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Since the advent of spin-torque nano-oscillators (STNOs) {1}, mutual synchronization of two or more STNOs has been of intense interest as it not only improves both the microwave signal power and the signal quality factor (Q-factor) appealing to communication technology but can also be used directly for neuromorphic computing due to the tunable magnetic nature of the interaction between STNOs. Thanks to the spin Hall effect, a new class of spintronic oscillators known as spin Hall nano-oscillators (SHNOs) has emerged. Compared to STNOs, they rely on the current flowing in-plane, which makes their fabrication easier and allow for a large number of SHNOs to synchronize in both chains and arrays. {5,6}&lt;br/&gt;In this work, we explore mutual synchronization in nano-constriction (NC) based SHNO chains and demonstrate robust synchronization of SHNOs for longer chains with up to 21 Oscillators [Fig. 1(a&amp;b)]. We investigate both NiFe(4 nm)/Pt(5 nm) {6,7} and W(5 mm)/CoFeB(1.4 nm)/MgO(2 nm) {8,9} SHNOs. We report that the robust mutual synchronization can deliver an enhanced output power and significantly lower linewidth (Fig. 2(a&amp;b)). A sub-MHz linewidth [Fig. 2(b), as low as 300 kHz for NiFe/Pt] can be achieved for 21 synchronized oscillators. The high-frequency operation results in a very high quality factor (Q=f/△f) of &amp;gt;30,000 for NiFe/Pt and &amp;gt;25000 for W/CoFeB/MgO, which is the highest reported in chains. A linear decrease in linewidth and increase in output power (up to in-phase synchronization) is observed with the number of oscillators [Fig. 2(c)]. The low current and low field operation of these oscillators along with wide frequency tunability (2-28 GHz) with both current and magnetic fields, make these oscillators ideal candidates for various spintronic applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/f0e099e3c61e0350cd61b894af51a975.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c1278063a10ddeee4cc0d0ca490c6969.jpg)

Robust mutual synchronization of spin Hall nano-oscillator chains

2022 Joint MMM-INTERMAG

Robust mutual synchronization of spin Hall nano-oscillator chains

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.

The 2022 Joint Conference will offer both in-person and prerecorded on-demand content.

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Please register for the Joint MMM-Intermag conference to join the event.

Since the advent of spin-torque nano-oscillators (STNOs) {1}, mutual synchronization of two or more STNOs has been of intense interest as it not only improves both the microwave signal power and the signal quality factor (Q-factor) appealing to communication technology but can also be used directly for neuromorphic computing due to the tunable magnetic nature of the interaction between STNOs. Thanks to the spin Hall effect, a new class of spintronic oscillators known as spin Hall nano-oscillators (SHNOs) has emerged. Compared to STNOs, they rely on the current flowing in-plane, which makes their fabrication easier and allow for a large number of SHNOs to synchronize in both chains and arrays. {5,6} In this work, we explore mutual synchronization in nano-constriction (NC) based SHNO chains and demonstrate robust synchronization of SHNOs for longer chains with up to 21 Oscillators [Fig. 1(a&b)]. We investigate both NiFe(4 nm)/Pt(5 nm) {6,7} and W(5 mm)/CoFeB(1.4 nm)/MgO(2 nm) {8,9} SHNOs. We report that the robust mutual synchronization can deliver an enhanced output power and significantly lower linewidth (Fig. 2(a&b)). A sub-MHz linewidth [Fig. 2(b), as low as 300 kHz for NiFe/Pt] can be achieved for 21 synchronized oscillators. The high-frequency operation results in a very high quality factor (Q=f/△f) of &gt;30,000 for NiFe/Pt and &gt;25000 for W/CoFeB/MgO, which is the highest reported in chains. A linear decrease in linewidth and increase in output power (up to in-phase synchronization) is observed with the number of oscillators [Fig. 2(c)]. The low current and low field operation of these oscillators along with wide frequency tunability (2-28 GHz) with both current and magnetic fields, make these oscillators ideal candidates for various spintronic applications.

![](https://assets.underline.io/uploads/markdown_image/1/image/f0e099e3c61e0350cd61b894af51a975.jpg)

![](https://assets.underline.io/uploads/markdown_image/1/image/c1278063a10ddeee4cc0d0ca490c6969.jpg)

Robust mutual synchronization of spin Hall nano-oscillator chains

technical paper

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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![](https://assets.underline.io/uploads/markdown_image/1/image/096f42262ccb202322a88b054bf2a8a1.jpg)

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).

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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)

Machine Learning Detection Channel Enabling Wide Reader for Bit Patterned Media

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.

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![](https://assets.underline.io/uploads/markdown_image/1/image/256f37dab48ea38e1c2550f583dbc4f5.jpg)

Experimental evolution of two parametric mechanisms of magnetization reversal in FeCoB nanomagnet.

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

Properties of higher-order magnetic anisotropy constants in soft-hard nanocomposite materials still attract much debate [1]. We investigated the magnetic anisotropy in a L10/A1 FePt system using the VAMPIRE software package [2]. An elongated, faceted cylindrical core-shell was constructed with a L10-FePt core of varied size surrounded by an A1-FePt shell. The system exchange interaction was 3-dimensional and accounted up to the third-nearest neighbours. A 2-ion Fe-Pt anisotropy component was incorporated to the system Hamiltonian following Mryasov et al. [3]. The angular dependence of the restoring torque was calculated from 0K to 1000K in 5K steps using a constrained Monte-Carlo integrator. Temperature-dependent anisotropy constants were then determined from fitting to the system torque as a function of the constrained angle. We find that the core-shell structure exhibits an unexpected 4th-order anisotropy term of which magnitude depends on the core-size ratio R. The K2/K1 ratio, with K1 and K2 being the 2nd and 4th-order anisotropy constant respectively, displays a non-monotonic pattern with a peak occurring at R ~ 0.55 [Fig.1]. We find that K2 scales with (M/Ms)~2 at temperatures below Tc [Fig.2] - a remarkable deviation from the established Callen-Callen theory [4] which instead predicts a scaling with (M/Ms)10. A simple analytical model shows the 4th-order term to arise from canting of the core and shell magnetisation. Further, the model demonstrates that the magnitude of the 4th-order term is proportional to K12/J, with J the exchange coupling. Given that the 2-ion K1 term scales approximately with M2 and J with M2, the predicted scaling exponent is 2 in agreement with the simulations. Generally, the 4th-order anisotropy constant is shown to exhibit a strong dependence on the system geometry, thus suggesting that the Callen-Callen power law is not universal and valid only for single-ion anisotropies.

![](https://assets.underline.io/uploads/markdown_image/1/image/22a9ca96de68d358f16ce046a83fffba.jpg)

Fig.1: A low temperature scan displays a non-monotonic dependence of K2/K1 on core size ratio R with a peak at R ~ 0.55.

![](https://assets.underline.io/uploads/markdown_image/1/image/bb578e32eb2732e857794fddce38fa58.jpg)

Fig.2: K2 scaling with M/Ms for R=0.50 results in a scaling exponent β ~ 1.81 not 10 as predicted by Callen-Callen.

Higher-order magnetic anisotropy in soft-hard nanocomposite materials

Embedded Mask Patterning (EMP) has been demonstrated as a potential HAMR media solution with formation of ultra-fine and highly-ordered L10-phase FePt grains[1]. We used a hybrid model including both reactive and pair-wise interatomic potentials in the classic Molecular Dynamic (MD) simulation to study the methanol-based reactive plasma etching mechanism of the FePt lattice. The major reactive redical etchants in the methanol plasma are identified as Carbon monoxide and Hydrogen spieces[2]. Adsorbed Carbon monoxide molecules reacts with the Fe and Pt atoms and forms caronyl bonds. With assisted ion beams such as Ar+ or He+, we show the chemical etch yield is increased. The ordering change of FePt crystal surface during the etch are also simulated.

![](https://assets.underline.io/uploads/markdown_image/1/image/83abf9422e8c50f158b238db1a099582.jpg)

MD Simulation of Plasma Etch of FePt Media

Reactive Molecular Dynamic Simulation of Plasma Etching Process of L10-FePt HAMR Media in Embedded Mask Patterning

In granular FePt-L10 HAMR media. sufficient grain volume is critical for achieving expected areal density capability (ADC) [1][2]. Grain height needs to be increased as the grain size decreases. We present an experimental study on the fabrication of HAMR media with tall/high aspect ratio FePt-L10 grains. The underlayer stack consists of Ta(5nm)/Cr(40nm)/MgO(8nm) prior to the magnetic layer deposition. A 0.5 nm FePt layer is deposited on the MgO underlayer for initial grain nucleation, followed by the deposition of 2 nm FePt-BN (35% boron nitride) both at 700 oC. Over the FePt/FePt-BN stack, FePt-SiOx of 10nm thickness is deposited in the following manner: The first 3.5nm are deposited at 600 oC followed by immediately turning-off of the substrate heating and the rest of the layer is then deposited while the substrate undergoes naturally cooling. The ending temperature is 430 oC . The volumetric SiOx concentration of the FePt-SiOx layer is also graded from 40% at the bottom to 18% at the top. The L10 order parameter is S=0.72, calculated based the XRD measurement. Figure 1 shows the plan view HAADF TEM image (left) and cross-section view TEM image (right). The plan view image clearly shows well separated grains with average grain size around 6nm. The cross-section image shows columnar grains with well-defined grain boundaries and a grain aspect ratio ranging from 1.7 to 2. In this film stack, the SiOx grain boundaries are vertically matched with boron-nitride grain boundaries at the interface of the two layers. If the deposition temperature exceeds 650 oC, the majority of the adjacent FePt grains could become laterally connected over the entire thickness of the FePt-SiOx layer whereas the BN grain boundaries remains intact. While we vary the deposition conditions of the FePt-SiOx layer, the FePt/FePt-BN stack acts as a fixed template layer for the grain growth on top. For the FePt-SiOx layer, the graded SiOx composition combined with the graded deposition temperature serves the key to (1) ensure columnar grains that are well separated by SiOx grain boundaries and (2) avoid the formation of 2nd layer FePt grains.

![](https://assets.underline.io/uploads/markdown_image/1/image/89ab165f3824e2641ad4a23daad4429d.jpg)

Fig. 1. Planview HAADF (Left) and Cross-section (Right) TEM image of the entire medium stack.

Fabrication of Granular FePt-L10 HAMR Media with High Grain Aspect Ratio

Transition curvature limits the performance of Heat-assisted Magnetic Recording (HAMR), especially when bit length is reduced below 10nm. The dependence of this transition curvature on bit length was obtained micromagnetically in our previous work [1]. In the current study, the dependence of signal-to-noise ratios (SNRs) and bit error rates (BERs) on HAMR transition curvatures is further investigated. More than 20,000 bits are written ideally (with an infinite thermal gradient) with various bit lengths and realistic transition curvatures. A pseudorandom binary sequence is used. The width of the read head is 20nm, shield to shield distance is 22nm, and element thickness is 4nm. Magnetic fly height is 6nm. A Viterbi algorithm is applied to decode the readback signals and calculate BERs. Fig. 1 and 2 show how SNRs and BERs change with transition curvatures (characterized by the coefficient to the quadratic term of the defining parabola) for a minimum bit length of 7.5nm. Clearly, larger transition curvatures result in lower SNRs and higher BERs, thus negatively affecting HAMR performance. Although the results in the figures represent very small bits compared to the readback resolution, our calculations for longer bits and/or narrower shield-shield spacing show similar results, albeit with improved SNR and BER, as will be shown in the presentation.

![](https://assets.underline.io/uploads/markdown_image/1/image/16d047464ce2c11df0f3338173afaea4.jpg)

Fig. 1 Dependence of SNRs on HAMR transition curvatures with a bit length of 7.5nm.

![](https://assets.underline.io/uploads/markdown_image/1/image/53a95ed559b573a5cfb00cb65785b952.jpg)

Fig. 2 Dependence of BERs on HAMR transition curvatures with a bit length of 7.5nm.

Dependence of Bit Error Rates on HAMR Transition Curvatures

Acoustically-driven ferromagnetic resonance (ADFMR) (1,2) is a powerful technique used to transmit RF surface acoustic waves (SAWs) and tune their transmission using a thin magnetic film and a static magnetic field HDC. We explore tunability of ADFMR devices for their potential in agile RF communications applications. Two examples are nonreciprocal ADFMR devices, and devices with curved interdigital transducers (IDTs), which focus SAWs with enhanced intensity in the magnetic film. Nonreciprocity of RF transmission has an important role in critical components like isolators and circulators. We demonstrate that a thin synthetic antiferromagnet using FeGaB (3) can selectively absorb waves travelling in one direction with 48.4 dB isolation- performance that can compete with state-of-the-art commercial devices despite much smaller package size and power draw. Another tuning knob which can have device impacts is nonlinearity. With curved interdigitated transducers (IDTs), we focus SAW energy to a small, intense region near the center of the magnet. We then study the dependence of the magnetoacoustic interaction on input power. Reaching moderate input powers of 10 dBm or less allows access to a nonlinear regime previously unavailable in these devices. Using a scanning acoustic-wave interferometer, we can observe the change in amplitude of the acoustic waves as they travel across the device surface. The power dependence is studied in depth, and an applied magnetic field modifies the amplitude wherever the magnet is present. Using these tools we gain new insight into how the magnetoelastic coupling works in ADFMR, which guides our understanding in the pursuit of new tunable RF communications device types.

![](https://assets.underline.io/uploads/markdown_image/1/image/2590b73047f4f871dd45b187b9cd8f14.jpg)

Operation of a magnetoacoustic isolator. With external magnetic field applied in one direction, the device transmits RF unidirectionally with 48.4 dB isolation. Reversing the external field switches the direction of RF transmission.

![](https://assets.underline.io/uploads/markdown_image/1/image/bd4fddee8bbe14c38d434b0fda5a4473.jpg)

A) Image of a focused IDT ADFMR device. Curved IDTs transmit and receive SAWs, which travel across a 20-nm-thick Ni film on a y-cut LiNbO3 substrate. B) ADFMR pattern showing output with 860-MHz 27-dBm input as a function of HDC angle and magnitude. C) SAW amplitude measured by interferometry.

Robust mutual synchronization of spin Hall nano-oscillator chains

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Robust mutual synchronization of spin Hall nano-oscillator chains

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