Micromagnetic study of magnetization reversal in inhomogeneous permanent magnets

Macroscopic magnetic properties of magnets strongly depend on the magnetization process and the microstructure of the magnets.Complex materials such as hard-soft exchange-coupled magnets or just real technical materials with impurities and inhomogeneities exhibit complex magnetization behavior.Here we investigate the effects of size,volume fraction,and surroundings of inhomogeneities on the magnetic properties of an inhomogeneous magnetic material via micromagnetic simulations.The underlying magnetization reversal and coercivity mechanisms are revealed.Three different demagnetization characteristics corresponding to the exchange coupling phase,semi-coupled phase,and decoupled phase are found,depending on the size of inhomogeneities.In addition,the increase in the size of inhomogeneities leads to a transition of the coercivity mechanism from nucleation to pinning.This work could be useful for optimizing the magnetic properties of both exchange-coupled nanomagnets and inhomogeneous single-phase magnets.

Investigation on mechanism of magnetization reversal for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element methods

Magnetization configurations were calculated under various magnetic fields for nanocrystalline Pr-Fe-B permanent magnets by micromagnetic finite element method.According to the configurations during demagnetization process, the mechanism of magnetization reversal was analyzed.For the Pr2Fe14B with 10 nm grains or its composite with 10vol.% α-Fe, the coercivity was determined by nucleation of reversed domain that took place at grain boundaries.However, for Pr2Fe14B with 30 nm grains, coercivity was controlled by pinning of the nucle-ated domain.For Pr2Fe14B/α-Fe with 30vol.% α-Fe, the demagnetization behavior was characterized by continuous reversal of α-Fe moment.

Micromagnetic studies of perpendicular recording FePt media with controllable grain size distributions

A 3-dimensional (3D) micromagnetic model combined with Fast Fourier Transform (FFT) method was built up to study the writability in the L10 FePt perpendicular medium. The effects of controllable grain size distributions were studied by grain growth simulation. It is found that the cross-track-averaged magnetization changes little between the L10 FePt medium with uniform or non-uniform grain size distribution.

Micromagnetic simulations of reversal magnetization in cerium-containing magnets

Single-grain models with different cerium contents or structural parameters have been introduced to investigate the reversal magnetization behaviors in cerium-containing magnets. All the micromagnetic simulations are carried out via the object oriented micromagnetic framework(OOMMF). As for single(Nd,Ce)_2 Fe_(14)B type grain, the coercivity decreases monotonously with the increase of the cerium content. Four types of grain structure have been compared: single(Nd,Ce)_2 Fe_(14)B type, core((Nd,Ce)_2 Fe_(14)B)-shell(Nd_2 Fe_(14)B) type with 2 nm thick shell, core(Ce_2 Fe_(14)B)-shell(Nd_2 Fe_(14)B) type, and core(Nd_2 Fe_(14)B)-shell(Ce_2 Fe_(14)B) type. It is found that core((Nd,Ce)_2 Fe_(14)B)-shell(Nd_2 Fe_(14)B)type grain with 2 nm thick shell always presents the largest coercivity under the same total cerium content. Furthermore,the relationship between the coercivity and the shell thickness t in core((Nd,Ce)_2 Fe_(14)B)-shell(Nd_2 Fe_(14)B) type grain has been studied. When the total cerium content is kept at 20.51 at.%, the analyzed results show that as t varies from 1 nm to 7 nm, the coercivity gradually ascends at the beginning, then quickly descends after reaching the maximum value when t = 5 nm. From the perspective of the positions of nucleation points, the reasons why t affects the coercivity are discussed in detail.

Micromagnetic simulation on the dynamic susceptibility spectra of cobalt nanowires arrays:the effect of magnetostatic interaction

Micromagnetic simulations have been performed to obtain the dynamic susceptibility spectra of 4×4 cobalt nanowire arrays with different spatial configurations and geometries. The susceptibility spectra of isolated wires have also been simulated for comparison purposes. It is found that the susceptibility spectrum of nanowire array bears a lot of similarities to that of an isolated wire, such as the occurrences of the edge mode and the bulk resonance mode. The simulation results also reveal that the susceptibility spectrum of nanowire array behaves like that of single isolated wire as the interwire distance grows to an extent, which is believed due to the decrease of magnetostatic interaction among nanowires, and can be further confirmed by the static magnetic hysteresis simulations. In comparison with single nanowire, magnetostatic interaction may increase or decrease the resonance frequencies of nanowire arrays assuming a certain interwire distance when the length of array increases. Our simulation results are also analysed by employing the Kittel equation and recent theoretical studies.

Micromagnetic simulation of Sm–Co/α-Fe/Sm–Co trilayers with various angles between easy axes and the film plane

Hysteresis loops and energy products have been calculated systematically by a three-dimensional （3D） software OOMMF for Sm-Co/α-Fe/Sm-Co trilayers with various thicknesses and β, where β is the angle between the easy axis and the field applied perpendicular to the film plane. It is found that trilayers with a perpendicular anisotropy possess considerably larger coercivities and smaller remanences and energy products compared with those with an in-plane anisotropy. Increase of β leads to a fast decrease of the maximum energy product as well as the drop of both remanence and coercivity. Such a drop is much faster than that in the single-phased hard material, which can explain the significant discrepancy between the experiment and the theoretical energy products. Some modeling techniques have been utilized with spin check procedures performed, which yield results in good agreement with the one-dimensional （1D） analytical and experimental data, justifying our calculations. Further, the calculated nucleation fields according to the 3D calculations are larger than those based on the 1D model, whereas the corresponding coercivity is smaller, leading to more square hysteresis loops and better agreement between experimental data and the theory.

Investigation on Hard Magnetic Properties of Nanocomposite Permanent Magnets with Precipitate-Typed Microstructure by Micromagnetic Finite-Element Methods

The demagnetization curves were calculated using micromagnetic finite-element method for nanocomposite Pr 2Fe 14B/α-Fe permanent magnets with precipitate-typed microstructure. Due to intergrain exchange coupling, both remanence enhancement and a single magnetic phase behavior in demagnetization curve were found. For the samples with the hard phase as the precipitate and the soft one as the matrix, a coercivity μ 0H c of 0.78 T, a remanence J r of 1.18 T and a large energy product (BH) max of 200 kJ·m -3 are obtained for the sample with hard grain size being 23 nm. While, for the sample with the soft phase as the precipitate, μ 0H c of 0.95 T, J r of 1.24 T and (BH) max of 240 kJ·m -3 are obtained for the sample with soft grain size being 10 nm. The calculating results were compared with the experimental Pr 8Fe 87B 5 ribbons. The dependence of remanence and coercivity on the microstructure was discussed extensively.

Micromagnetic simulation with three models of FeCo/L1_0 FePt exchange-coupled particles for bit-patterned media

Compositing soft and hard materials is a promising method to decrease the coercivity of L10 FePt, which is considered to be a suitable material for bit-patterned media. This paper reports the simulation of three models of FeCo/L10 FePt exchange-coupled composite particles for bit patterned media by the OOMMF micromagnetic simulation software： the enclosed model, the side-enclosed model, and the top-covered model. All of them have the same volumes of the soft and hard parts but different shapes. Simulation results show that the switching fields for the three models can be reduced to about 10 kOe （1 Oe = 79.5775 A/m） and the factor gain can be improved to 1.4 when the interface exchange coefficient has a proper value. Compared to the other models, the enclosed model has a wider range of interface exchange coefficient values, in which a low switching field and high gain can be obtained. The dependence of the switching fields on the angle of the applied field shows that none of the three models are easily affected by the stray field of a magnetic head.

Micromagnetic Simulation of Magnetization Reversal in SmCo_5/Sm_2Co_(17) Magnets

A three-dimensional finite element micromagnetic algorithm was developed to study the magnetization reversal of the SmCo 5/Sm 2Co 17 based magnets. The influences of the microstructure and magnetic parameters on the coercivity were studied based on the model consisting of 64 irregular cells according to the experimental microstructure. Numerical results show that the coercivity increases with increasing the 2∶17-type cell size. Large cell boundary thickness leads to small coercivity. The drop of anisotropy constant of 1∶5 phase leads to the coercivity reducing, while the effect of exchange constant of 1∶5 phase on coercivity is contrary to that of exchange constant. The calculated field dependence of coercivity can be predicted by an inhomogeneous domain-wall pinning model. The microstructure parameter was analyzed by comparing the calculated coercivity.

Machine Learning and Micromagnetic Studies of Magnetization Switching

Magnetization switching is one of the most fundamental topics in the field of magnetism.Machine learning(ML)models of random forest(RF),support vector machine(SVM),deep neural network(DNN)methods are built and trained to classify the magnetization reversal and non-reversal cases of single-domain particle,and the classification performances are evaluated by comparison with micromagnetic simulations.The results show that the ML models have achieved great accuracy and the DNN model reaches the best area under curve(AUC)of 0.997,even with a small training dataset,and RF and SVM models have lower AUCs of 0.964 and 0.836,respectively.This work validates the potential of ML applications in studies of magnetization switching and provides the benchmark for further ML studies in magnetization switching.

Micromagnetic simulation of FeCo write head in perpendicular recording hard disk drives

The single-pole tip (SPT) heads made of the high saturation FeCo ferromagnetic metals are crucial for the actualization of ultrahigh density perpendicular recording. The effective head field distribution in the medium is of key importance for the design of the SPT head, which would be analyzed by micromagnetic simulations in this work. Two 3D micromagnetic models of the SPT head were established to select a more appropriate method of modeling, with a magnetostatic image effect or a real soft magnetic material to model the image of the SPT head in soft under layer (SUL). The results from these two designs were tested and compared to the ideal head field calculated by the Jacobi finite element method (FEM); and the design with the real soft magnetic material as image was proved suitable for simulating the ultrahigh density perpendicular recording write head.

Micromagnetic Analysis on Demagnetization Process of Single-Phase Nanocrystalline Permanent Magnets with Different Degrees of Orientation

A three-dimentional finite element micromagnetic algorithm was developed to study the magnetization reversal of Pr2Fe14B single-phase nanocrystalline permanent magnets. A single-phase nanocrystalline Pr2Fe14B magnets composed of 216 irregular shaped grains was built. The magnetic hysteresis loops were simulated by micromagnetic finite element method. The contribution of intergrain exchange coupling ment degree （IGEC） to remanence enhancement is considered related to the alignin oriented magnets, and decreased with improved grain alignment. For the magnets with perfectly crystallo- graphic alignment of grains, the contribution of IGEC to remanence enhancement is nearly zero. The shape of demagnetization curve is not only dependent on grain alignment degree but also on the strength of IGEC in magnets.

Micromagnetic simulation for high field sensors with perpendicular magnetizations

In this paper, we present a micromagnetic design for high field sensors. The hard layer of the sensors is L10-FePt which is magnetized perpendicularly to film plane and the sense layer is NiFe which is magnetized in the film plane. The magnetization configurations of the hard and sense layers at different external magnetic fields have been simulated. In micromagnetic simulation, the sense field up to one tesla can be reached by using this sensor. We find that whether the sensor has a symmetric or an asymmetric field-sensing window is determined by the coercive field of the hard layer and the demagnetizing field of the sense layer.

Investigation of L1_0 FePt-based soft/hard composite bit-patterned media by micromagnetic simulation

The soft/hard composite patterned media have potential to be the next generation of magnetic recording, but the composing modes of soft and hard materials have not been investigated systematically. L10 FePt-based soft/hard composite patterned media with an anisotropic constant distribution are studied by micromagnetic simulation. Square arrays and hexagonal arrays with various pitch sizes are simulated for two composing types： the soft layer that encloses the hard dots and the soft layer that covers the whole surface. It is found that the soft material can reduce the switching fields of bits effectively for all models. Compared with the first type, the second type of models possess low switching fields, narrow switching field distributions, and high gain factors due to the introduction of inter-bit exchange coupling. Furthermore, the readout waveforms of the second type are not deteriorated by the inter-bit soft layers. Since the recording density of hexagonal arrays are higher than that of square arrays with the same center-to-center distances, the readout waveforrns of hexagonal arrays are a little worse, although other simulation results are similar for these two arrays.

Micromagnetic Structure of Co-Rich Amorphous Microwires

Results on the magneto-optical investigation of near-surface micromagnetic structure (MMS) of Co69Fe4Si12B15 amorphous wires 10～50 μm in diameter are presented. The wires were prepared by the rapid solidification technique. The magnetic field H was applied along or perpendicular to the wire length. By scanning the light spot of 1 μm-diameter along the wire length, distributions of magnetization components (both parallel and perpendicular to the applied magnetic field) and also local hysteresis characteristics of the wires were measured. It was experimentally established that owing to the compressive stresses from quenching coupled with negative magnetostriction of Co-rich amorphous materials, the examined microwires have a circumferential magnetic anisotropy. In consequence, there are the near-surface alternate left- and right-handled circular domains in these samples. The dependencies of the circular domain width on the wire diameter and length were found. It was discovered that in the axial magnetic field local hysteresis loops are unhysteretic. It was proved that in this case the dominant mechanism of the wire magnetization reversal is rotation of local magnetization vectors in circular domains.

Effects of notches on the order of flux-closure state formation in bi-rings by micromagnetic simulation

The effects of the number and the location of notches on the formation of flux-closure states in bi-rings with fields applied in the x direction （i.e., along the short axis direction of hi-rings） and y direction （i.e., along the long axis direction of bi-rings） are investigated using micromagnetic simulation. For the bi-rings with one notch and the bi-rings with two notches symmetric about y axis, the order of flux-closure state formation in each ring can be controlled. But the flux-closure state forms simultaneously in each ring for the bi-rings with two notches symmetric about x axis. For the bi-rings with two notches that are symmetric neither about x axis nor about y axis, only one ring can form a flux- closure state in the y-direction field and no fluxclosure state can be found in rings in the x-direction field. Therefore, logic states can be defined by controlling the order of flux-closure state formation, which can be utilized in future logic devices.

Magnetization Reversal for Ni Nanowires Studied by Micromagnetic Simulations

The magnetization reversal mechanisms for Ni nanowires with different diameters were investigated by micromagnetic simulations. The results show that the reversal mechanisms are significantly dependeht on the diameter of wire. For very thin wires, the reversal occurs by pseudo-coherent rotation. With increasing diameter, magnetization reversal takes place via different nucleation （the transverse domain wall and the vortex domain wall） and subsequent propagation. The reason of transition from the transverse domain wall to the vortex domain wall is given by analytical studies. With further increase of the diameter, the reversal nuclear domain wall becomes tundishoshaped form. As the diameter increases, the width of wall becomes larger.

Periodic Boundary Conditions for Finite-Differentiation-Method Fast-Fourier-Transform Micromagnetics

We describe an accurate periodic boundary condition （PBC） called the symmetric PBC in the calculation of the magnetostatie interaction field in the finite-differentiation-method fast-Fourier-transform （FDM-FFT） micromagneties. The micromagnetic cells in the regular mesh used by the FDM-FFT method are finite-sized elements, but not geometrical points. Therefore, the key PBC operations for FDM-FFT methods are splitting and relocating the micromagnetic cell surfaces to stay symmetrically inside the box of half-total sizes with respect to the origin. The properties of the demagnetizing matrix of the split micromagnetic cells are discussed, and the sum rules of demagnetizing matrix are fulfilled by the symmetric PBC.

Micromagnetic Investigation of Microwave Permeability of Magnetic Artificial Spin Ice

The complex permeability of the artificial spin ice array at different magnetic states is calculated using the micromagnetic simulation method. It is observed that the permeability spectra are dependent on the magnetization distributions of the array. The dependence of the permeability spectrum on the applied magnetic field strength and on the spacing gap between the neighboring elements is also investigated. Depending on the initial magnetization saturating direction, the permeability spectrum exhibits different sensitivity to the strength of the external applied magnetic field and to the spacing distance between the comprising elements of the artificial spin ice array.

Micromagnetic Studies of Finite Temperature M-H Loops for FePt-C Media

We have recently developed a new micromagnetie method at finite temperature, where the Hybrid Monte Carlo method is employed to realize the Boltzmann distribution with respect to the magnetic free energy. Hence, the hysteresis loops and domain structures at arbitrary temperature below the Curie point Tc can be simulated. The Haxnilton equations are used to find the magnetization distributions instead of the Landau-Lifshitz （LL） equations. In our previous work, we applied this method on a simple uniaxial anisotropy nano-paxticle and compared it with the mieromagnetic method using LL equations. In this work, we use this new method to simulate an LIO FePt-C granular thin film at finite temperatures. The polycrystalline Voronoi microstructure is included in the model, and the effects of the misorientation of FePt grains are also simulated.