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.

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 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.

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.

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.

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.

Providing insight into exchange coupling within nanomagnetism:mechanism,micromagnetic simulation,synthesis and biomedical application

Exchange coupling within nanomagnetism is a rapidly evolving field with significant implications for that plays a crucial role in the development of magnetic nanomaterials.Manipulating exchange coupling interaction enables the magnetic systems to overcome limitations associated with size-dependent magnetic behavior within nano scale,thereby improving their magnetic properties and providing for superior performance in biomedical applications compared with single-phase magnetic materials.Understanding the underlying mechanism of exchange coupling and its impact on macroscopic magnetic properties is crucial for the design and application of such magnetic materials.This review provides an overview of recent advances in interfacial exchange coupling among different magnetic modalities-ferromagnetism,ferrimagnetism,and antiferromagnetism-based on core-shell magnetic nanoparticles(MNPs).Additionally,this review discusses micromagnetic simulations to gain insights into the relationship between the microscopic magnetic structure(size,shape,composition,and exchange coupling)and the resulting macroscopic properties.The controlled synthesis of MNPs is summarized,including one-step method and two-step method.The precise manipulation of interfacial characteristics is of great importance,albeit challenging,as it allows for the finetuning of magnetic properties tailored for specific applications.The review also explores potential applications of coreshell MNPs in magnetic resonance imaging,hyperthermia therapy,targeted drug delivery,and advanced neuromodulation.

Optimizing magnetoelastic properties by machine learning and high-throughput micromagnetic simulation

Magnetoelastic couplings in giant magnetostrictive materials(GMMs)attract significant interests due to their extensive applications in the fields of spintronics and energy harvesting devices.Understanding the role of the selection of materials and the response to external fields is essential for attaining desired functionality of a GMM.Herein,machine learning(ML)models are conducted to predict saturation magnetostrictions(λ_(s))in RFe_(2)-type(R=rare earth)GMMs with different compositions.According to ML-predicted composition–λsrelations,it is discovered that the values ofλshigher than1100×10^(-6)are almost situated in the composition space surrounded by 0.26≤x≤0.60 and 1.90≤y≤2.00 for the ternary compounds of Tb_(x)Dy_(1-x)Fe_(y).Assisted by ML predictions,the compositions are further narrowed down to the space surrounded by 0.26≤x≤0.32 and 1.92≤y≤1.97 for the excellent piezomagnetic(PM)performance in the Tb_(x)Dy_(1-x)Fe_(y)based PM device through our developed high-throughput(HTP)micromagnetic simulation(MMS)algorithm.Accordingly,high sensitivities up to10.22-13.61 m T·MPa^(-1)are observed in the optimized range within which the available experimental data fall well.This work not only provides valuable insights toward understanding the mechanism of magnetoelastic couplings,but also paves the way for designing and optimizing highperformance magnetostrictive materials and PM sensing devices.

MicroMagnetic.jl:A Julia package for micromagnetic and atomistic simulations with GPU support

MicroMagnetic.jl is an open-source Julia package for micromagnetic and atomistic simulations.Using the features of the Julia programming language,MicroMagnetic.jl supports CPU and various GPU platforms,including NVIDIA,AMD,Intel,and Apple GPUs.Moreover,MicroMagnetic.jl supports Monte Carlo simulations for atomistic models and implements the nudged-elastic-band method for energy barrier computations.With built-in support for double and single precision modes and a design allowing easy extensibility to add new features,MicroMagnetic.jl provides a versatile toolset for researchers in micromagnetics and atomistic simulations.

Growth and micromagnetic simulation of magnetite nanoparticles

Magnetite nanoparticles with different sizes and different assemblies were synthesized via hydrothermal method.Micromagnetic simulation shows the magnetite nanocubes with different sizes have different energy states,which determines the assembly mode.Magnetite nanocubes with the side length of 30-60 nm tended to be dispersed while both nanochains and dispersed nanoparticles were found to grow for the nanocubes with the side length less than 30 nm,which can be explained in the fact that the above two assembly modes have very close energies.The assembly mode of nanocubes with the size bigger than 60 nm is generally nanorings consisting of connected inter-grown nanocubes and the nanocubes are no longer single domain.The simulations are consistent with the experimental results.

Micromagnetic simulation of Au interlayer in L1_0-FePt nanocomposite recording medium

Owing to the epitaxial inducement of Au atom,Au interlayer was introduced to increase the perpendicular anisotropy and the coercivity in L10-FePt nanocomposite film.Micromagnetics can be used to reveal the relationship between microstructure and magnetic properties of materials,and give the information of the perpendicular anisotropy and coercivity.In this work,the effect of the Au interlayer on annealed[Fe（0.5 nm）/Pt（0.5 nm）/Au（d nm）]10 nanocomposite recording medium by a micromagnetic model was studied.The model contains three phases：hard magnetic phase,soft magnetic phase,and nonmagnetic phase.The calculated result shows that perpendicular orientation degree of the texture and proportion of a hard magnetic phase to the total phase in the annealed film are both enhanced by increasing Au interlayer thickness.This result can be conducive to the improvement of the perpendicular anisotropy and the coercivity of the FePt nanocomposite film in the experiments.

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.

Shape-influenced non-reciprocal transport of magnetic skyrmions in nanoscale channel

Skyrmions, with their vortex-like structures and inherent topological protection, play a pivotal role in developing innovative low-power memory and logic devices. The efficient generation and control of skyrmions in geometrically confined systems are crucial for the development of skyrmion-based spintronic devices. In this study, we focus on investigating the non-reciprocal transport behavior of skyrmions and their interactions with boundaries of various shapes. The shape of the notch structure in the nanotrack significantly affects the dynamic behavior of magnetic skyrmions. Through micromagnetic simulation, the non-reciprocal transport properties of skyrmions in nanowires with different notch structures are investigated in this work.

Creation and annihilation of artificial magnetic skyrmions with the electric field

Recent theory and experiments show that artificial magnetic skyrmions can be stabilized at room temperature without the need for the external magnetic field,casting strong potentials for the device applications.In this work,we study the electric field manipulation of artificial magnetic skyrmions imprinted by Co disks on CoPt multilayers utilizing the micromagnetic simulations.We find that the reversible annihilation and creation of skyrmions can be realized with the electric field via the strain mediated magnetoelastic coupling.In addition,we also demonstrate controllable manipulation of individual skyrmion,which opens a new platform for constructing magnetic field-free and low-energy dissipation skyrmion based media.

Consistency between domain wall oscillation modes and spin wave modes in nanostrips

Investigations on domain wall(DW) and spin wave(SW) modes in a series of nanostrips with different widths and thicknesses have been carried out using micromagnetic simulation. The simulation results show that the frequencies of SW modes and the corresponding DW modes are consistent with each other if they have the same node number along the width direction. This consistency is more pronounced in wide and thin nanostrips, favoring the DW motion driven by SWs.Further analysis of the moving behavior of a DW driven by SWs is also carried out. The average DW speed can reach a larger value of ~ 140 m/s under two different SW sources. We argue that this study is very meaningful for the potential application of DW motion driven by SWs.

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 L1_(0)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 L1_(0)FePt medium with uniform or non-uniform grain size distribution.

Micromagnetism simulation on effects of soft phase size on Nd2Fe14B/α-Fe nanocomposite magnet with soft phase imbedded in hard phase

In this study, micromagnetism simulation by using timte dltterence method is cameo out on the Ncl21-el415/a-Fe nanocomposite magnet with soft phase imbedded in hard phase. The effects of soft magnetic phase size （S） on the magnetic properties and magnetic reversal modes are systematically analyzed. As S increases from 1 nm to 48 nm, the remanence （Jr） increases, while the coercivity （Hci） decreases, leading to the result that the magnetic energy prod- uct [（BH）max] first increases slowly, and then decreases rapidly, peaking at S = 24 nm with the （BH）max of 72.9 MGOe （1 MGOe = 7.95775 kJ.m-3）. Besides, with the increase of S, the coercivity mechanism of the nanocomposite magnet changes from nucleation to pinning. Furthermore, by observing the magnetic moment evolution in demagnetization pro- cess, the magnetic reversal of the soft phase in the nanocomposite magnet can be divided into three modes with the increase of S： coherent rotation （S 〈 3 nm）, quasi-coherent rotation （3 nm≤S 〈 36 nm）, and the vortex-like rotation （S ≥36 nm）.

Magnonic band-pass and band-stop filters with structurally modulated waveguides

Magnonics is a fascinating and emerging field, which mainly studies processing information with spin waves.Magnonic devices with in-plane magnetization have recently been realized. Because of the isotropic propagation, magnonic devices based on perpendicular magnetization are attracting extensive interest. Here, we numerically demonstrate two magnonic filters with out-of-plane magnetization using micromagnetic simulations. The band-pass and the band-stop functions have been realized in two structurally modulated waveguides, respectively. The intensity of spin waves is manipulated when they arrive at the uniformly/non-uniformly magnetized modulators, which results in the variation of transmission coefficients. It is found that the proposed filters can work at multiple frequencies, which can be further adjusted by the external magnetic field. Our designed magnonic devices with Néel-type skyrmion could promote the development of spin wave computing using spin textures.

Skyrmion-based logic gates controlled by electric currents in synthetic antiferromagnet

Skyrmions in synthetic antiferromagnetic(SAF) systems have attracted much attention in recent years due to their superior stability, high-speed mobility, and completely compensated skyrmion Hall effect. They are promising building blocks for the next generation of magnetic storage and computing devices with ultra-low energy and ultra-high density.Here, we theoretically investigate the motion of a skyrmion in an SAF bilayer racetrack and find the velocity of a skyrmion can be controlled jointly by the edge effect and the driving force induced by the spin current. Furthermore, we propose a logic gate that can realize different logic functions of logic AND, OR, NOT, NAND, NOR, and XOR gates. Several effects including the spin–orbit torque, the skyrmion Hall effect, skyrmion–skyrmion repulsion, and skyrmion–edge interaction are considered in this design. Our work may provide a way to utilize the SAF skyrmion as a versatile information carrier for future energy-efficient logic gates.

In-plane spin excitation of skyrmion bags

Skyrmion bags are spin structures with arbitrary topological charges, each of which is composed of a big skyrmion and several small skyrmions. In this work, by using an in-plane alternating current(AC) magnetic field, we investigate the spinwave modes of skyrmion bags, which behave differently from the clockwise(CW) rotation mode and the counterclockwise(CCW) rotation mode of skyrmions because of their complex spin topological structures. The in-plane excitation power spectral density shows that each skyrmion bag possesses four resonance frequencies. By further studying the spin dynamics of a skyrmion bag at each resonance frequency, the four spin-wave modes, i.e., a CCW-CW mode, two CW-breathing modes with different resonance strengths, and an inner CCW mode, appear as a composition mode of outer skyrmion–inner skyrmions. Our results are helpful in understanding the in-plane spin excitation of skyrmion bags, which may contribute to the characterization and detection of skyrmion bags, as well as the applications in logic devices.