nm. In addition, we succeeded to fabricate a milli-size DC brush-less motor with a PLD-made Nd–Fe–B film.

Numerical micromagnetics of the bit writing process revealed the theoretical limits for remanence, coercive field, switching behaviour at a short time scale of less than 1 ns for patterned recording media. We discuss our recent results concerning the influence of the granular microstructure on the fast switching processes of typical CoCrPtX, FePt and CoPd thin films used for high density magnetic recording with longitudinal and perpendicular anisotropy. In detail, we will show that the degree of the exchange coupling between neighbouring grains, the grain size and its distribution and the offset between recording head and bit structure finally control the magnetization reversal properties of the individual bits.

The fabrication of ~3 nm FePt nanoparticles and detailed studies of the effect of the annealing conditions (temperature and time) on the formation of the face-centred tetragonal phase and on the magnetic properties are described. Additionally, the effect of the precursor molar ratio on the final product and the composition of the as-prepared samples were studied. The main criteria for the determination of the best alloy are the properties desired for applications in the field of magnetic recording media.

The most important methods for determining the grain size, the grain size distribution and also the actual microstructure of nanocrystalline materials are: X-ray diffraction line profile analysis, transmission electron microscopy, and small-angle neutron scattering. For each of these three methods their specific advantages and disadvantages are discussed and an experimental example is given.

Micromagnetic simulations of a pulsed inductive microwave magnetometer (PIMM) experiment are performed using a well established model for exchange bias. The model (Interacting Grain Model) consists of ferromagnetic grains and antiferromagnetic grains with randomly distributed easy axes. A perfectly compensated interface between the ferromagnet and the antiferromagnet is assumed which leads to spin flop coupling. The antiferromagnetic layer is modelled as two totally antiparallel sublattices with a small intergrain exchange between each antiferromagnetic sublattice. Simulations of an experimental PIMM setup provide a shift of the minimum of the resonance frequency which is also observered experimentally.

A uniform mode theory is used to find the parameter range for realizing fast switching below the Stoner–Wohlfarth limit in weakly coupled granular tilted media. The theory is used to estimate the field amplitudes and directions for simultaneous switching of a family of uniformly magnetized and noninteracting grains with dispersion in the easy axis and initial magnetization directions. The effect of interactions is then studied numerically by using a 3D finite element micromagnetic simulations. The numerical results shows that the theory provides rather accurate estimate. In addition, it is verified that in an appropriate range of applied field amplitudes the switching time decreases by decreasing the external field.

Hysteresis loops were calculated for a model with ferromagnetic grains spin-flop coupled to interacting antiferromagnetic grains with randomly distributed easy axes. The interface between these two layers is assumed to be fully compensated. Field cooling simulated by a Monte-Carlo algorithm and subsequent calculation of the hystersis loop reveals asymmetries in the ascending and descending part of the hysteresis loop, respectively. On the descending branch a steep change of the magnetization can be observed. On the ascending branch homogeneous rotations of the magnetization cause a smoother change of the magnetization. The strong asymmetries vanish after a few hysteresis loop calculations.

In order to achieve an areal density of 10 Tbit/in2 in perpendicular recording, grains with diameters of about 3 nm are required. However, for such grain sizes, common hard disk materials are magnetically too soft to be thermally stable. Extremely hard magnetic materials such as FePt have a too large coercive field and cannot be reversed with conventional head fields. The proposed FePt (2 nm)/Fe3Pt (14 nm)/FePt (2 nm) trilayer reduces the coercive field by a factor of 8 compared to a single-phase FePt layer of the same thickness. At the same time the energy barrier is only decreased by 40%. A high signal to noise ratio can be expected for the multilayer structure since the switching field distribution is insensitive on the angle α between the easy axis of the hard layers and the external field. A change from α = 0.1 ° to 1° changes the coercive field by less than 2.5% (10% for conventional perpendicular media). Thus, small distribution of the anisotropy axes angles have less effect than in conventional perpendicular media.

CoPt nanoparticles with an average size of 3 nm and narrow distribution were synthesized by chemical reduction of Co(CH(3)COO)(2) and Pt(acac)(2) by polyethyleneglycol-200. The as-prepared nanoparticles have a disordered fcc structure which transformed after thermal treatment to an ordered fct structure, which results in coercivity up to 6 kOe at room temperature and 9 kOe at 5 K because of the high magnetocrystalline anisotropy of the tetragonal structure [Formula: see text].

The magnetic domain size of melt-spun Nd 60 Fe 30 Al 10 has been determined by means of small-angle neutron scattering (SANS). An average domain size of 300 nm was found. High resolution electron micrography and magnetic measurements revealed the precipitation of Nd-rich multi-phases embedded in an amorphous matrix. The 57 Fe Mossbauer spectroscopy showing two peaks in the hyperfine field distribution with high and low moment values, respectively.

Micromagnetics is a continuum theory to describe magnetization processes on a length scale which is large enough to replace the atomic spins by a continuous magnetization vector and small enough to resolve the magnetization transition inside a domain wall. Depending on the magnetocrystalline anisotropy the characteristic length scale, the domain wall width or the minimum discretization size, is in the order of several nanometres to micrometres. Typical examples for numerical micromagnetic simulations are shown, where the role of a granular microstructure and precipitates on hysteresis properties is significant, such as in FePt nanocrystals, granular CoCrPtX thin films for longitudinal magnetic recording and modern bulk rare earth permanent magnets.

The high-temperature magnetic properties of the Sm 1− x Gd x (Co 0.74 Fe 0.10 Cu 0.12 Zr 0.04 ) 7.50 ( x =0, 0.2, 0.4, 0.6, 0.8) series of magnets are investigated in the range between 50 and 650 °C. The pertinent properties are the saturation magnetization, the coercivity H c and their temperature coefficients, α and β , respectively. Gd substitution is made in order to improve the temperature coefficient of magnetization. The values of the coefficient α are in the range (−0.3, 0.3%/°C) while the values of the coefficient β are in the range (−0.2, 0.2%/°C). The best results were obtained for the x =0.4 sample, for which the saturation magnetization was almost independent of temperature in the range between 150 and 500 °C.

The importance of newly developed permanent magnetic materials in many electromechanical, magnetomechanical and electronic applications is attributed to the drastic improvement in microstructure related properties, such as the remanence, the magnetic energy density product and the coercive field. The influence of the microstructure on the magnetic properties of the magnets will be discussed, where special emphasis is laid on rare earth permanent magnets. Highest performance, anisotropic Nd?Fe?B magnets with Jr>1.5?T, (BH)max>450?kJ?m?3 and JHc> 750?kA?m?1, which are produced by the powder metallurgy route, show a strong influence of composition and processing parameters on the magnetic properties. The magnetic properties of Sm(Co,Cu,Fe,Zr)z sintered magnets, which are used nowadays for high temperature applications between?300 and 500??C, are determined by the cellular precipitation microstructure, which is developed during a complex heat treatment and by the microchemistry. Special hard magnetic powder materials, such as Sm2Fe17N3 and nanocrystalline, composite Nd2Fe14B /(?-Fe,Fe3B) materials have been developed especially for usage in bonded magnetic materials, which show the strongest annual increase in the production of permanent magnets. The phenomenon of the enhancement of remanence, occurring in single phase and composite Nd2Fe14B based magnets with isotropic grain alignment, is attributed to intergrain exchange interactions.

The relaxation of magnetostatic spin waves in a square NiFe nano-element (100×100×20 nm3) has been simulated by micromagnetic finite element modeling after the excitation by a rotational field of μ0H=0.2 T with various frequencies between 1 and 16 GHz. The micromagnetic simulations are based on the Landau–Lifshitz–Gilbert equation of motion with a Gilbert damping parameter α=0.02. The relaxation after switching off the external field led to a damped oscillation of the magnetization, which is related to changes of the exchange and magnetostatic field energies of the system. Finally, depending on the frequency of the rotating field “C-” and “S-” domain configurations were observed after approximately 10 ns. The different inhomogeneous magnetostatic and exchange field strength values inside the square for the “C-” and “S-” state lead to different frequencies of the magnetostatic spin-wave modes, such as about 4.5 GHz for the C-state and 3 GHz for the S-state, respectively.

The change in the resistivity in a Co nanowire due to the anisotropic magnetoresistivity effect is investigated using the finite element method. The wire has a square cross-section of 200×200 nm 2 . We compare our results with experimental investigations. The numerical results show reduction of the resistivity during hysteresis. Magnetoresistance (MR) decreases gradually until the coercive field is reached and then jumps back to the initial value. If we move the electrodes into the centre of the nanowire the MR effect is reduced because we neglect the formed domains at the end of the nanowire.

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.

We have investigated the magnetic properties of submicron soft magnetic cylindrical nanodots using an analytical model as well as three dimensional numerical finite element simulations. A detailed comparison of the magnetic vortex state shows the differences between these two models. It appears that the magnetic surface charges play a crucial role in the equilibrium magnetization distribution especially for shifted vortices. Finally, the magnetic phase diagram for soft magnetic particles with varying aspect ratio is presented.

Three-dimensional micromagnetic simulations were performed to study the magnetisation reversal processes of granular nanoelements using a hybrid finite element/boundary element model. Transient magnetisation states during switching are investigated numerically in granular, thin Ni80Fe20 and Co square shaped nanoelements (100×100 nm2) with 10 nm grain size and a thickness of 10 nm and taking into account a random orientation of the grains. Switching dynamics are calculated for external fields between 80 and 280 kA/m, which were uniformly applied after a rise time of 0.05 and 0.1 ns, respectively, and in comparison for a 10 GHz rotational field. Reversal in the unidirectional field proceeds by the nucleation and propagation of end domains towards the centre of the granular thin film elements. The formation of a vortex magnetisation structure leads to an increase of the switching time in the granular Co element. The switching time strongly depends on the Gilbert damping parameter α. Small values of α(⩽0.1) lead to shorter switching times at small field strength values (h

Domain wall pinning is the coercivity mechanism of permanent magnets used in high temperature applications. In SmCo based magnets domain walls get trapped at the cellular precipitation structure causing a high coercive field. The motion of domain walls and their propagation velocity are important in soft magnets as used in sensor applications. A finite element micromagnetic algorithm was developed to study the motion of domain walls in complex microstructures. The cellular microstructure of SmCo magnets or the cylindrical soft wires can be easily built using tetrahedral finite elements. The pinning of the domain walls has been studied for different material compositions. Attractive and repulsive domain wall pinning are observed and their behaviour for increasing thickness of the precipitation structure is explained. The motion of domains in magnetic nanowires was calculated using adaptive mesh refinement. The wall velocity strongly depends on the domain wall structure. Transverse and vortex walls have been observed and their velocity in wires of different thickness has been studied.

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.

The magnetization reversal process of magnetic nano-wires was investigated using a moving mesh finite element method. The nucleation and expansion of reversed domains is calculated by solving the Gilbert equation of motion. For a wire diameter of d=20 nm either a transverse wall or a vortex wall is formed, depending on the strength of the initial applied field. Once a reversed domain is nucleated, the wall configuration remains the same during the complete reversal process. The vortex wall moves faster than the transverse wall. The domain wall velocities are in the order of 300–800 m/s for an external field in the range from 300 to 600 kA/m for a Gilbert damping constant α=1. The domain wall velocity increases with increasing wire diameter and decreasing damping constant, reaching 2000 m/s for d=40 nm, α=0.05, and an applied field of 250 kA/m.

Internal tin Nb 3 Sn strands manufactured by Europa Metalli where subjected to heat treatments at a final annealing temperature of 675 °C at variable time from 1 to several hundred hours. The growth of the Nb 3 Sn layer and grains is monitored using LVSEM, EDX and TEM. The critical parameters (critical temperature T C , upper critical field H C2 and the scaling parameter C ) as well as hysteresis and coupling losses and the magneto resistance of these strands have been deduced by experiment. From these results we will show, that the behavior of a given strand can be optimized with respect to the desired conditions of operation.