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^{1,a)}, V. E. Demidov

^{1}and S. O. Demokritov

^{1}

### Abstract

We present a numerical study of magnetization dynamics in a recently introduced spin torque nano-oscillator, whose operational principle relies on the spin-Hall effect—spin-Hall nano-oscillators. Our numerical results show good agreement with the experimentally observed behaviors and provide detailed information about the features of the primary auto-oscillation mode observed in the experiments. They also clarify the physical nature of the secondary auto-oscillation mode, which was experimentally observed under certain conditions only.

This work was supported in part by the Deutsche Forschungsgemeinschaft (DFG).

### Key Topics

- Electric currents
- 18.0
- Charged currents
- 9.0
- Static magnetic fields
- 7.0
- Magnetization dynamics
- 6.0
- Electrodes
- 4.0

##### H01F13/00

##### H01L27/20

##### H01L27/22

##### H01L41/12

##### H01L43/00

##### H03B

## Figures

(a) Schematic drawing of the investigated SHNO and visualization of the charge current flow (arrows). For illustration purposes, one quarter of the structure was left out. (b) Distribution of the charge current density in the Pt layer in the lateral section through the middle of the gap along the x-axis for two different values of the total current, as indicated. (c) Charge current distribution across the vertical section through the Pt/Py bilayer in the center of the gap.

(a) Schematic drawing of the investigated SHNO and visualization of the charge current flow (arrows). For illustration purposes, one quarter of the structure was left out. (b) Distribution of the charge current density in the Pt layer in the lateral section through the middle of the gap along the x-axis for two different values of the total current, as indicated. (c) Charge current distribution across the vertical section through the Pt/Py bilayer in the center of the gap.

(a) Typical power spectrum of STT-induced magnetic auto-oscillations in the studied system obtained at I = 20 mA and H = 1200 Oe. The dashed line marks the frequency of the ferromagnetic resonance in the Permalloy film. (b) and (c) Normalized spatial power maps corresponding to the two auto-oscillation modes at frequencies f a and f h, respectively. Dashed lines show the contours of the electrodes. (d) Sections along x-direction through the power maps shown in (b) and (c). Dashed line shows the theoretical prediction for the shape of the tails of the bullet mode.

(a) Typical power spectrum of STT-induced magnetic auto-oscillations in the studied system obtained at I = 20 mA and H = 1200 Oe. The dashed line marks the frequency of the ferromagnetic resonance in the Permalloy film. (b) and (c) Normalized spatial power maps corresponding to the two auto-oscillation modes at frequencies f a and f h, respectively. Dashed lines show the contours of the electrodes. (d) Sections along x-direction through the power maps shown in (b) and (c). Dashed line shows the theoretical prediction for the shape of the tails of the bullet mode.

(a) Current dependence of the frequency f a of the primary auto-oscillation mode and of the frequency f h of the secondary auto-oscillation mode, as labeled, obtained for H = 1200 Oe. Solid line marks the FMR frequency f 0. (b) Current dependence of integral intensity of the primary and secondary auto-oscillation modes. (c) Static-field dependences of the FMR frequency f 0 and of auto-oscillation frequencies f a and f h corresponding to currents close to the auto-oscillation onset. Dashed lines are guides to the eye.

(a) Current dependence of the frequency f a of the primary auto-oscillation mode and of the frequency f h of the secondary auto-oscillation mode, as labeled, obtained for H = 1200 Oe. Solid line marks the FMR frequency f 0. (b) Current dependence of integral intensity of the primary and secondary auto-oscillation modes. (c) Static-field dependences of the FMR frequency f 0 and of auto-oscillation frequencies f a and f h corresponding to currents close to the auto-oscillation onset. Dashed lines are guides to the eye.

(a) Spatial width of the bullet's profile in terms of the full-width at half-maximum measured along the x-direction as a function of current at fixed H = 1200 Oe (filled symbols) and as a function of field at the fixed current of 20 mA (open symbols). (b) Spatial decay rate of the bullet's tail as a function of current at fixed H = 1200 Oe (filled symbols) and as a function of field at a fixed current of 20 mA (open symbols). Dashed lines in (a) and (b) are guides for the eye. (c) Dependence of the frequency f a on k ^{2} for the simulated auto-oscillation mode (symbols) and that predicted by analytical theory of the bullet mode (solid line).

(a) Spatial width of the bullet's profile in terms of the full-width at half-maximum measured along the x-direction as a function of current at fixed H = 1200 Oe (filled symbols) and as a function of field at the fixed current of 20 mA (open symbols). (b) Spatial decay rate of the bullet's tail as a function of current at fixed H = 1200 Oe (filled symbols) and as a function of field at a fixed current of 20 mA (open symbols). Dashed lines in (a) and (b) are guides for the eye. (c) Dependence of the frequency f a on k ^{2} for the simulated auto-oscillation mode (symbols) and that predicted by analytical theory of the bullet mode (solid line).

Spatial profiles of the time-averaged x-component of magnetization ⟨m x⟩t and the time-averaged internal magnetic field ⟨H int,x⟩t in the x-section through the middle of the device determined at H = 1200 Oe and I = 20 mA. Arrows mark the positions of the minima of the internal magnetic field.

Spatial profiles of the time-averaged x-component of magnetization ⟨m x⟩t and the time-averaged internal magnetic field ⟨H int,x⟩t in the x-section through the middle of the device determined at H = 1200 Oe and I = 20 mA. Arrows mark the positions of the minima of the internal magnetic field.

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