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First Order Reversal Curve (FORC) diagrams are a popular tool in geophysics and materials science for the characterization of magnetic particles of natural and synthetic origin. However, there is still a lot of controversy about the rigorous interpretation of the origin of certain features in a FORC diagram. In this study, we analyze FORCs computed by micromagnetic simulations of Co cubes with dimensions of 50, 100 and 150 nm and uniaxial magnetocrystalline anisotropy. For the larger cubes we observe the formation of a stable two-domain state. The nucleation of a reversed domain and its subsequent annihilation are clearly visible as separate peaks in the FORC diagram. They spread out along the coordinate axis in the FORC diagram, which is associated with the bias field $H_U$ of a Preisach hysteron. Based on our findings, we state that a FORC diagram peak spreading along the $H_U$ axis can have its origin in the step-wise magnetization reversal driven by nucleation of domains in a single particle. This means that we have identified another mechanism apart from the well-known magnetostatic interaction between a set of particles that leads to features in the FORC diagram extending along the $H_U$-axis. Our study demonstrates that if FORCs shall be used as a quantitative tool to assess the microstructure of samples containing magnetic material, more information from other methods will be required to identify the correct physical mechanism by which a certain "fingerprint" in a FORC diagram is produced.

The impact of granular microstructure in permanent magnets on eddy current losses are investigated. A numerical homogenization procedure for electrical conductivity is defined. Then, an approximated simple analytical model for the homogenized conductivity able to capture the main features of the geometrical and material dependences is derived. Finally eddy current losses analytical calculations are given, and the two asymptotic expressions for losses in the stationary conduction limit and advanced skin effect limit are derived and discussed., 5 pages, 7 figures

Recently 1:12 magnets of Sm-(Fe,V) have shown promising coercivities and the potential to be alternative rare-earth-lean permanent magnets. In this work, we investigated the effects of partial substitution of Cu, Mo and Ti for V in the magnets prepared by hot compaction and hot deformation of mechanically milled powders. The microstructure of the Sm-Fe-(V,Cu) and Sm-Fe-(V,Ti) hot-deformed magnets consisted in fine grains with sizes between 50 and 150 nm. The Sm-Fe-(V,Cu) magnet showed the best performance with μ0H c = 0.96 T, μ0M r = 0.49 T, (BH) max = 42 kJ m − 3 and T C = 362 ∘ C. Atom probe tomography of this magnet revealed the presence of a thin Sm17.5Fe71.5V8Cu3intergranular phase of 3-6 nm surrounding the 1:12 nanograins. The addition of a small amount of Cu, not only improved the magnetic properties but also hindered the grain growth during hot deformation. Micromagnetic simulations of the magnetization reversal agreed with the experimental values of coercivity. The presence of the intergranular phase reduces the number of grains that switch simultaneously.

We demonstrate the use of model order reduction and neural networks for estimating the hysteresis properties of nanocrystalline permanent magnets from microstructure. With a data-driven approach, we learn the demagnetization curve from data-sets created by grain growth and micromagnetic simulations. We show that the granular structure of a magnet can be encoded within a low-dimensional latent space. Latent codes are constructed using a variational autoencoder. The mapping of structure code to hysteresis properties is a multi-target regression problem. We apply deep neural network and use parameter sharing, in order to predict anchor points along the demagnetization curves from the magnet's structure code. The method is applied to study the magnetic properties of nanocrystalline permanent magnets. We show how new grain structures can be generated by interpolation between two points in the latent space and how the magnetic properties of the resulting magnets can be predicted., 17 pages, 8 figures

Low power-loss semiconductor devices are necessary to achieve a carbon-neutral society. The optimization of device structures is known as a time-consuming process. In this work, we investigated an optimization approach with the help of machine learning. We applied an active learning scheme to optimize a gallium oxide Schottky barrier diode structure and demonstrated how this approach helps to reduce the number of time-consuming simulations for the optimization process. For the investigated work, the active learning strategy almost reduced the number of simulations by a factor of 2 in contrast to the conventional genetic optimization. In addition, we also demonstrated that machine learning models can be used to estimate the performance variations caused by process variations. This approach can also contribute to reducing the number of simulations and speeding up the structure design process.

We investigated the effect of nitrogenation on $3 \times 3 \times 2$ supercell structures of NdFe12- x Ti x from $x = 0.028$ to $x = 1.56$ (~0.2Ti at. % to ~12Ti at. %). We used the molecular dynamics and Boltzmann probabilities to permeate titanium into NdFe12- x Ti x across the investigated range, before nitrogenating the minimum energy structures that resulted at each permutation step. By comparison of the nitrogenated and base structures, we found that the cohesive energy gains caused by nitrogenation are mainly due to a large asymmetry introduced into the $c$ lattice parameter and the efficacy of nitrogenation decreases with increasing titanium at. %.

Partial differential equations and variational problems can be solved with physics informed neural networks (PINNs). The unknown field is approximated with neural networks. Minimizing the residuals of the static Maxwell equation at collocation points or the magnetostatic energy, the weights of the neural network are adjusted so that the neural network solution approximates the magnetic vector potential. This way, the magnetic flux density for a given magnetization distribution can be estimated. With the magnetization as an additional unknown, inverse magnetostatic problems can be solved. Augmenting the magnetostatic energy with additional energy terms, micromagnetic problems can be solved. We demonstrate the use of physics informed neural networks for solving magnetostatic problems, computing the magnetization for inverse problems, and calculating the demagnetization curves for two-dimensional geometries., 22 pages, 9 figures

International audience; Nd2Fe14B-type materials exhibit the highest energy product around room temperature and hence dominate the high-performance permanent magnet market. Intensive research efforts aim at alternative material systems containing less critical elements with similar or better magnetic properties. Nd-and Sm-based compounds with a ThMn12-type structure exhibit intrinsic properties comparable or even superior to Nd2Fe14B. However, it has not been possible to achieve technically relevant coercivity and remanent magnetization in ThMn12-based bulk sintered magnets. Using SmFe11Ti as a prototypical representative, we demonstrate that one important reason for the poor performance is the formation of twins inside micro-crystalline grains. The nature of the twins in SmFe11Ti was investigated in twinned "single crystals" and both bulk and thin film poly-crystalline samples, using advanced electron microscopy and atom probe tomography as well as simulations and compared with benchmark Nd2Fe14B. Both micro-twins and nano-twins show a twin orientation of 57±2 • and an enrichment in Sm, which could affect domain wall motion in this 2 material. Micromagnetic simulations indicate that twins act as nucleation centers, representing the magnetically weakest link in the microstructure. The relation between twin formation energies and geometrical features are briefly discussed using molecular dynamic simulations.

Microstructural features play an important role in the quality of permanent magnets. The coercivity is greatly influenced by crystallographic defects, like twin boundaries, as is well known for MnAl-C. It would be very useful to be able to predict the macroscopic coercivity from microstructure imaging. Although this is not possible now, in the present work we examine a related question, namely the prediction of simulated nucleation fields of a quasi-three-dimensional (rescaled and extruded) system constructed from a two-dimensional image. We extract features of the image and analyze them via machine learning. A large number of extruded systems are constructed from 10 × 10 pixel sub-images of an Electron Backscatter Diffraction (EBSD) image using an automated meshing procedure. A local nucleation field is calculated by micromagnetic simulation of each quasi-three-dimensional system. Decision trees, trained with the simulation results, can predict nucleation fields of these quasi-three-dimensional systems from new images within seconds. As for now we cannot quantitatively predict the macroscopic coercivity, nevertheless we can identify weak spots in the magnet and see trends in the nucleation field distribution.

We investigated the atomic fill site probability distributions across supercell structures of RT12-xTi (R=Nd, Sm, T=Fe, Co). We use a combined molecular dynamics and Boltzmann distribution approach to extrapolate the probability distributions for Ti substitution from lower to higher temperatures with an equilibrium condition to assess how temperature affects the predictability of the structures fill path. It was found that the Nd and Sm based Fe systems have the highest filling probability path at lower temperatures but the cohesive energy change due to Ti substitution in Sm and Nd based crystals indicates that a more stable system could be achieved with a combination Co and Fe in the transition metal site., Comment: 5 pages, 4 figures, 2 tables

We revisited the microstructure of Sm2Co17-type sintered magnets to understand the underlying mechanism of substantial decrease of coercivity from 2.56 T for the optimally annealed sample to 0.14 T for the sample re-annealed at aging temperature of 850 °C for just 1 min and quenched (quenched sample). This low coercivity can be recovered by annealing of the magnet at 850 °C, slow cooling to 400 °C followed by quenching (slowly cooled sample) and with this is fully reversible between the two states. Magnetic domain observations of thermally demagnetized samples with c-axis out-of-plane showed an ultra-fine maze-like domain pattern comparable to the cell size in the slowly cooled sample. However, annealing at 850 °C, even for a short time, followed by quenching resulted in a substantial increase in the size of maze-like domain pattern. Microchemistry of the SmCo5 cell boundary phase for two samples was analyzed using 3D atom probe. 8.6 at. % Cu and 7.7 at. % Fe was found in the cell boundary of the quenched sample while the SmCo5 cell boundary phase of the slowly cooled sample contains 15.4 at. % Cu and 3.0 at. % Fe. Unlike the slowly cooled sample, a broader distribution of Cu than Sm was found in the cell boundary of the quenched sample. High resolution STEM-HAADF results showed SmCo5/Sm2Co17 interface is sharp and defect free for the slowly cooled sample while it is rough and zigzag shaped for the quenched sample. Diffused Cu into the matrix phase from the cell boundary results in a gradual increase of magnetocrystalline anisotropy form matrix to the cell boundary phase. Large Fe concentration in the cell boundary phase reduces its magnetocrystalline anisotropy. Micromagnetic simulations showed that these microstructural features of the quenched sample cause a weak pinning strength of the cell boundary phase explaining its low coercivity.

We investigated, using molecular dynamics, how pressure affects the melting point of the recently theorised and epitaxially grown structure NdFe12. We modified Morse potentials using experimental constants and a genetic algorithm code, before running two-phase solid-liquid coexistence simulations of NdFe12 at various temperatures and pressures. The refitting of the Morse potentials allowed us to significantly improve the accuracy in predicting the melting temperature of the constituent elements.

Multiscale simulation is a key research tool in the quest for new permanent magnets. Starting with first principles methods, a sequence of simulation methods can be applied to calculate the maximum possible coercive field and expected energy density product of a magnet made from a novel magnetic material composition. Iron (Fe)-rich magnetic phases suitable for permanent magnets can be found by means of adaptive genetic algorithms. The intrinsic properties computed by ab initio simulations are used as input for micromagnetic simulations of the hysteresis properties of permanent magnets with a realistic structure. Using machine learning techniques, the magnet’s structure can be optimized so that the upper limits for coercivity and energy density product for a given phase can be estimated. Structure property relations of synthetic permanent magnets were computed for several candidate hard magnetic phases. The following pairs (coercive field (T), energy density product (kJ·m−3)) were obtained for iron-tin-antimony (Fe3Sn0.75Sb0.25): (0.49, 290), L10-ordered iron-nickel (L10 FeNi): (1, 400), cobalt-iron-tantalum (CoFe6Ta): (0.87, 425), and manganese-aluminum (MnAl): (0.53, 80). Keywords: Rare-earth, Permanent magnets, Micromagnetics

The development of permanent magnets containing less or no rare-earth elements is linked to profound knowledge of the coercivity mechanism. Prerequisites for a promising permanent magnet material are a high spontaneous magnetization and a sufficiently high magnetic anisotropy. In addition to the intrinsic magnetic properties the microstructure of the magnet plays a significant role in establishing coercivity. The influence of the microstructure on coercivity, remanence, and energy density product can be understood by using micromagnetic simulations. With advances in computer hardware and numerical methods, hysteresis curves of magnets can be computed quickly so that the simulations can readily provide guidance for the development of permanent magnets. The potential of rare-earth reduced and free permanent magnets is investigated using micromagnetic simulations. The results show excellent hard magnetic properties can be achieved in grain boundary engineered NdFeB, rare-earth magnets with a ThMn12 structure, Co-based nano-wires, and L10-FeNi provided that the magnet's microstructure is optimized.

Deep neural networks are used to model the magnetization dynamics in magnetic thin film elements. The magnetic states of a thin film element can be represented in a low dimensional space. With convolutional autoencoders a compression ratio of 1024:1 was achieved. Time integration can be performed in the latent space with a second network which was trained by solutions of the Landau-Lifshitz-Gilbert equation. Thus the magnetic response to an external field can be computed quickly.

MnAl-C is a prominent candidate for the replacement of rare earth magnets with a moderate energy density product. Crystallographic defects have a strong effect on magnetization properties. In this work, we show the influence of twinning defects in the nanometer regime on the quality of the magnet. Standard micromagnetic simulations and computations of the saddle point configuration for magnetization reversal highlight the importance of optimizing the fraction of and reducing the width of crystallographic twin defects. Switching field distributions and the maximum possible coercive field for ideal microstructures without defects are estimated using a reduced order micromagnetic model.

Magnetization reversal in permanent magnets occurs by the nucleation and expansion of reversed domains. Micromagnetic theory offers the possibility to localize the spots within the complex structure of the magnet where magnetization reversal starts. We compute maps of the local nucleation field in a Nd2Fe14B permanent magnet using a model order reduction approach. Considering thermal fluctuations in numerical micromagnetics we can also quantify the reduction of the coercive field due to thermal activation. However, the major reduction of the coercive field is caused by the soft magnetic grain boundary phases and misorientation if there is no surface damage.

We use a machine learning approach to identify the importance of microstructure characteristics in causing magnetization reversal in ideally structured large-grained Nd$_2$Fe$_{14}$B permanent magnets. The embedded Stoner-Wohlfarth method is used as a reduced order model for determining local switching field maps which guide the data-driven learning procedure. The predictor model is a random forest classifier which we validate by comparing with full micromagnetic simulations in the case of small granular test structures. In the course of the machine learning microstructure analysis the most important features explaining magnetization reversal were found to be the misorientation and the position of the grain within the magnet. The lowest switching fields occur near the top and bottom edges of the magnet. While the dependence of the local switching field on the grain orientation is known from theory, the influence of the position of the grain on the local coercive field strength is less obvious. As a direct result of our findings of the machine learning analysis we show that edge hardening via Dy-diffusion leads to higher coercive fields., Comment: 17 pages, 15 figures

The electronic structure, magnetic properties, and phase formation of hexagonal ferromagnetic Fe3Sn-based alloys have been studied from first principles and by experiment. The pristine Fe3Sn compound is known to fulfill all the requirements for a good permanent magnet, except for the magnetocrystalline anisotropy energy (MAE). The latter is large, but planar, i.e., the easy magnetization axis is not along the hexagonal c direction, whereas a good permanent magnet requires the MAE to be uniaxial. Here we consider Fe3Sn0.75M0.25, where M= Si, P, Ga, Ge, As, Se, In, Sb, Te, Pb, and Bi, and show how different dopants affect the MAE and can alter it from planar to uniaxial. The stability of the doped Fe3Sn phases is elucidated theoretically via the calculations of their formation enthalpies. A micromagnetic model is developed to estimate the energy density product (BH)max and coercive field μ0Hc of a potential magnet made of Fe3Sn0.75Sb0.25, the most promising candidate from theoretical studies. The phase stability and magnetic properties of the Fe3Sn compound doped with Sb and Mn have been checked experimentally on the samples synthesised using the reactive crucible melting technique as well as by solid state reaction. The Fe3Sn-Sb compound is found to be stable when alloyed with Mn. It is shown that even small structural changes, such as a change of the c/a ratio or volume, that can be induced by, e.g., alloying with Mn, can influence anisotropy and reverse it from planar to uniaxial and back., Authors acknowledge support from NOVAMAG project, under Grant Agreement No. 686056, EU Horizon 2020 Framework Programme. The computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at PDC and NSC centers. O.E. acknowledges support from STandUPP, eSSENCE, the Swedish Research Council and the KAW foundation (Grants No. 2012.0031 and No. 2013.0020). O.G. acknowledges the Hessen LOEWE Response Programme. Authors are thankful to Dr. Y. Kvashnin for useful discussions.

The maximum coercivity that can be achieved for a given hard magnetic alloy is estimated by computing the energy barrier for the nucleation of a reversed domain in an idealized microstructure without any structural defects and without any soft magnetic secondary phases. For Sm$_{1-z}$Zr$_z$(Fe$_{1-y}$Co$_y$)$_{12-x}$Ti$_x$ based alloys, which are considered an alternative to Nd$_2$Fe$_{14}$B magnets with lower rare-earth content, the coercive field of a small magnetic cube is reduced to 60 percent of the anisotropy field at room temperature and to 50 percent of the anisotropy field at elevated temperature (473K). This decrease of the coercive field is caused by misorientation, demagnetizing fields and thermal fluctuations., Comment: 5 pages, 4 figues

In this paper we apply an extended Landau-Lifschitz equation, as introduced by Ba\v{n}as et al. for the simulation of heat-assisted magnetic recording. This equation has similarities with the Landau-Lifshitz-Bloch equation. The Ba\v{n}as equation is supposed to be used in a continuum setting with sub-grain discretization by the finite-element method. Thus, local geometric features and nonuniform magnetic states during switching are taken into account. We implement the Ba\v{n}as model and test its capability for predicting the recording performance in a realistic recording scenario. By performing recording simulations on 100 media slabs with randomized granular structure and consecutive read back calculation, the write position shift and transition jitter for bit lengths of 10nm, 12nm, and 20nm are calculated., Comment: 5 pages, 3 figures, IEEE International Magnetics Conference INTERMAG 2017

In the search for rare-earth free permanent magnets, various ideas related to shape anisotropy are being pursued. In this work we assess the limits of shape contributions to the reversal stability using micromagnetic simulations. In a first series of tests we altered the aspect ratio of single phase prolate spheroids from 1 to 16. Starting with a sphere of radius $4.3$ times the exchange length $ L_{\mathrm{ex}}$ we kept the total magnetic volume constant as the aspect ratio was modified. For a ferromagnet with zero magnetocrystalline anisotropy the maximum coercive field reached up to $0.5$ times the magnetization $M_{\mathrm{s}}$. Therefore, in materials with moderate uniaxial magnetocrystalline anisotropy, the addition of shape anisotropy could even double the coercive field. Interestingly due to non-uniform magnetization reversal there is no significant increase of the coercive field for an aspect ratio greater than 5. A similar limit of the maximum aspect ratio was observed in cylinders. The coercive field depends on the wire diameter. By decreasing the wire diameter from $8.7 L_{\mathrm{ex}}$ to $2.2 L_{\mathrm{ex}}$ the coercive field increased by 40%. In the cylinders nucleation of a reversed domain starts at the corners at the end. Smoothing the edges can improve the coercive field by about 10%. In further simulations we compacted soft magnetic cylinders into a bulk-like arrangement. Misalignment and magnetostatic interactions cause a spread of $0.1 M_{\mathrm{s}}$ in the switching fields of the rods. Comparing the volume averaged hysteresis loops computed for isolated rods and the hysteresis loop computed for interacting rods, we conclude that magnetostatic interactions reduce the coercive field by up to 20%., Comment: 3 pages, 4 figures

In this paper, we investigate the potential of tetragonal L1 0 -ordered FeNi as the candidate phase for rare-earth-free permanent magnets considering anisotropy values from recently synthesized, partially ordered FeNi thin films. In particular, we estimate the maximum energy product (BH)max of L1 0 -FeNi nanostructures using micromagnetic simulations. The maximum energy product is limited due to the small coercive field of partially ordered L1 0 -FeNi. Nano-structured magnets consisting of 128 equi-axed, platelet-like, and columnar-shaped grains show a theoretical maximum energy product of 228, 208, and 252 kJ m -3 , respectively.

Permanent magnet materials require a high uniaxial magneto-crystalline anisotropy. Exchange coupling between small crystallites with easy-plane anisotropy induces an effective uniaxial anisotropy if arranged accordingly. Nanostructuring of materials with easy-plane anisotropy is an alternative way to create hard-magnetic materials. The coercivity increases with decreasing feature size. The resulting coercive field is about 12 percent of the anisotropy field for a crystal size of 3.4 times the Bloch parameter.

A new continuum approach to snowdrift modelling is introduced. In addition, numerical studies are carried out to identify the influence of time-varying wind conditions on snowdrift simulations. We compare the snowdrift patterns at Grimming mountain, Austria, derived using a time-averaged wind field and a time-varying wind field obtained from the numerical weather prediction model INCA. The results show significant differences in the deposition patterns and snow depth even after a 6 hour drift period. Using time-averaged boundary conditions leads to an underprediction of the resulting snow depth caused by averaging the wind speed, which lets gusts of wind disappear while snow transport is a non-linear function of the wind speed. Using numerical weather prediction models for snowdrift simulation therefore provides enhanced knowledge of the snow depth for local avalanche warning services.

We investigate the switching field distribution and the resulting bit error rate of exchange coupled ferri-/ferromagnetic bilayer island arrays by micromagnetic simulations. Using islands with varying microstructure and anisotropic properties, the intrinsic switching field distribution is computed. The dipolar contribution to the switching field distribution is obtained separately by using a model of a triangular patterned island array resembling $1.4\,\mathrm{Tb/in}^2$ bit patterned media. Both contributions are computed for different thickness of the soft exchange coupled ferrimagnet and also for ferromagnetic single phase FePt islands. A bit patterned media with a bilayer structure of FeGd($5\,\mathrm{nm}$)/FePt($5\,\mathrm{nm}$) shows a bit error rate of $10^{-4}$ with a write field of $1.16\,\mathrm{T}$., Comment: 10 pages, 11 figures

The coercive field of permanent magnets decays with temperature. At non-zero temperature the system can overcome a finite energy barrier through thermal fluctuations. Using finite element micromagnetic simulations, we quantify this effect, which reduces coercivity in addition to the decrease of the coercive field associated with the temperature dependence of the anisotropy field, and validate the method through comparison with existing experimental data.

A fully-automated pole-tip shape optimization tool, involving write head geometry construction, meshing, micromagnetic simulation and evaluation, is presented. Optimizations have been performed for three different writing schemes (centered, staggered and shingled) for an underlying bit patterned media with an areal density of 2.12 Tdots/in$^2$ . Optimizations were performed for a single-phase media with 10 nm thickness and a mag spacing of 8 nm. From the computed write field and its gradient and the minimum energy barrier during writing for islands on the adjacent track, the overall write error rate is computed. The overall write errors are 0.7, 0.08, and 2.8 x 10$^{-5}$ for centered writing, staggered writing, and shingled writing.

One approach to construct powerful permanent magnets while using less rare-earth elements is to combine a hard magnetic material having a high coercive field with a soft magnetic material having a high saturation magnetization at the nanometer scale and create so-called nanocomposite magnets. If both materials are strongly coupled, exchange forces will form a stable magnet. We use finite element micromagnetics simulations to investigate the changing hysteresis properties for varying arrays of soft magnetic spherical inclusions in a hard magnetic body. We show that the anisotropy arising from dipolar interactions between soft magnetic particles in a hard magnetic matrix can enhance the nucleation field by more than 10% and strongly depends on the arrangement of the inclusions.

We propose to use a compound of magnetic nanoparticles (20-100 nm) embedded in a flexible polymer (Polydimethylsiloxane PDMS) to filter circulating tumor cells (CTCs). The analysis of CTCs is an emerging tool for cancer biology research and clinical cancer management including the detection, diagnosis and monitoring of cancer. The combination of experiments and simulations lead to a versatile microfluidic lab-on-chip device. Simulations are essential to understand the influence of the embedded nanoparticles in the elastic PDMS when applying a magnetic gradient field. It combines finite element calculations of the polymer, magnetic simulations of the embedded nanoparticles and the fluid dynamic calculations of blood plasma and blood cells. With the use of magnetic active polymers a wide range of tunable microfluidic structures can be created. The method can help to increase the yield of needed isolated CTCs.

Micromagnetic beads are widely used in biomedical applications for cell separation, drug delivery, and hyperthermia cancer treatment. Here we propose to use self-organized magnetic bead structures which accumulate on fixed magnetic seeding points to isolate circulating tumor cells. The analysis of circulating tumor cells is an emerging tool for cancer biology research and clinical cancer management including the detection, diagnosis and monitoring of cancer. Microfluidic chips for isolating circulating tumor cells use either affinity, size or density capturing methods. We combine multiphysics simulation techniques to understand the microscopic behavior of magnetic beads interacting with soft magnetic accumulation points used in lab-on-chip technologies. Our proposed chip technology offers the possibility to combine affinity and size capturing with special antibody-coated bead arrangements using a magnetic gradient field created by Neodymium Iron Boron permanent magnets. The multiscale simulation environment combines magnetic field computation, fluid dynamics and discrete particle dynamics.

Finite element micromagnetic simulations are used to compute the temperature-dependent hysteresis properties of Nd2Fe14B permanent magnets in order to assess the influence of a hard (Dy,Nd)2Fe14B shell. The simulations show that the 4 nm thick shell cancels out the reduction in coercivity from an outer defect layer, which is known to exist at the grain boundaries in NdFeB permanent magnets. Activation volumes are computed and shown to depend on the structure's configuration as well as the temperature.

By application of a magnetic field on an amorphous metallic strip, the orientation of magnetization of Weiss domains can be changed. When the strip changes its length, this e!ect is called magnetostriction. We simulate this e!ect using a finite element method. In particular we calculate the change of the mechanical resonance frequency of a magnetic platelet as a function of the applied field. This gives a quantitative model of the influence of the applied magnetic field on the e!ective Young's Modulus of the material.