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.

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.

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.

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.

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.

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.

Multi-segmented nanowires for vortex magnetic domain wall racetrack memory

A vortex domain wall's(VW) magnetic racetrack memory's high performance depends on VW structural stability,high speed, low power consumption and high storage density. In this study, these critical parameters were investigated in magnetic multi-segmented nanowires using micromagnetic simulation. Thus, an offset magnetic nanowire with a junction at the center was proposed for this purpose. This junction was implemented by shifting one portion of the magnetic nanowire horizontally in the x-direction(l) and vertically(d) in the y-direction. The VW structure became stable by manipulating magnetic properties, such as magnetic saturation(M_(4)) and magnetic anisotropy energy(K_(u)). In this case, increasing the values of M_(4) ≥ 800 kA/m keeps the VW structure stable during its dynamics and pinning and depinning in offset nanowires,which contributes to maintenance of the storage memory's lifetime for a longer period. It was also found that the VW moved with a speed of 500 m/s, which is desirable for VW racetrack memory devices. Moreover, it was revealed that the VW velocity could be controlled by adjusting the offset area dimensions(l and d), which helps to drive the VW by using low current densities and reducing the thermal-magnetic spin fluctuations. Further, the depinning current density of the VW(J_(d)) over the offset area increases as d increases and l decreases. In addition, magnetic properties, such as the M_(4) and K_(u),can affect the depinning process of the VW through the offset area. For high storage density, magnetic nanowires(multisegmented) with four junctions were designed. In total, six states were found with high VW stability, which means three bits per cell. Herein, we observed that the depinning current density(J_(d)) for moving the VW from one state to another was highly influenced by the offset area geometry(l and d) and the material's magnetic properties, such as the M_(4) and K_(u).

Optimization of the grain boundary diffusion process by doping gallium and zirconium in Nd–Fe–B sintered magnets

As the channel for grain boundary diffusion(GBD)in Nd–Fe–B magnets,grain boundary(GB)phases have a very important effect on GBD.As doping elements that are commonly used to regulate the GB phases in Nd–Fe–B sintered magnets,the influences of Ga and Zr on GBD were investigated in this work.The results show that the Zr-doped magnet has the highest coercivity increment(7.97 kOe)by GBD,which is almost twice that of the Ga-doped magnet(4.32 kOe)and the magnet without Ga and Zr(3.24 kOe).Microstructure analysis shows that ZrB_(2)formed in the Zr-doped magnet plays a key role in increasing the diffusion depth.A continuous diffusion channel in the magnet can form because of the presence of ZrB_(2).ZrB_(2)can also increase the defect concentration in GB phases,which can facilitate GBD.Although Ga can also improve the diffusion depth,its effect is not very obvious.The micromagnetic simulation based on the experimental results also proves that the distribution of Tb in the Zr-doped magnet after GBD is beneficial to coercivity.This study reveals that the doping elements Ga and Zr in Nd–Fe–B play an important role in GBD,and could provide a new perspective for researchers to improve the effects of GBD.

Nonadiabatic spin-torque and damping effects on vortex core switching triggered by a single current pulse

Switching the orientation of a vortex core by spin-polarised pulse current introduces a promising concept for the reliable addressing of a single nanodisc element inside dense arrays. In this paper, micromagnetic simulations are employed to study the vortex core switching behaviour excited by a short in-plane Gaussian current pulse. We find that both the switching mechanism and the switching time are not sensitive to changes in the phenomenological parameters of spin-torque nonadiabaticity and Gilbert damping. The switching time, however, strongly depends on the current strength. In addition, we have theoretically predicted the parameter range of current pulses to achieve a single switching event.

Influence of Dzyaloshinskii-Moriya interaction on the magnetic vortex reversal in an off-centered nanocontact geometry

The influence of Dzyaloshinskii-Moriya interaction(DMI)on the vortex reversal driven by an out-of-plane spin-polarized current in an off-centered nanocontact structure is investigated.The simulation results show that DMI plays a vital role in vortex core reversal,including reversal current density,reversal velocity and reversal time.Under the influence of DMI,magnetic vortices still reverse polarity through the nucleation and annihilation of vortex and anti-vortex,with some peculiar characteristics.These results open up new possibilities for the application of magnetic vortex-based spin-transfer encryption nano-storage.

Effects of dipolar interactions on magnetic properties of Co nanowire arrays

Magnetic properties and magnetization processes of Co nanowire arrays with various packing densities are investigated by means of object-oriented micromagnetic framework（OOMMF） software package with finite difference micromagnetic simulations. The packing density of nanowires is changed with the diameter, number of nanowires and center-to-center spacing between the wires. The magnetization reversal mechanism and squareness of the hysteresis loops of the nanowire arrays are very sensitive to the packing density of nanowires. Clear steps and plateaux on the demagnetization are visible,which turns out that dipolar interactions among the wires have a significant influence on switching field.

Nonmonotonic effects of perpendicular magnetic anisotropy on current-driven vortex wall motions in magnetic nanostripes

In a magnetic nanostripe, the effects of perpendicular magnetic anisotropy（PMA） on the current-driven horizontal motion of vortex wall along the stripe and the vertical motion of the vortex core are studied by micromagnetic simulations.The results show that the horizontal and vertical motion can generally be monotonously enhanced by PMA. However, when the current is small, a nonmonotonic phenomenon for the horizontal motion is found. Namely, the velocity of the horizontal motion firstly decreases and then increases with the increase of the PMA. We find that the reason for this is that the PMA can firstly increase and then decrease the confining force induced by the confining potential energy. In addition, the PMA always enhances the driving force induced by the current.