**Author details**

The efficiency of SOT switching can be calculated using the following

*SOT efficiency (η) as a function of T in Bi2Se3/BaM and Pt/BaM. The data were all measured at a field applied at an angle of 45 degrees away from the film normal direction. The data on Pt/BaM were measured with a Hall bar structure that had the same dimension as the Bi2Se3/BaM Hall bar. Source: [10], p. 6.*

*Effects of I*dc *on R*AHE *hysteresis loops at T = 3 K in Bi2Se3/BaM. Source: [10], p. 6.*

*Magnetic Materials and Magnetic Levitation*

T is > > Debye, the efficiency is proportional to *T*�<sup>1</sup>

< < Debye (at T = 100 K), the efficiency is proportional to *T*�<sup>5</sup>

*<sup>η</sup>* <sup>¼</sup> *<sup>H</sup>*SWð Þ� *<sup>I</sup>*dc <sup>&</sup>gt;<sup>0</sup> *<sup>H</sup>*SWð Þ *<sup>I</sup>*dc <sup>&</sup>lt; <sup>0</sup>

where *H*SW is the switching field, w is the Hall bar width, and t is Bi2Se3 or Pt thickness. The increase of SOT efficiency as the temperature decreases is demonstrated in **Figure 18**. The blue data points show *η* of Bi2Se3/BaM as a function of temperature. Note that the Debye temperature of Bi2Se3 is about 180 K [59]. When

efficiency is also shown as a function of temperature on the same plot (red points). The data show that decreasing the temperature has a negligible effect on the efficiency in Pt/BaM bilayers. The exponential improvement in SOT efficiency of Bi2Se3/BaM is caused by the fact that the surface conductance in TIs increases with decreasing temperatures, while the bulk conductance decreases. This means that the decrease in T enhances the TSS in TIs, resulting in a higher charge current to spin current conversion efficiency, increasing the spin polarity in TIs and therefore

<sup>2</sup>∣*I*dc∣*=*ð Þ *wt* (6)

, but when the temperature is

. Pt/BaM SOT

expression [58]:

**Figure 18.**

**56**

**Figure 17.**

Laith Alahmed and Peng Li\* Department of Electrical and Computer Engineering, Auburn University, Auburn, USA

\*Address all correspondence to: peng.li@auburn.edu

© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
