United States

Spin current is one of the key technologies for spintronics devices. Especially, generation of spin currents via electrical charge current has attracted a great deal of attentions from both fundamental physics and application point of views because it can manipulate magnetization vector of the ferromagnet [1]. This charge-to-spin conversion phenomena originate from spin-orbit coupling and has been widely studied in non-magnetic materials. Recently, the interest in spin conversion materials has extended to ferromagnetic materials (FMs). FMs can generate magnetization-dependent charge-to-spin conversion (MD-CSC), which is caused by the reduced mirror symmetry due to the presence of magnetization, and this MD-CSC can be used as a writing source for high-density MRAM (Fig. 1) [2]. However, the origin of this MD-CSC has not been calrified yet, for instance, whether the interfacial or bulk contribution is domoinant. In addition to this, a guideline for high spin conversion efficiency is highly required for realizing energy-efficient writing in MRAM devices. In this presentation, we systematically studied the charge-to-spin conversion in ferromagnetic material to clarify its origin [3]. Through precise measurement of spin conversion efficiency via spin-torque ferromagnetic resonance [4], we experimentally revealed that two different mechanisms, which originate from the bulk and at interface, contribute to the charge-to-spin conversion in ferromagnet. Next, we demonstrated a guideline to enhance the spin conversion efficiency which is to control the interface structure between Ni-Co alloy and non-magnetic spacer Cu spacer layer (Fig.2) [3]. Moreover, we show that even the sign of the MD-CSC can be tuned by changing the non-mangetic spacer material [5]. These findings would be a milestone toward realizing a high-density and energy-efficient spin-orbit torque MRAMs. This work was partly supported by Grant-in-Aid for Scientific Research (Nos. JP16J03105, JP25220604, JP15H05702, and JP19J01643) and CREST program (No. JPMJCR18T3) of JST. Part of this work was conducted at the AIST Nano-Processing Facility, supported by Nanotechnology Platform Program of the Ministry of Education, Culture, Sports, Science and Technologies (MEXT), Japan.&lt;br&gt;
**References** &lt;br&gt;[1] A. Manchon et.al, Rev. Mod. Phys. 91, 035004 (2019). [2] S. C. Baek et.al, Nat. Mater. 17, 509-513 (2018). &lt;br&gt;[3] Y. Hibino et al., Nat. Commun. 8, 15848 (2021). &lt;br&gt;[4] Y. Hibino et.al, Phys. Rev. B 101, 174441 (2020). [5] Y. Hibino et al., APL Mater. 8, 041110 (2020).&lt;br&gt;

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MMM 2022

Clarifying the Origin of Charge to

Spin current is one of the key technologies for spintronics devices. Especially, generation of spin currents via electrical charge current has attracted a great deal of attentions from both fundamental physics and application point of views because it can manipulate magnetization vector of the ferromagnet [1]. This charge-to-spin conversion phenomena originate from spin-orbit coupling and has been widely studied in non-magnetic materials. Recently, the interest in spin conversion materials has extended to ferromagnetic materials (FMs). FMs can generate magnetization-dependent charge-to-spin conversion (MD-CSC), which is caused by the reduced mirror symmetry due to the presence of magnetization, and this MD-CSC can be used as a writing source for high-density MRAM (Fig. 1) [2]. However, the origin of this MD-CSC has not been calrified yet, for instance, whether the interfacial or bulk contribution is domoinant. In addition to this, a guideline for high spin conversion efficiency is highly required for realizing energy-efficient writing in MRAM devices. In this presentation, we systematically studied the charge-to-spin conversion in ferromagnetic material to clarify its origin [3]. Through precise measurement of spin conversion efficiency via spin-torque ferromagnetic resonance [4], we experimentally revealed that two different mechanisms, which originate from the bulk and at interface, contribute to the charge-to-spin conversion in ferromagnet. Next, we demonstrated a guideline to enhance the spin conversion efficiency which is to control the interface structure between Ni-Co alloy and non-magnetic spacer Cu spacer layer (Fig.2) [3]. Moreover, we show that even the sign of the MD-CSC can be tuned by changing the non-mangetic spacer material [5]. These findings would be a milestone toward realizing a high-density and energy-efficient spin-orbit torque MRAMs. This work was partly supported by Grant-in-Aid for Scientific Research (Nos. JP16J03105, JP25220604, JP15H05702, and JP19J01643) and CREST program (No. JPMJCR18T3) of JST. Part of this work was conducted at the AIST Nano-Processing Facility, supported by Nanotechnology Platform Program of the Ministry of Education, Culture, Sports, Science and Technologies (MEXT), Japan. 
**References** [1] A. Manchon et.al, Rev. Mod. Phys. 91, 035004 (2019). [2] S. C. Baek et.al, Nat. Mater. 17, 509-513 (2018). [3] Y. Hibino et al., Nat. Commun. 8, 15848 (2021). [4] Y. Hibino et.al, Phys. Rev. B 101, 174441 (2020). [5] Y. Hibino et al., APL Mater. 8, 041110 (2020). 

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technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

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Neuromorphic systems are of great interest for modeling and solving complex problems, offering an alternative to conventional deterministic computers1. They generally aim to emulate the functionality and structure of the human brain and thus require many independent true random noise signal sources. In recent years, the stochasticity of spin-transfer-torque switching of magnetic tunnel junctions (MTJs) has gained interest for such applications. Focusing on in-plane MTJs with low energy barriers, the devices investigated thus far have fast thermally driven random fluctuations2,3. However, they are highly susceptible to small changes in temperature and device parameters. Here we show the room-temperature operation of medium energy barrier (Δ=394) perpendicularly magnetized MTJs (pMTJs) in the ballistic switching limit (ns duration pulses) and discuss why their operation is much less sensitive to temperature and material parameters. In the ballistic limit the resulting junction state is random mainly because of the thermal distribution of the initial magnetization state. We denote this a stochastic magnetic actuated random transducer (SMART) device because the pulse activates the junction to generate a random bit stream, much like a coin flip. In fact, we analyze the stochastic nature of our SMART devices by comparing their statistics to that expected of Bernoulli trials (see Figs.1 and 2). We also test our bit stream with the NIST statistical test suite for random number generators which investigates their suitability for cryptography. We find that by whitening the bit stream with only one XOR operation, we pass all NIST tests. Our results demonstrate that medium energy barrier pMTJs are very promising candidates for true random number generation due to their easily controllable characteristics, while being robust towards environmental changes and material parameter variations. 
**References** 1Schuman, C. D. et al., arXiv:1705.06963.
2Vodenicarevic, D. et al., Physical Review Applied Vol. 8, 054045 (2017).
3Safranski, C. et al., Nano Letters Vol. 21, 2040–2045 (2021).
4Rehm, L. et al., Physical Review Applied Vol. 15, 034088 (2021).
 
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Stochastic Magnetic Actuated Random Transducer Devices based on Perpendicular Magnetic Tunnel Junctions

Artificial neural networks (ANNs) are powerful tools for data intensive classification and regression, but the memory wall in von Neumann architectures prevents efficient processing [1]. Though there are many candidates for devices and architectures to realize ANNs, there are no comprehensive solutions to implement hardware Bayesian NNs (BNNs). BNNs are much less susceptible to overfitting when available data is sparse or unreliable, accomplished by representing and learning the weights of the network as distributions instead of deterministic values [2]. We propose a novel spintronic synaptic cell design that can implement tunable distributions by taking advantage of the intrinsic stochasticity of magnetic materials. The design of the cell is composed of a noise and weight encoding element respectively (see Fig. 1). The noisy element is a circular in-plane magnetic tunnel junction (MTJ) that relies on thermal activation to output a random conductance within the range of its TMR. This TMR can then be controlled through several methods such as voltage-controlled magnetic anisotropy (VCMA) [3] or magneto-ionics [4]. Combined with a weight encoding conductance element like a domain wall-magnetic tunnel junction (DW-MTJ) artificial synapse [5,6], we propose a novel cell design that can represent the distributions necessary for inference in a hardware BNN. We demonstrate device functionality through Landau-Lifshitz-Gilbert and micromagnetics [7] models, model analog Bayesian inference in CrossSim [8] for regression (see Fig. 2) and classification to detect out-of-distribution data, and compare the systemâ€™s energy efficiency to CMOS implementations. These results propose a novel synapse implementation for accurate and efficient Bayesian inference, a foundational step toward hardware BNN accelerators. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.

Hardware Aware Bayesian Variational Inference Using Magnetic Tunnel Junction Noise Distributions in Artificial Synapse Arrays

Dzyaloshinskii–Moriya interaction (DMI) induced ferromagnetic (FM) skyrmions in chiral magnets have been reported last decade1,2. On the other hand, chiral antiferromagnet could be a great candidate to host antiferromagnetic (AFM) skyrmions, which have not been studied yet. The emergence of room-temperature FM skyrmions has been reported in the field β-Mn type Fe2-xPdxMo3N epitaxial thin films1. We report Pd doping effect on magnetic and transport properties of a series of chiral antiferromagnetic filled β-Mn type Co2-xPdxMo3N (CPMN) thin films.
A series of CPMN (x = 0 ~ 1.61) thin films were fabricated on c-plane sapphire substrates. Figure 1(a) shows the 2θ/θ scan XRD pattern of a CPMN thin film with x = 1.01, indicating that CPMN films grown epitaxially in the (110) direction, as in case of Fe2-xPdxMo3N/Al2O31. Figure 1(b) shows the x dependence of c0 indicating the on-site doping of Pd. Figure 1(c) shows the M-T curve of a CPMN film with x = 1.01, where two anomalies are identified, which appeared in all CPMN films. The high-temperature anomaly could be related to the Néel temperature TN, as in case of bulk Co2Mo3N3. The magnetization MS at 200 K is 3×10-2 μB/f.u., which is 70 times smaller than that of ferromagnetic Fe2-xPdxMo3N films1, which suggests that the high-temperature magnetic phase is a canted antiferromagnetic (AFM) phase. The low-temperature anomaly can be ascribed to the spin reorientation, at which temperature (TSR) the transition between AFM phase and spiral phase occurs as reported in chiral antiferromagnetic K2V3O84. The low-temperature spiral phase is also revealed by topological Hall effect (THE) at 4 K (Fig. 1(d)). The vanishing THE in canted AFM phase at 200 K (Fig. 1(d)) might be due to the AFM skyrmions. We will report the details of magnetic and transport properties of CPMN system. 
**References** [1] B. W. Qiang et al., Appl. Phys. Lett. 117, 142401 (2020).
[2] R. Saha et al., Nat. Commun. 10, 5305 (2019).
[3] W. Li et al. Phys. Rev. B 93, 060409(R) (2016).
[4] M. D. Lumsden et al., Phys. Rev. Lett. 86, 159 (2001)
 
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Magnetic and Transport Properties of Chiral Antiferromagnetic Co2 xPdxMo3N Thin Films

Spin-orbit interaction in metals and its ability to generate spin-current has been the hallmark of spintronics in the last decade. Beyond its fundamental interest as a source of spin-current, the manipulation of magnetization via transfer of the spin angular momentum has proven to be energy efficient for spin-based memory (e.g. SOT-MRAM) and also neuromorphic devices (e.g. using spin Hall nano-oscillators). Therein, charge to spin conversion is believed to be governed essentially by two main mechanisms, spin Hall effect in the bulk of heavy-metals and Rashba effect at interfaces [1], the latter being often considered negligible in all-metallic interfaces. However, in the case of atomically thin metallic layers, the underlying SOT physical mechanisms at play have not been experimentally fully tackled. 
In this study, we examine the impact of the insertion of a light element interface on the nature of the SOT as well as its efficiency in terms of damping-like (HDL) and field-like (HFL) effective fields in ultrathin ferromagnets. Importantly, we observe unexpectedly large HFL/HDL ratio (∼2.5) upon inserting a 1.4 nm thin Al layer in Pt|Co|Al|Pt as compared to Cu instead of Al as shown in Fig. 1. From our modeling (dotted lines in Fig.1), these experimental results strongly evidence the presence of a large interfacial Rashba effect at Co|Al interface producing giant HFL. The occurrence of such enhanced torques from an interfacial origin is further validated by reducing the contribution from SHE in the bottom Pt layer as well as by demonstrating current-induced magnetization reversal at reduced current. We believe that our results are important from the application point of view as they provide a clear route for reaching ultimate spin-torque efficiency for the associated devices[2]. 
**Acknowledgement:** DARPA TEE (MIPR no. HR0011831554), the Horizon2020 Framework Program of the European Commission under FET-Proactive Grant agreement No. 824123 (SKYTOP) and the the Agence Nationale de la Recherche, France, No. ANR-17-CE24-0025 (TOPSKY). 
**References:** [1] Manchon, A. et al., Rev. Mod. Phys. 91, (2019). 
[2] Krishnia S. et al., arXiv : 2205.08486. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/d8fd135b8e9157bc0dc4a5f819d2811b.png) 
Co thickness (tCo) dependence of (a) DL-SOT field and (b) FL-like SOT fields in Pt8|Co (tCo)|Al1.4|Pt3 (red ) and Pt8|Co (tCo)|Cu1.4|Pt3 (blue ) samples (c) ζ = HFL/HDL as a function of tCo.

Large interfacial Rashba interaction and giant spin orbit torque in atomically thin metallic multilayers

We compare thermal-gradient-driven transverse voltages in ferrimagnetic-insulator/heavy-metal bilayers (Tm3Fe5O12/W and Tm3Fe5O12/Pt) to corresponding electrically driven transverse resistances at and above room temperature1. The thermal gradient is created by an applying electric current in the lithographically patterned heater, electrically isolated from the device that is located approximately 50 μm away. We find for Tm3Fe5O12/W that the thermal and electrical effects can be explained by a common spin-current detection mechanism, the physics underlying spin Hall magnetoresistance (SMR)2,3. However, for Tm3Fe5O12/Pt the ratio of the electrically driven transverse voltages (planar Hall signal/anomalous Hall signal) is much larger than the ratio of corresponding thermal-gradient signals, a result which is very different from expectations for a SMR-based mechanism alone. We ascribe this difference to a proximity-induced magnetic layer at the Tm3Fe5O12/Pt interface4. By analyzing the ratio of electrically and thermally driven transverse voltages we find that the dominant contribution of the transverse spin-current is the intrinsic spin-Hall effect that is driven by the longitudinal electrical field either provided by the thermal gradient due to the Seebeck effect or by applying the electric current. 
**References:** 1. Bose, A. et al. Origin of transverse voltages generated by thermal gradients and electric fields in ferrimagnetic-insulator/heavy-metal bilayers. Phys. Rev. B 105, L100408 (2022). 
2. Nakayama, H. et al. Spin Hall Magnetoresistance Induced by a Nonequilibrium Proximity Effect. Phys. Rev. Lett. 110, 206601 (2013). 
3. Meyer, S. et al. Observation of the spin Nernst effect. Nat. Mater. 16, 977–981 (2017). 
4. Huang, S. Y. et al. Transport Magnetic Proximity Effects in Platinum. Phys. Rev. Lett. 109, 107204 (2012). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/add0712631d46afa26b1f6505752d938.png) 
FIG.1. Results for TmIG/W. Hall resistance of TmIG/W for (a) out-of-plane magnetic-field sweep and (b) in-plane field rotation for a field magnitude of 2.7 kOe. Thermally-induced transverse voltages, (c) Vxy z and (d) Vxy φ, for a heater power of 630 mW and for two different heater spacings, d = 15 μm (closed squares) and 50 μm (open circles).

Origin of transverse voltages generated by thermal gradients and electric fields in ferrimagnetic insulator/heavy

The direct interference of short wavelength spin waves in continuous layers is bringing new opportunities for efficient signal processing [1-2]. Several pionneer works established the possibility to shape the propagation of spin waves in ferromagnetic thin films using concepts borrowed from optics [3-5]. Along these ideas, we demonstrated that the focused emission of spin waves beams in ferromagnetic thin films from constricted coplanar waveguide follows directly the near-field interference pattern of the constriction geometry [6]. In this communication, we investigate the interference patterns of spin waves excited by curvilinear shaped antennas, which produce either a concentrating or a diffusing effect. Namely, we focused our study on two different types of demonstrators: (i) a spin wave â€œconcentratorâ€ as shown in Fig. 1, and (ii) the equivalent of a â€œYoung double-slitâ€ experiment for spin waves shown in Fig. 2. Firstly, we will present a near-field interference model that can be readily implemented for all spin wave modes and any arbitrary shape of antenna [7]. We show the validity and efficiency of our approach by comparing the near-field diffraction patterns obtained with our model and the corresponding MuMax3 micromagnetic simulations for a wide scope of geometries. Secondly, we present series of propagating spin wave spectroscopy done on 30nm YIG films and a 20nm Ni80Fe20 film magnetized out-of-plane, allowing for a discrete mapping of the spin wave intensity with a spatial resolution of about 1Âµm. We show that the transmission signals S21 measured at different locations follow very closely the simulated interference patterns for all the demonstrators, thus paving the way for future prototypes of magnon interferometric devices. This work was supported by the French ANR project â€œMagFuncâ€, and the DÃ©partement du FinistÃ¨re through the project â€œSOSMAGâ€.

Spin Wave Diffraction in Curvilinear Antennas

Complex magnetic materials hosting topologically non-trivial particle-like objects such as skyrmions are intensely researched and could fundamentally change the way we
store and process data. One important class of materials are helimagnetic materials with Dzyaloshinskii-Moriya interaction. Recently, it was demonstrated that nanodisks consisting of two
layers with opposite chirality can host a single stable Bloch point of two different types [1]. The Bloch point represents an interesting topological excitation in a helimagnetic system, which
expands the set of well-known magnetic states such as domain walls, vortices, and skyrmions.
In this work [2], we use micromagnetic simulations [3, 4] to show that FeGe nanostrips consisting of two layers with opposite chirality can host multiple coexisting Bloch points. We
demonstrate that the two different Bloch-point types (Fig. 1) can be geometrically arranged in any arbitrary order, and these magnetization configurations are meta-stable (within certain
constraints on the strip width and length). We can determine an optimal spacing between Bloch points within a line of Bloch points (corresponding to a distance over which a Bloch point
extends). This allows us to predict strip geometries suitable for an arbitrary number of Bloch points, which we verify for an example 80-Bloch-point configuration (Fig. 2). 
**References** [1] M. Beg et al., Scientific Reports, Vol. 9, p. 7959 (2019).
[2] M. Lang et al. arXiv:2203.13689 (2022).
[3] M. Beg, M. Lang and H. Fangohr, IEEE Transactions on Magnetics, Vol. 58, p. 7300205 (2022)
[4] M. Beg, R. A. Pepper and H. Fangohr, AIP Advances, Vol. 7, p. 56025 (2017) 

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Fig. 1 (a) The Bloch-point configuration originates from vortices with identical circularity, but opposite polarisation, which are stabilised through the DMI of the material, which fixes the
core orientation relative to circularity through the left- or right-handed chirality. (b, c) Simulation results for the two different Bloch-point types. 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/3af0ce5bf816d28b6250862025c394dc.png) 

Fig. 2 ASCII encoding of the string "Blochpoint" using 80 Bloch points. The two cross sections show an xy plane in the top layer and an xz plane at the Bloch-point position. The strip
length is chosen according to the predicted value for a nanostrip with width w = 100 nm.

Bloch points in helimagnetic nanostrips

The distance between islands must be reduced to increase an areal density (AD) in bit-patterned media recording (BPMR) [1]-[2], which means both inter-symbol interference (ISI) and inter-track interference (ITI) effects are avoidably increased. Therefore, BPMR system performance is effortlessly degraded [3]. In prior work [4], constrained code working with a multilayer perceptron (MLP) decoder in a staggered-array BPMR system was proposed. However, to get more improvement in the overall system performance of the magnetic recording system, we propose to apply the three-dimensional (3-D) magnetic recording that has double recording layers [5] with the constrained code performing with the MLP decoder. Here, a double recording layer medium is designed as a staggered pattern as shown in Fig. 1. Each layer is arranged as a regular array. Both of them are then arranged in a staggered pattern. The proposed double recording layer not only avoids the significant signal degradation from inter-layer interference (ILI) but also mitigates ISI and ITI effects. An input sequence, uk∈{±1}, is encoded by LDPC code and the rate-3/5 constrained encoder to obtain two encoded data sequences, [xk,0, xk,1] as shown in Fig. 2. The odd, xk,0, and even, xk,1, data sequences are recorded in the upper and lower layers, respectively. A single reader is always positioned between two desirable tracks to retrieve the readback signal, which is then oversampled at time t = kTx/2 to obtain a data sequence, rk, where Tx is a bit period. The 1-D equalizer and 1-D modified-soft output Viterbi algorithm (m-SOVA) are used to equalize and determine a log-likelihood ratio (LLR), λk, respectively. Then, it is decoded and produced the improved LLR values, respectively, with the rate-3/5 decoder and LLR estimator based on MLP, λ"k. Finally, the estimated user bit, ûk, is produced using an LDPC decoder. Simulation results indicate that, at the same user density (UD), the proposed system (AD = 5 Tb/in2) provides BER performance over the previous system [4]. 
**References** 
Y. Shiroishi et al., IEEE Trans. Magn., vol. 45, pp. 3816-3822 (2009) 
R. L. White, R. M. H. New, and R. F. W. Pease, IEEE Trans. Magn., pp. 990-995 (1997) 
P. W. Nutter et al., IEEE Trans. Magn., vol. 41, pp. 3214-3216 (2005) 
N. Rueangnetr et al., 19th ECTI-CON 2022, pp. 1-4 (2022) 
Y. Nakamura et al., IEEE Trans. Magn., vol. 58, pp. 1-5 (2022) 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/98b679bf2da99a70724f673c1d515de5.png) 
Fig. 1. Cross-section of head-media geometry for double recording layer medium.

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/4d2b2cd6f60fdce3351df357175cceef.png) 
Fig. 2. A code BPMR channel model with the rate-3/5 constrained code.

Double Layer Magnetic Recording with Multilayer Perceptron Decoder for Single

Nd-Fe-B magnets are widely used in electric vehicles (EVs), wind turbines, and electronic devices in civilian and defence sectors due to their high magnetic performance. Alternate to the sintering route, the hot-deformation route does not require heavy rare elements (HRE) such as Dy and Tb and is a promising route to produce Nd-Fe-B magnets at low cost [1]. Hot deformed magnets are produced through melt spinning and hot pressing/deformation techniques [2]. Nd-Fe-B powder prepared from the melt-spun ribbon is used as precursors and hence optimization of melt spinning parameters is important to obtain desirable grain size and hard magnetic properties [3]. Hence a study was undertaken to prepare Nd-Fe-B melt-spun ribbons to tailor the microstructure and hard magnetic properties.
Melt spun ribbons with a nominal composition of Nd13.6Fe73.6Co6.6Ga0.6B5.6 alloy were prepared at various wheel speeds from 17 to 25 m/s. While the structure of the ribbons was obtained using X-Ray diffraction, the microstructure was obtained by transmission electron microscope (TEM). The magnetic properties and thermo-magnetic properties were obtained using a vibrating sample magnetometer (VSM). XRD analysis showed Nd2Fe14B phase with strong (00l) texture in all ribbons and texture fades away at higher wheel speeds. Thermal stability studied by calorimetry showed that the Nd2Fe14B phase was stable up to 500oC, beyond which precipitation of the α-Fe phase takes place. TEM analysis (Fig.1) showed that the Nd2Fe14B phase was distributed uniformly throughout the sample with a grain size of 50-150 nm. The average grain size was found to decrease with an increase in the wheel speed. The remanence (Br) and coercivity (Hc) values were found to increase with the increase in wheel speed up to 23 m/s and beyond which it starts decreasing gradually (Fig.2). Ribbons with the highest magnetic properties having a Br value of 6.6 kG and Hc value of 12.3 kOe were obtained at 23 m/s and may be best suited for the fabrication of hot deformed Nd-Fe-B magnets. 
**References:** 1 N.J. Yu, M.X. Pan, P.Y. Zhang, and H.L. Ge, J. Magn. 18, 235 (2013). 
2 K. Hioki, Sci. Technol. Adv. Mater. 22, 72 (2021). 
3 C. Rong and B. Shen, Chinese Phys. B 27, 117502 (2018). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/0eba546af9c83328c8a792d6bbcd2171.png) 
Fig.1: TEM image showing the microstructure of Nd-Fe-B ribbon prepared at a wheel speed of 23 m/s 
![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/cb92d75e28c54dad0e4f00e8be180f65.png) 
Fig.2: Magnetic properties (Br and Hc) of Nd-Fe-B ribbon prepared at different wheel speeds

Processing and characterization of melt spun Nd

As the era of Moore's law in transistor based computing comes to an end, it is possible that society will rely on new systems to process information [1]. Nanomagnets are an appealing candidate to supercede transistors as they may theoretically reach the Landauer limit of efficiency at room temperature [2]. Arrays of magnetic material may be patterned in nearly any 2D pattern conceivable and made of a myriad of materials to engineer a wide variety of phases, from standard ferromagnetic order to skyrmions. The interactions between domains creates Ising like behavior which naturally maps onto a variety of computing schemes, such as nanomagnetic logic [3], Hopfield networks [4], and QUBO algorithms [5]. The nonlinear field response even effectively performs the function of a reservoir in the neuromorphic computing framework of "reservoir computing" [6]. This richness of behaviors is messy and more difficult to control than CMOS systems, but offers incredible efficiency and naturally organic structure if given the appropriate problems. Artificial spin ice, nanomagnet arrays patterned to simulate the difficult to study problem of frustrated magnetism [7], has recently branched into the field of nanomagnetic computing. Here we will incorporate principles from artificial spin ice to better understand how interacting nanomagnets process information. We will also introduce a model for the mean-field dynamics of nanomagnets that illuminates how external field can drive collective behavior in such a way that the spin system's dynamics perform useful information processing. We then apply the results of this model to reservoir computing to attain a lower error signal prediction framework comprised of nanomagnets. 

**References:** 
[1] T. Theis, and H-S. P. Wong, Computing in Science & Engineering., Vol. 19.2, p.41-50 (2017) 
[2] B. Lambson, D. Carlton, and J. Bokor, Physical review letters., Vol. 107.1, p.010604 (2011) 
[3] H. Arava, et al, Nanotechnology, Vol. 29.26, p.265205 (2018) 
[4] M. Saccone, et al, Nature Physics, Vol. 18.5, p.517-521 (2022) 
[5] A. Lucas, Frontiers in physics, Vol. 1 p.5 (2014) 
[6] J. Gartside, et al, Nature Nanotechnology, Vol. 17.5, p.460-469 (2022) 
[7] S. Skjærvø, et al, Nature Reviews Physics, Vol. 2.1, p.13-28 (2020)

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