Fig. 4. Mechanism for field-free switching.

(A) Magnetization switching behavior as a function of the injected current density at 340 K without an applied field. (B) Schematics of intermediate states in the switching process occurring on the positive current branch. The blue arrow represents the net magnetization direction. The current pulse injection is represented by the waveform in green. The spin polarization direction $\widehat{\mathbf{p}}\mathbf{\parallel }\mathbf{-}\widehat{\mathbf{y}}$ is represented by the green arrow. (C) Schematics of the intermediate steps for switching. The beginning (end) state of the net magnetization in each step is represented by a light (dark) blue arrow. An additional light blue arrow is shown in step 2 → 3 between the beginning and end states to illustrate the competition of damping-like (τ_α) and antidamping SOT (τ_SOT) from the spin current injection. (D) Simulated magnetization dynamics from the macrospin model. The current density $j$ , effective OOP anisotropy field $H_{\mathrm{k},\text{eff}}^{\text{OOP}}$ , and magnetization components ( $m_x$ , $m_y$ , $m_z$ ) are plotted as a function of time $t_j$ , which shows the switching process through the SRT and IP switching, followed by the SRT. (E) The average and standard deviation of the final OOP magnetization, $⟨m_z^f⟩$ and $\mathrm{\sigma }\left(m_z^f\right)$ for simulation performed over a range of thermal rise times, is plotted as a function of the current density to illustrate switching regimes. The initial OOP magnetization is written as $m_z^i$ . (F) Switching regimes plotted as a function of the current density and miscut. (G) Threshold current density $j_{\text{thres}}$ for the SRT process and IP switching process plotted as a function of the relevant material parameters. (H) $j_{\text{thres}}$ for the SRT process and IP switching process plotted as a function of the EuIG film thickness $t$ . The current density colored in red shows the overall $j_{\text{thres}}$ for field-free switching.