# Magnetic Elements for Neuromorphic Computing

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Magnetic Tunnel Junctions–Domain Wall Propagation and Different Switching Mechanisms

## 3. Skyrmions

## 4. Magnetic Nanowires and Other Magnetic Nanostructures

_{0}and P

_{1}. The external fields rotate in the x-y plane, either clockwise (R) or counterclockwise (L). Thus, four input combinations of first and second input are possible: LL, LR, RL, and RR, resulting in different output signals, P

_{0}and P

_{1}. Figure 7 depicts the case of RL.

_{1}did not get a signal. Rotating the lower external magnetic field S

_{1}counterclockwise apparently blocked signal transport into the lower right arm of the system. Correspondingly, signal transport into the lower left arm of the system was blocked by the second signal rotating clockwise (LR and RR). In addition, there was also an influence of the first signal S

_{0}, as can be seen by comparing, e.g., the upper left images, depicting 10 ns after starting with LL or RL signals. This influence, however, was reduced as compared to the impact of the signal S

_{1}, showing that this system could not be described by a simple logic table, but rather by fuzzy logic.

## 5. Memristors and Other Nonmagnetic Neuromorphic Computing Elements

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Spin neuron with three terminals based on the domain wall motion depicted in (

**b**), (

**c**) contribution from the spin Hall effect (SHE) to speed up domain wall motion, (

**d**) resulting domain wall motion as a function of current density. Reprinted with permission from [14]. Copyright (2018) by AIP Publishing.

**Figure 2.**(

**a**) Synaptic “learning” and “forgetting” with a mono-domain MTJ: The input stimuli frequency must be high enough to enable crossing the energy barrier separating to two stable states (STP and LTP, indicating short- and long-term plasticity). For (

**b**) low input stimuli frequencies, (

**d**) switching is not possible, while for (

**c**) higher input frequencies, (

**e**) switching is enables. Reprinted with permission from [22]. Copyright (2018) by AIP Publishing.

**Figure 3.**(

**a**) Micromagnetic simulation of a symmetric Néel skyrmion with negative polarity; (

**b**) ferromagnet/heavy metal bilayer with skyrmion, current in the heavy metal j

_{HM}and anisotropy gradient G; (

**c**) top view on the ferromagnetic layer with the skyrmion Hall angle and the aforementioned driving parameters. Reprinted with permission from [40]. Copyright (2018) by the American Physical Society.

**Figure 4.**Generic skyrmion device consisting of a thin film ferromagnet/heavy metal bilayer, showing the manipulation of skyrmion between injection and readout. Reprinted with permission from [46]. Copyright (2018) by the American Physical Society.

**Figure 5.**Time-dependent position of (

**a**–

**d**) Néel, (

**e**–

**h**) Bloch Skyrmion due to a fixed voltage without local pinning. Reprinted with permission from [47]. Copyright (2018) by the American Physical Society.

**Figure 6.**Time-dependent domain wall oscillations in a curved nanowire. Reprinted with permission from [57]. Copyright (2017) by the American Physical Society.

**Table 1.**Results of different rotational orientations at both inputs after 10 ns and 40 ns, respectively.

t (ns) | LL | RL | LR | RR |
---|---|---|---|---|

10 | ||||

M_{x} | ||||

M_{y} | ||||

40 | ||||

M_{x} | ||||

M_{y} |

Properties | MTJ–Domain Wall Based | MTJ–Spiking Neurons | Skyrmions | Nanowires | Memristors |
---|---|---|---|---|---|

Endurance | High [83] | High [84] | High [85] | High [86] | High [87] |

Programming accuracy | High [88] | Low, algorithmic scaling is necessary [88] | Can be high [89] | High [86] | Can be sufficiently controlled [90] |

Power consumption | Low [13,83,91] | Very low (~100 nW) possible [83] | Low [92] | Low [83] | Low [93] |

Speed | High (few ns) [13,83] | High (~100 ns) [88] | High [92] | Low (e.g., <100 kHz) [93] | High (~10 ns) [90] |

Area consumption | Relatively high [13] | High due to high synaptic density [88] | Low [92] | Low, depends on technique [94,95] | Low [87] |

Retention | <10 years [91] or more with sophisticated concepts [96] | ~10 years with a sophisticated concept [96] | High [85] | ~10 years [86] | Enabling short- and long-term memory [97] |

Scalability | Possible [13] | Possible, but challenging [88] | Improvable based on recent findings [85] | Possible [98] | Good [87,92] |

CMOS process integration | Possible [91] | Not yet possible [88] | Not possible/planned [45] | Not possible/planned [98] | Possible [93] |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Blachowicz, T.; Ehrmann, A.
Magnetic Elements for Neuromorphic Computing. *Molecules* **2020**, *25*, 2550.
https://doi.org/10.3390/molecules25112550

**AMA Style**

Blachowicz T, Ehrmann A.
Magnetic Elements for Neuromorphic Computing. *Molecules*. 2020; 25(11):2550.
https://doi.org/10.3390/molecules25112550

**Chicago/Turabian Style**

Blachowicz, Tomasz, and Andrea Ehrmann.
2020. "Magnetic Elements for Neuromorphic Computing" *Molecules* 25, no. 11: 2550.
https://doi.org/10.3390/molecules25112550