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A new mechanism of recording for a MRAM cell, which is based on a parametric resonance, has been proposed [1] and experimentally studied. The parametric mechanism requires a substantially smaller spin torque for the magnetization reversal due to the resonance nature of this recording mechanism and, therefore, it can be a solution for further reduction of the recording energy for the MRAM operation.&lt;br/&gt;Two parametric mechanisms for the magnetization reversal are proposed, studied and experimentally evaluated. The first mechanism is due to a modulation of the magnetic field of the Spin- Orbit Torque. The second mechanism is due to modulation of the anisotropy field. For both mechanisms, a parametric torque is created by a RF modulated current, which resonantly enhances the magnetization precession until a magnetization reversal.&lt;br/&gt;Additionally, a parametric mechanism for magnetization reversal by a DC current is proposed and studied. This parametric mechanism may occur in a magneto-resistive structure, in which a magnetization precession modulates an electrical current. It results in a positive feedback loop, in which a magnetization precession creates a torque, which more enhances the precession.

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Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

2022 Joint MMM-INTERMAG

Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

The 15th Joint MMM-INTERMAG Conference (2022 Joint) is sponsored jointly by AIP Publishing and the IEEE Magnetics Society. Members of the international scientific and engineering communities interested in recent developments in fundamental and applied magnetism are invited to attend and contribute to the technical sessions. The technical program will include invited and contributed papers in oral and poster sessions, invited symposia, a plenary session, and an evening session, with about 1500 presentations overall. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

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A new mechanism of recording for a MRAM cell, which is based on a parametric resonance, has been proposed [1] and experimentally studied. The parametric mechanism requires a substantially smaller spin torque for the magnetization reversal due to the resonance nature of this recording mechanism and, therefore, it can be a solution for further reduction of the recording energy for the MRAM operation. Two parametric mechanisms for the magnetization reversal are proposed, studied and experimentally evaluated. The first mechanism is due to a modulation of the magnetic field of the Spin- Orbit Torque. The second mechanism is due to modulation of the anisotropy field. For both mechanisms, a parametric torque is created by a RF modulated current, which resonantly enhances the magnetization precession until a magnetization reversal. Additionally, a parametric mechanism for magnetization reversal by a DC current is proposed and studied. This parametric mechanism may occur in a magneto-resistive structure, in which a magnetization precession modulates an electrical current. It results in a positive feedback loop, in which a magnetization precession creates a torque, which more enhances the precession.

![](https://assets.underline.io/uploads/markdown_image/1/image/542c9b5a32048ecc7a06babee370e4ca.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/256f37dab48ea38e1c2550f583dbc4f5.jpg)

Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

technical paper

The wave reversal mode is a magnetization reversal mechanism that appears in ferromagnetic nanotubes of certain geometric parameters when an external magnetic field is applied perpendicular to their axes. The distinctive feature of this mode is that leads to well-defined S-shaped hysteresis curves [1]. In order to gain insight into the stability of this latter effect, we have performed micromagnetic simulations for permalloy and nickel nanotubes obtaining a non-monotonic behavior for coercivity as well as for remanence as a function of nanotube diameter for both materials. Motivated on these latter intriguing results, we found that measuring the area that encloses the hysteresis curve is a novel and simple strategy to identify the appearance of the wave reversal mode [2]. An additional contribution of this work is the proposal of a new magnetic phase diagram that allows determining the stability of this reversal mechanism as a function of the geometric and magnetic parameters of the tubes [2]. The authors acknowledge the access to Mendieta cluster (CCAD-UNC) and financial support from SECYT-UNC, MINCyT 2019, Fondecyt 1200302, Basal Project AFB180001 and Programa Escala Docente AUGM.

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Wave reversal mode: A new magnetization reversal mechanism in magnetic nanotubes

With the rise of deep learning, physics informed neural networks [1] became an alternative to finite element simulation in many fields of materials and device design. Physics informed neural networks bring several advantages as compared to traditional numerical methods for solving partial differential equations like finite differences or finite elements: 1. There is no need for mesh generation. 2. Inverse problems may be solved effectively. 3. A whole family of problems may be solved with a single neural network. We demonstrate how physics informed neural networks can be applied in magnetostatics and micromagnetics. The approach is like the Ritz method for computing the magnetic field or the magnetization. However, instead of finite element basis functions [2], we use dense neural networks to approximate the unknowns. The underlying physics is incorporated through the loss function which is minimized during training of the neural network. We first applied physics informed neural network to solve a classical inverse problem in magnetism. We searched for the magnetization in a hollow cylinder that produces a uniform field in the hole and has zero field outside. The mean relative error between the neural network estimate and the analytic solution for the magnetization was 0.27 percent. We computed the demagnetization curve of a Nd2Fe14B particle. The difference between the finite element solution and the neural network estimate was 0.9 percent. We computed the lowest eigenvalue of Brown's linearized micromagnetic euqation to get the nucleation field for a soft magnetic defect in a hard magnetic matrix. The mean realtive error for the nucleation field of an Fe inclusion in Sm2Fe17N3 as function of defect size was 0.4 percent as compared to the analytic solution [3]. Because of the ability to solve multiple problems simulateneously, physics informed neural networks have a great potential for optimization and tailoring the magnet's internal structure to achieve a specific demagnetiation curve. The financial support by the Austrian Federal Ministry for Digital and Economic Affairs, the National Foundation for Research, Technology and Development and the Christian Doppler Research Association is gratefully acknowledged.

Physics informed neural networks for computational magnetism

The motion of electrons and therefore the topological Hall effect (THE) are governed by the flux density (B-field), as contrasted to the applied magnetic field (H-field). Maxwell's equations predict that the relevant perpendicular flux density (B-field) in laterally homogeneous thin films is µoH, independent of the magnetization M. However, transport measurements and nonvanishing THEs at H = 0 indicate that the motion of the electrons depends on M. This paradox is solved by noting that electrons are point-like objects moving in exchange-and-correlation holes. Their magnetostatic interaction with the crystalline environment is realized through Lorentz cavities [1, 2] where B = µo(H + DL M) with DL ~ 1/3, intermediate between B = µoH and B = µo(H + M). This approximation includes inhomogeneities, because the local magnetization vector M(r) is not necessarily parallel to the volume-averaged magnetization &lt;M&gt;. The separation of the THE from the magnetization contribution to the anomalous Hall-effect is therefore not straightforward and the use of &lt;M&gt; can lead to systematic errors [3-5]. For example, in nanogranular structures (Fig. 1), changes in &lt;M&gt; may be dominated by loosely coupled regions (inside the dashed circles) where conductivity, current density &lt;j&gt;, and Hall-effect contribution are disproportionally small. Another field consideration is that the THE reflects electrons adiabatically exchange-interacting with atomic magnetic moments. The corresponding Berry phase changes the motion of the electrons. The change is formally equivalent to the effect of a fictitious magnetic field, but this field does not obey Maxwell's equations in a micromagnetic sense. This work is supported by NSF-EQUATE (OIA-2044049), NSF-DMREF (No. 1729288), the NU Collaborative Initiative, and NCMN.

![](https://assets.underline.io/uploads/markdown_image/1/image/7dfda3153223eb4af3edd7e68fc7833e.jpg)

Fig. 1. Effect of structural inhomogeneities on the THE: (a) current density in a nanoparticulate thin film, (b) Bruggeman description of the current, (c) spin-structure in the interaction-domain limit, and (d) spin structure in the non-cooperative limit. The yellow region in (c) fully contributes to the magnetization but only partially to the Hall effect.

Berry-Phase Interpretation of Thin-Film Micromagnetism

An efficient method for computing thermodynamic equilibrium states at the micromagnetic length scale is introduced [1], based on the Markov chain Monte Carlo method. Trial moves include not only rotations of spins, but also a change in their magnetization length. The method is parameterized using the longitudinal susceptibility, reproduces the same Maxwell-Boltzmann distribution as the stochastic Landau-Lifshitz-Bloch equation, and is applicable both below and above the Curie temperature. The algorithm has been implemented in Boris [2], is fully parallel [3], can be executed on graphical processing units, and efficiently includes the long range dipolar interaction. Applications to finite-temperature hysteresis loop modelling, chiral magnetic thin films, granular magnetic media, and artificial spin ices are discussed. A typical application is exemplified in relation to Figure 1, where finite-temperature hysteresis loops in a 2 nm thin Co film with interfacial Dzyaloshinsky-Moriya interaction are computed. Simulation of such hysteresis loops in chiral films is problematic with quasi-zero temperature methods such as steepest descent energy minimizer, since the nucleation and annihilation of skyrmions and labyrinth domain structure is principally a thermally activated process. Furthermore, the method is also extended to two-sublattice systems, allowing modelling of ferrimagnetic and antiferromagnetic materials at the micromagnetic length scale. Using a multi-layered computation, which includes both ferromagnetic and antiferromagnetic layers, exchange bias may be simulated in bilayers, as well as more complex multi-layered structures including synthetic antiferromagnetic stacks. Moreover we show the method may also be applied to study of thermal and athermal training effects in exchange bias.

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Figure 1 - Hysteresis loops in a 2 nm thin Co film on Pt, using a uniform 300 K temperature (thin dashed line), and a Gaussian temperature profile varying from 300 K at extremities to 400 K at the centre (thick dashed line). The insets show the perpendicular magnetization component on the increasing field sweep, with blue denoting magnetization into the plane, and red out of the plane.

Parallel Micromagnetic Monte Carlo Method for Computation of Thermodynamic Equilibrium States in One and Two-Sublattice Systems

Micromagnetics requires calculation of the demagnetization field, anisotropy field, applied field and exchange field. With the MagTense framework, demagnetization is calculated analytically [1] and both anisotropy and applied field are local, leaving only the exchange field in the form of a second order partial derivative. Standard micromagnetics are limited to finite element methods with large, extraneous simulation volumes or finite difference methods with homogeneous simulation grids, as the demagnetization is calculated using a fast Fourier transform [2], but with MagTense, no such limitation exists. However, here an optimal method of calculating second order partial derivatives on arbitrary meshes in micromagnetics must be determined, continuing previous research [3]. We present solutions to the mumag standard micromagnetic problems (mumag) 3[4] and 4[5] using a direct second order partial derivate technique on four different meshes: Prismal, tetrahedral, grained prismal and grained tetrahedral. The grained meshes consist of voronoi generated and Lloyd iterated grain regions with lower resolution towards the center and higher towards the edges, along with high resolution intergrain regions. In fig. 1a) is shown an example of a grained prismal mesh with 9 grains and an intergrain region in gray. Of course, in the mumag standard problems considered, all regions have the same material properties, but it is easy to envision scenarios where they do not. In fig. 1b) is shown the exchange crossover length of mumag 3 as a function of resolution for three different meshes compared to published solutions. All mesh types converge to the correct value, with the tetrahedral meshes converging faster. In fig. 2 is shown the error compared to published solutions of mumag 4 as a function of resolution using regular-, 4 grained- and 9 grained prismal meshes. The unstructured meshes converge to the correct result in a way similar to a regular grid. In both cases it is apparent that while for these problems grained meshes offer few advantages, they are nonetheless correctly implemented and open up a slew of possibilities for accurately simulating complex geometries with far fewer elements in irregular meshes.

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Fig. 1

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Fig. 2

Solving the Standard Micromagnetic Problems using Unstructured Meshes with MagTense

Recently, Ke proposed alnico permanent magnet (PM) model and simulated it using micromagnetic simulation (MS) for magnetic properties [1]. The model is based on the branch (B) on the bottom (U-shaped), the top and bottom (O-shaped), and the middle (H-shaped) on Z-axis. The U-shaped and O-shaped alnico structures showed low coercivity (Hci). However, there is still a lack of comprehensive studies on B dimensions such as B thickness (TB), width (WB), and length (LB) when α1-phase rods experience coherent rotation and curling [2-4]. Further, the B can be formed as a Y-shaped structure during the thermal magnetic process [3,4]. We have simulated the effects of TB, WB, and LB on Hci for five structures, including H-, U-, O-, YU-, and YH-structures, using LLG micromagnetic simulator v2.63b [5]. Fig. 1 shows the alnico structures used in the simulation. For all structures, α1-phase rod having a diameter (Dα1) of 10 nm was used, representing coherent rotation. The simulation setup used in [1] is adopted. Fig. 2 shows the Hci as a function of TB, LB, and WB for Dα1 of 10 nm. As the TB increases, the Hci first decreases and then remains constant for all the structures. For LB, a positive linear trend of Hci is found for H- and Y-shaped structures, while there is a negative linear trend for the other two structures. As the WB increases, nearly constant Hci appears for the H- and Y-shaped structures, but for the U- and O-shaped structures, the Hci shows a positive quadratic trend. As a simulation result, the following dimensions are suggested to realize a high Hci of Alnico PM: thin TB, long LB, and WB with 40 % of Dα1 for the H- and Y-shaped structures and thin TB, short LB, and WB with 40-60 % of Dα1 for the U- and O-shaped structures. Furthermore, among the five studied structures, the B on the middle location of either H- or YH-shaped is desired to realize a high Hci. We will further discuss the alnico PM rod experiencing curling. This work was supported in part by NSF-I/UCRC for EV-STS under Grant No. 1650564.

![](https://assets.underline.io/uploads/markdown_image/1/image/40747f39a59bccf511044e45ea8883db.jpg)

Fig. 1. Alnico structure: Overall view of (a) H-, (b) U-, (c) O-, (d) YU-, and (e) YH-; top view of (f) H-, U-, or O- and (g) YU- or YH-.

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Fig. 2. Hci as a function of (a) TB, (b) LB, (c) WB for Dα1 of 10 nm.

Effects of α1-phase Branch Shapes on Coercivity of Rare-earth Free Alnico Permanent Magnet

I Introduction Accurate simulation of hysteresis properties of magnetic materials is of great significance for the optimal design of electromagnetic devices. At the state of the art, the inverse Preisach model are widely used in the FEM procedures as it is easily to implementation [1]. The hysteresis operator of the exist inverse model cannot guarantee the overall positive definiteness of the distribution function on the Preisach plane, which make cause the large errors in calculating the small major hysteresis loop [2]. In this paper, an inverse Preisach model based on inverse switched hysteresis operator is proposed, which only identify the parameters of the limiting hysteresis loop. The limiting hysteresis loop and small major hysteresis loop can be accurately simulated. II Method and Discussion As shown in Fig. 1, an improved inverse Preisach switched hysteresis operator is proposed based on the classical Preisach hysteresis operator. To find the inverse distribution function corresponding to the inverse hysteresis operator, the analytic function is used to approximate the distribution function of the inverse model based on the variation of branches. A hybrid algorithm of velocity control particle swarm optimization and conjugate gradient method (VCPSO-CGM) is used to identify the function's parameters through the data of the limiting hysteresis loop. To achieve efficient numerical calculation, the inverse Preisach plane is discretized into n×n square grids. The double integral of every unit grid is calculated, and V matrix is formed. To get the output, the F matrix is obtained by accumulating the elements of the V matrix. The input coordinates are obtained by coordinate transformation of the original Preisach plane, and the output can be obtained by interpolating the F matrix. The simulation results are shown in Fig. 2, which are in good agreement with the experimental data. III Conclusion In this paper, an inverse Preisach model based on the inverse switched hysteresis operator is established, which ensures the overall positive definiteness of the distribution function. The results show that the limiting hysteresis loop and small major hysteresis loop can be accurately simulated by inverse Preisach model.

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Accurate Small Major Hysteresis Loops Calculation by the Preisach Model With Inverse Switched Hysteresis Operator

Microwave-assisted magnetic recording (MAMR) is one of the promising techniques for the next generation hard disk drive (HDD) [1]. For MAMR, a spin torque oscillator (STO) embedded in the write head is suitable for microwave generation. Recently, we have proposed a new STO structure with two field generation layers (FGLs) [2]. The magnetizations of dual FGLs oscillate with keeping anti-parallel direction in the in-plane, which provides an ideal microwave profile for MAMR [2,3]. In this talk, we propose another dual FGL structure, which shows substantial oscillation amplitude with a smaller current. In the dual FGL structure, the oscillation of FGLs is driven by the spin-transfer torque (STT) passed to each FGLs from a SIL and one of the poles, respectively [2] (Fig. 1(a)). In the new structure, we insert another SIL between FGLs, forming a dual SIL dual FGL structure (Fig. 1(b)). We simulated the oscillation behavior of the dual FGL structures by solving Landau-Lifshitz-Gilbert (LLG) equation with an STT term. We prepared three simulators; (I) macrospin simulator, (II) micromagnetic simulator for simplified square layers (Fig. 2), and (III) micromagnetic simulator modeling whole write head. In all simulators, the new dual FGL structure showed larger oscillation amplitudes than in the previous structure. Figure 2(a) shows the result in the simulator (II), where FGLs’ magnetic thicknesses are 15.6 nmT for both FGLs and for both structures. The cone angle was defined as the angle between the z-axis (Fig. 1(a)) and the magnetization. We confirmed the stable antiparallel oscillation (Fig. 2(b)), indicating that the merits of the dual FGL structure [2] are maintained in the new structure. In our presentation, we will further discuss the oscillation behavior, including the dynamics of SILs.

![](https://assets.underline.io/uploads/markdown_image/1/image/9f9f9598fe1025be100c6a8fee48bd75.jpg)

Fig.1 Dual FGL structure embedded in a write pole. (a) Structure in the previous work [2]. (b) SIL-inserted structure. Magnetic layers are separated by non-magnetic spacers whose spin diffusion lengths are long (white) or short (gray).

![](https://assets.underline.io/uploads/markdown_image/1/image/f6dcbc3e26e8e37058debcf98b1e8996.jpg)

Fig.2 Simulation results in the simulator (II) (a) Current dependence of the cone angle. (b) Time dependence of the normalized in-plane magnetization of FGLs in the SIL-inserted structure.

Multiple spin injection into coupled field generation layers for low current operation of MAMR heads

To increase an areal density (AD) of an ultra-high density bit-patterned magnetic recording (BPMR) system [1], we have proposed track mis-regristration (TMR) correction method combined with the soft information adjustor (SIA) to cope with the effects of TMR and two-dimensional (2D) interference [2]. However, we found that soft information or log-likelihood ratio (LLR) can be improved to earn better bit-error rate (BER) performances. Therefore, we propose to use two deep neural networks (DNNs), e.g., multi-layer perceptron (MLP) [3] and long short-term memory (LSTM) network [4] that are operated together with an early SIA on a two-head/two-track (2H2T) BPMR system as shown in Fig. 1. The user sequences, xl,k ∈ {±1} of the l-th track and k-th bit, are recorded onto the medium. All readback signals are produced using two readers, which are then sent to TMR predictor [2]; meanwhile, they are equalized by the consistent 2D equalizers. Then, the equalized sequences, zl,k, are fed into the 2D detectors to output LLRs. The SIA is used to first improve the reliability of each LLR sequence before passing them to our proposed schemes based on DNNs to decide the estimated recorded bits, x'l,k.. The LLR that is obtained from SIA under various TMR effects is given as an input dataset, while the recorded sequence is fixed as an output dataset of DNNs. All of readback signals that relate to considered datasets are interrupted with several electronic noise levels. Here, we set all input and output datasets as 5,200 files, each file consists of 2×32,768 bits, which are directly mapped to be as a pair of input and output datasets. Fig. 2 shows BER performances between the proposed and conventional SIA systems [2]. It is clear that the proposed systems yield better BER performances over the conventional system at all TMR levels with and without position jitter. At BER = 10-5, the proposed LSTM gains for about 4.0 and 4.4 dBs over the conventional SIA system for both cases at TMR 0%. We found that LSTM network slightly provides better performance.

![](https://assets.underline.io/uploads/markdown_image/1/image/afd71bdcfbf70e159df7e3a4f923b601.jpg)

A 2H2T BPMR channel with the DNNs based soft-information improvement.


![](https://assets.underline.io/uploads/markdown_image/1/image/2e01171687412c0b995a541bf1789349.jpg)

BER performances of the conventional SIA [2] and proposed systems.

Deep Neural Networks based Soft-Information Improvement for Two-Head/Two-Track Bit-Patterned Magnetic Recording

Bit patterned media (BPM) technology is intended to provide ultimate areal recording density for hard disk drives. However, for data read back, if a reader has to only read a single track, the read width might become the limiting factor, rather than that of the technology itself. In this study, a machine learning data detection channel is employed to a relatively wide reader with a read width covering two data tracks, as shown in Fig. 1(a). Adjacent data tracks are staggered by half of the bit separation B, which is also the pitch of patterned bits, in the down-track direction. Perpendicular magnetization is assumed for each patterned bit. The read-back signal consists of equal contributions from both the targeted track and interference tracks and is sampled at equal time intervals as input to the neural network. A convolution neural network (CNN) is applied here. This network has four hidden layers with 40 channels per hidden layer and all the filters in each hidden layer have a kernel size of three. The number of input neurons is determined to cover the entire spread of inter symbol interference. The number of input neurons is 9 in the case shown here, corresponding to the PW50/B=1.4 used. The weights of the filters are determined through the training process. Specifically, the rectified linear unit (ReLU) is used for the taps. Only the corresponding binary data of the target track are used in the training process for the “learning” purpose. The entire network consists of 15,000 learnable parameters or weights. Figure 1(b) shows the detection error rates, as a function of the number of bits used in training. For the case in which the signal is sampled at an interval of B (blue curve), the detection error becomes zero over one million different bit sequences after the network is trained over 50,000 bits. If the sampling frequency doubles (red curve), i.e. sampled at an interval of B/2, the zero error detection can be achieved with just 1,000 training bits. Note that the two cases shown here are noise-free. With noise added, more training bits will be needed. In the talk, results on the detection bit error rates for practical signal-to-noise ratios will be presented.

![](https://assets.underline.io/uploads/markdown_image/1/image/5e641bb8ed57ba10ad8b1314d15f0209.jpg)

Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

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Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

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