# Theoretical Study of Field-Free Switching in PMA-MTJ Using Combined Injection of STT and SOT Currents

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## Abstract

**:**

## 1. Introduction

## 2. Landau–Lifshitz–Gilbert Equation with Spin-Transfer Torque (STT) and Spin-Orbit Torque (SOT) Terms

## 3. Results

#### COMBINED STT-SOT Induced Switching in PMA-MTJ

^{12}(refer Figure 2c). Thus, we were able to derive the relation between ${J}_{SOT}$ and ${J}_{STT}$ by linearizing the LLG equation. The magnetization dynamics of the FL under combined injection, as described by Equation (1), can be modified to the following form:

## 4. Conclusions

## 5. Methods

#### Micromagnetic Model

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**A schematic of the (

**a**) spin-transfer torque (STT) device (

**b**) spin-orbit torque (SOT) device and (

**c**) STT-SOT device.

**Figure 2.**(

**a**) Schematic of the STT-SOT device configuration used (

**b**) Magnetization m relaxing to a point of equilibrium along the ${\overrightarrow{H}}_{eff}$ direction before reversal. (

**c**) Magnetization dynamics of the FL in an STT, SOT and STT-SOT device.

**Figure 3.**Dependence of ${J}_{critical}^{STT}$ on ${\beta}_{STT}$ for $\alpha $ = 0.005, 0.01, 0.02. The solid lines and symbols represent the results obtained from Equation (6) and micromagnetic simulations respectively.

**Figure 4.**The solid line represents boundary Equation (7) above switching takes place from P to AP state (

**a**), with changing ${\beta}_{STT}$ and (

**b**) with increasing ${\beta}_{SOT}$. Symbols represent results obtained from micromagnetic simulations.

**Figure 5.**The solid line represents the boundary Equation (7). The symbols represent the results obtained from micromagnetic simulations.

Parameters | Numerical Values |
---|---|

$\gamma $ | $17.32\times {10}^{11}rad{T}^{-1}{s}^{-1}$ |

$\alpha $ | $0.005$ |

$\eta $ | $0.33$ |

${M}_{s}$ | $1.5\times {10}^{6}A/m$ [23] |

${t}_{FM}$ | 1 nm [23] |

${H}_{Keff}$ | $540Oe$ [23] |

${\theta}_{SHE}(\beta -Ta)$ | $0.1$^{4} |

${\widehat{p}}_{STT}$ | ${\widehat{e}}_{z}$ |

${\widehat{p}}_{SOT}$ | ${\widehat{e}}_{y}$ |

${\beta}_{SOT}$ | 2 |

${\beta}_{STT}$ | 1 |

A_{exchange} | 20 pJ/m |

T_{rise} (J_{STT}, J_{SOT}) | 0.5 ns |

T_{fall} (J_{STT}, J_{SOT}) | 0.5 ns |

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**MDPI and ACS Style**

Wasef, S.; Fariborzi, H. Theoretical Study of Field-Free Switching in PMA-MTJ Using Combined Injection of STT and SOT Currents. *Micromachines* **2021**, *12*, 1345.
https://doi.org/10.3390/mi12111345

**AMA Style**

Wasef S, Fariborzi H. Theoretical Study of Field-Free Switching in PMA-MTJ Using Combined Injection of STT and SOT Currents. *Micromachines*. 2021; 12(11):1345.
https://doi.org/10.3390/mi12111345

**Chicago/Turabian Style**

Wasef, Shaik, and Hossein Fariborzi. 2021. "Theoretical Study of Field-Free Switching in PMA-MTJ Using Combined Injection of STT and SOT Currents" *Micromachines* 12, no. 11: 1345.
https://doi.org/10.3390/mi12111345