Magnetic skyrmions are topologically-protected magnetization textures characterized by a non-trivial topology [1]. They have been observed in bulk materials [2] and asymmetric multilayers [3,4] in presence of a finite Dzyaloshinskii-Moriya interaction (DMI). The manipulation (nucleation, shifting, and detection) of skyrmions usually occurs via electrical currents [3], however, thermal effects have been also used to reshuffle skyrmions for low-power unconventional applications [5]. Recently, thermal gradients have been applied to magnetic multilayers where thermally-generated skyrmions unidirectionally diffuse from hot regions to cold regions [6]. This observation has been explained through the combination of repulsive forces between skyrmions, thermal spin-orbit torques, magnonic spin torques as well as entropic forces. Here, inspired by Ref. [6], we study, by means of micromagnetic simulations, the effect of thermal gradients on skyrmion motion from a fundamental point of view. We have previously demonstrated [7] that temperature induces a variation of the magnetic parameters (exchange, interfacial DMI, perpendicular anisotropy constants) which reduce with temperature following atomistically-computed scaling relations. The set of scaled values of those parameters can be used to deterministically simulate the effect of thermal fluctuations instead of a stochastic thermal field [7]. With this in mind, we consider a linear thermal gradient applied along the x-axis (Fig. 1) with the hot and cold regions placed on the left and right side, respectively. We firstly study a 1-repetition ferromagnetic sample with a number of cells Ncx=300, Ncy=300, and Ncz=1 where a Néel skyrmion is initially placed at the center of the sample. We analyze the effect of a linear gradient of only one parameter at time. The skyrmion exhibits two velocity components that follow the generalized Thiele equation [8], where the component parallel to the gradient direction depends on the parameter varied. In particular, the perpendicular anisotropy and exchange gradients move the skyrmion from the cold to the hot region, therefore to the region where those parameters are smaller. On the contrary, the saturation magnetization (magnetostatic field) and the DMI shift the skyrmion from the hot to the cold region, thus towards the region where those parameters are larger. Afterward, we study the effect of the gradients all at once, observing an overall skyrmion motion from the cold to the hot region (Fig. 1). Furthermore, we study the effect of the skyrmion profile on the thermal gradient-driven skyrmion motion. In magnetic multilayers, the skyrmion is characterized by a thickness-dependent profile which gives rise to the so-called hybrid skyrmion [4]. Therefore, we study the effect of the thermal gradients on a single hybrid skyrmion as a function of the number of ferromagnetic repetitions. Fig.1 shows a comparison of the skyrmion trajectories, where a dependence on the number of repetitions is observed. Our results can be useful for a deeper understanding of the effect of thermal gradients and therefore for the design of low-power thermally-driven skyrmion applications. This work was supported by the project “ThunderSKY,” funded by the Hellenic Foundation for Research and Innovation (HFRI) and the General Secretariat for Research and Technology (GSRT), under grant agreement No. 871.

**References:**

[1] G. Finocchio et al., J. Phys. D. Appl. Phys. 49, 423001 (2016). [2] X. Z. Yu et al., Nature 465, 901 (2010). [3] S. Woo et al., Nat. Mater. 15, 501 (2016). [4] W. Li et al., Adv. Mater. 1807683, 1 (2019). [5] J. Zázvorka et al., Nat. Nanotech. 14, 658 (2019). [6] Z. Wang et al., Nat. Electron. 3, 672 (2020). [7] R. Tomasello et al. Phys. Rev. B 97, 060402 (2018). [8] R. Tomasello et al. Phys. Rev. B 98, 024421 (2018).

**Images:**

![](https://assets.underline.io/uploads/markdown_image/1/image/e7af58671e85206fb87cfe24d058a58f.jpg)
Figure 1: skyrmion trajectory under a thermal gradient (gradients of the parameters all at once) in a magnetic multilayer for different ferromagnetic repetitions, as obtained by micromagnetic simulations. The hot and cold regions are located on the left and right side, respectively.

 Micromagnetic study of thermal gradient-driven skyrmion motion in magnetic multilayers

*Session Chair: Chun-Yeol You, Daegu Gyeongbuk Institute of Science and Technology*

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Micromagnetic study of thermal gradient-driven skyrmion motion in magnetic multilayers

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