# Tuning Intrinsic Spin Hall Effect in Platinum/Ferrimagnetic Insulator Heterostructure in Moderately Dirty Regime

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) AFM images of the surface morphology, (

**b**) surface roughness, (

**c**) XRD profiles and (

**d**) resistivity for the Pt (4 nm)/TmIG (4 nm) bilayers annealed at different temperatures. The Hall bar devices were used for the resistivity measurement by conventional four-probe method.

**Figure 2.**(

**a**) Schematic of the setup for the AHE resistance measurement. (

**b**) The typical AHE resistance curves of the Pt (4 nm)/TmIG (4 nm) devices. The SOT measurements for the devices (

**c**) annealed at 100 ${}^{\circ}$C and (

**d**) 500 ${}^{\circ}$C by sweeping ${H}_{\mathrm{z}}$ with ${H}_{\mathrm{x}}$ = 200 Oe. Slight vertical offsets for both AHE loops are introduced for clarity. (

**e**) ${H}_{\mathrm{x}}$ dependence of the SOT efficiency $\chi $ for different devices. (

**f**) The maximum SOT efficiency ${\chi}_{\mathrm{sat}}$ as a function of the annealing temperature.

**Figure 3.**(

**a**) The effective spin Hall angle ${\xi}_{\mathrm{DL}}$ by varying the annealing temperature, (

**b**) the effective spin Hall angle per unit electric field ${\xi}_{\mathrm{DL}}^{\mathrm{E}}$ = ${\xi}_{\mathrm{DL}}$/${\rho}_{\mathrm{xx}}$ by varying the annealing temperature and (

**c**) the spin Hall angle ${\theta}_{\mathrm{SHE}}$ = ${\xi}_{\mathrm{DL}}$/${T}_{\mathrm{int}}$ by varying the annealing temperature. The error bars denote the propagated error from $\chi $.

**Figure 4.**The spin Hall conductivity ${\sigma}_{\mathrm{SHE}}$ as a function of the electric conductivity ${\sigma}_{\mathrm{xx}}$. For comparison, the data in previous reports on Au${}_{\mathrm{x}}$Pt${}_{1-\mathrm{x}}$/Py [21], PtN${}_{\mathrm{x}}$/Py [15], Pt${}_{\mathrm{x}}$(MgO)${}_{1-\mathrm{x}}$/Co [19], Pt/Py [12], Pt/YIG [36], Pt/Co [37], PdO${}_{\mathrm{x}}$/Py [14], PtO${}_{\mathrm{x}}$/Py [16] and PtO${}_{\mathrm{x}}$/TmIG [38] were plotted. ${\sigma}_{\mathrm{SHE}}$∝${\sigma}_{\mathrm{xx}}$${}^{1.6}$ and ${\sigma}_{\mathrm{SHE}}$∝${\sigma}_{\mathrm{xx}}$${}^{2}$ are suggested by the AHE and SHE theories [3,39].

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**MDPI and ACS Style**

Li, T.; Liu, L.; Chen, Z.; Jia, W.; Ye, J.; Cai, X.; Huang, D.; Li, W.; Chen, F.; Li, X.;
et al. Tuning Intrinsic Spin Hall Effect in Platinum/Ferrimagnetic Insulator Heterostructure in Moderately Dirty Regime. *Nanomaterials* **2023**, *13*, 2721.
https://doi.org/10.3390/nano13192721

**AMA Style**

Li T, Liu L, Chen Z, Jia W, Ye J, Cai X, Huang D, Li W, Chen F, Li X,
et al. Tuning Intrinsic Spin Hall Effect in Platinum/Ferrimagnetic Insulator Heterostructure in Moderately Dirty Regime. *Nanomaterials*. 2023; 13(19):2721.
https://doi.org/10.3390/nano13192721

**Chicago/Turabian Style**

Li, Tianhui, Lin Liu, Zehan Chen, Wei Jia, Jianxin Ye, Xudong Cai, Doudou Huang, Wanshan Li, Fukang Chen, Xinjun Li,
and et al. 2023. "Tuning Intrinsic Spin Hall Effect in Platinum/Ferrimagnetic Insulator Heterostructure in Moderately Dirty Regime" *Nanomaterials* 13, no. 19: 2721.
https://doi.org/10.3390/nano13192721