Magnetic skyrmions are “topologically protected” solitons, that have recently received increased attention due to their potential application as information carriers and for unconventional computing [1]. While the current-driven dynamics has been explored deeply, the theory of temperature gradient-induced dynamics - Skyrmion-Caloritronics [2] - is still at its early stages of development but it is particularly promising due to its low energy consumption.
In this work, we study the effects of thermal gradients on skyrmion motion in different systems (single-layer FM with interfacial Dzyaloshinskii-Moriya interaction (IDMI), multilayer, and synthetic antiferromagnets (SAFs)) inspired by the experimental results of Ref. [2] and from a fundamental point of view. We observe that, when driven by the entropic torque, skyrmions in single layers move from the cold to the hot region with a finite skyrmion Hall angle (Fig. 1), while in multilayers they move in the opposite direction (from hot to cold region) (Fig. 2). The latter is in qualitative agreement with the experimental observations (Fig. 3a in Ref. [2]). We demonstrate that this difference is due to the distinct scaling relations characterizing the two systems, and to the existence of a magnetostatic field gradient linked to the variation of saturation magnetization (MS) which cannot be neglected in magnetic multilayers. The numerical results are corroborated by a generalized Thiele’s equation developed for this scenario. Moreover, we show that the skyrmion Hall angle is completely suppressed in SAFs, similarly to the current-driven skyrmions [3,4].
Our results have fundamental implications in the future development of skyrmionic devices combining thermal gradients and SOTs where the proper temperature dependence of the parameters should be taken into account.
See Ref. [5] for founding statement. 
**References** [1] J. Zázvorka, et al., Nat. Nanotechnol. 14, 658 (2019).

[2] Z. Wang, et al., Nat. Electron. 3, 672 (2020).

[3] X. Zhang, et al., Nat. Commun. 7, 10293 (2016).

[4] R. Tomasello, et al., J. Phys. D. Appl. Phys. 50, 325302 (2017).

[5] This work was supported by the Project No. PRIN 2020LWPKH7 funded by the Italian Ministry of University and Research, and by the PETASPIN association (www.petaspin.com). JB acknowledges support from the Royal Society through a University Research Fellowship. E.R. acknowledges the economical support of the COST Action CA 17123 (MAGNETOFON) within the STSM program. We would like to acknowledge networking support from COST Action No. CA17123 “Ultrafast opto magneto electronics for nondissipative information technology.”

[6] W. Li, et al., Adv. Mater. 31, 1807683 (2019). 

![](https://s3.eu-west-1.amazonaws.com/underline.prod/uploads/markdown_image/1/image/5f492fdb99a4414723d8429930359fb7.png)

Skyrmion Caloritronics: a promising Strategy to manipulate Skyrmions

Spintronic diodes (STDs) are emerging as a technology for the realization of high-performance microwave detectors [1]. In this paper, we use their rectification properties to perform the analog multiplication between any two numbers. For this purpose, we introduce the concept of degree of rectification (DOR) and we confirm its applicability with micromagnetic and experimental data. The proposed method is suitable for highly integrated implementations and has promising perspectives for neural networks applications [2]. The multiplication can be obtained by measuring the response of a parabolic phenomenon to three well-determined inputs [3][4][5]. Therefore, we analyze the DOR of spintronic diodes, which is the output dc voltage measured for a variable input dc current in injection-locked devices. This Vdc/Idc curve can be well approximated to a parabola as shown in Fig. 1, the experimental data are taken from [6]. The voltage can be approximated by the following equation [6]: Vdc=[(RAP-RP )/4] Iac,MAX cos(φ(Idc)) √p (1) where RAP and RP are the device resistances in the antiparallel and parallel state, respectively, p is the power of the magnetoresistive signal, φ(Idc) is the intrinsic phase shift between the ac current and the magnetoresistive signal, and the cosine can be well approximated with a parable using Taylor’s second-order expansion. Moreover, Eq. 1 can be fully characterized knowing the physical parameters of the device and the values of Idc,MAX, Vdc,MAX (both represented in Fig. 1) and the second derivative of Vdc with respect to Idc evaluated in Idc=Idc,MAX. Fig. 2 shows the application of the presented method for 200 cases with random inputs, the red line shows the ideal result; the correlation coefficient found is r=99.83%. We will show how the proposed method can be used to implement the convolution for neural networks applications with excellent results for image recognition.

![](https://assets.underline.io/uploads/markdown_image/1/image/8be5d570eb2198667334d746191b22a6.jpg)

Fig. 1: Output dc voltage depending on the input dc current (data taken from [4]) for an injection-locked diode (blue circles) and parabolic fit (red line).

![](https://assets.underline.io/uploads/markdown_image/1/image/ef2d86778d75be9a7a2f863250048857.jpg)

Fig. 2: 200 multiplications obtained with the proposed method (black circles) compared with the ideal result (red line).

Analog multiplication implemented with spin-torque diodes for neural networks applications

EOC: Skyrmions I

technical paper

#### Welcome to the 67th Annual Conference on Magnetism and Magnetic Materials, MMM 2022!

The Conference was held from October 31 to November 4 and offers both in-person and on-demand content.

MMM 2022 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 tutorial, and several special sessions. This Conference provides an outstanding opportunity for worldwide participants to meet their colleagues and collaborators and discuss developments in all areas of magnetism research.

<iframe width="560" height="315" src="https://s3.amazonaws.com/pf-user-files-01/u-59356/uploads/2022-11-02/un13zp7/MMM%20Welcome%20Video%20v5.mp4" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture" allowfullscreen></iframe>

For tickets to the event, please register at the following link: https://magnetism.org/registration

Please register for the MMM 2022 conference to join the event.

MMM 2022

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


GOL - MRAM, Magnetic Logic and Related Devices II

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.

For tickets to the event, please register at the following link: https://magnetism.org/register

Eleonora Raimondo

2

14

Presentations

Skyrmion Caloritronics: a promising Strategy to manipulate Skyrmions

Analog multiplication implemented with spin-torque diodes for neural networks applications

Stay up to date with the latest Underline news!

PRESENTATIONS

CONFERENCES

COMPANY

RESOURCES