Three-dimensional (3D) magnetic assemblies can accommodate unique topological features and exotic spin textures, along with embedded magnetic frustrations [1]. Recently, we have realized interconnected cobalt nanowire networks using multiple angle ion-tracking and electrodeposition; such networks exhibit new magnetization reversal behaviors, offering an interesting platform for 3D information storage [2]. Here we report magnetoresistance (MR) studies of such interconnected networks, to explore how the magnetic configurations can be correlated with spin transport. When a sizable collection of connected nanowires is measured, typical anisotropic magnetoresistance behavior with sharp minima near the coercive fields is found, suggesting that the current is largely bypassing the high resistance intersections. However, when only a few interconnected nanowires are measured, the MR curve exhibits multiple kinks and local minima, indicative of domain wall pinning by the intersections (Fig. 1). More interestingly, during the positive to negative field sweep, a significant MR minimum is observed at positive field, which is the largest among all the MR minima. These features are not seen in parallel nanowires and are a direct consequence of the intersections. Micromagnetic simulations using an equivalent resistor model based on two intersecting nanowires reproduces the experimental observations, including the multiple kinks and a large MR minimum in positive field. Furthermore, small angle neutron scattering has been used to characterize magnetic correlations in the networks under different applied magnetic field configurations. These results show that the intersections in the networks play an important role in pinning / depinning of domain walls, which may be utilized for 3D magnetic memory and memristive devices.<br/><br/>Work supported by the SRC/NIST nCORE SMART center and NSF.

![](https://assets.underline.io/uploads/markdown_image/1/image/33fe181bcbcc9e0f263230fd717c8566.jpg)

Figure 1: Magnetoresistance of a few interconnected Co nanowires showing multiple kinks, indicative of domain wall pinning and depinning during magnetization reversal.

Intersection-Mediated Magnetoresistance in 3D Nanowire Networks

Reservoir computing (RC) is a computational framework where a fixed, non-linear reservoir maps the inputs into higher-dimensional space and the readout is trained with linear regression and classification [1]. Spintronic nanomagnetic devices are well suited for physical reservoir computing due to their interactive non-linear dynamics, recurrence characteristic, enduring lifetime, and low energy consumption [2-3]. A frustrated nanomagnet layer can also implement physical RC [4]. In this work, we demonstrate via micromagnetic simulation that a nanomagnet array excited by surface acoustic waves (SAW) can be used as a reservoir to classify sine and square waves with high accuracy. The simulated nanomagnet array has an input, 7 outputs (Fig. 1) and a 4 GHz SAW is applied to the input nanomagnet. The SAW amplitude is varied in such a way that its envelope forms a random sequence of sine and square waves of 100 MHz frequency (Fig. 2 (a)). The non-linear responses of the output nanomagnets due to this input are processed by reading the reservoir state every 1 ns while the period of the input is 10 ns. The envelopes of the output magnets’ magnetization are shown in Fig. 2 (b) which are used to train the output weights obtained by regression via Moore-Penrose pseudoinverse. For the classification, a random sequence of 100 square and sine wave samples are used. About 80 % of the total samples are trained, and the rest of the samples are used for testing. Various combination of the output nanomagnets exhibit 100 % training accuracy and 100 % testing accuracy which is indicative of the nanomagnet oscillator array being well suited for physical reservoir computing applications. Thus, this proposed strategy to implement reservoir computing could lead to energy efficient neuromorphic devices.<br/>Acknowledgment: M.F.F.C, W.A, D.B and J.A are supported in part by the National Science Foundation grant CCF-1815033.

![](https://assets.underline.io/uploads/markdown_image/1/image/ba0e1e285d3ea4a4474a2b29418b77a9.jpg)

Figure 1: A micro-magnetic snapshot of the input, the reservoir and output nanomagnets.

![](https://assets.underline.io/uploads/markdown_image/1/image/0bbde6989de89be932a0e0791dc0c7a5.jpg)

Figure 2: (a) SAW and input response (b) The envelopes of the responses vs. time (ns) of several output nanomagnets.

Surface Acoustic Wave Induced Nano-oscillator Based Reservoir Computing

**Session chair:** Pavel Ripka, Czech Technical University



EOA - 3D Nanomagnetism and Nanowire Arrays

technical paper

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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This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

**Session chair:** Denys Makarov, Helmholtz-Zentrum Dresden-Rossendorf


Dhritiman Bhattacharya

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Intersection-Mediated Magnetoresistance in 3D Nanowire Networks

Surface Acoustic Wave Induced Nano-oscillator Based Reservoir Computing

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