Terahertz Antiferromagnetic Spin Hall Nano-Oscillator

We consider the current-induced dynamics of insulating antiferromagnets in a spin Hall geometry. Sufficiently large in-plane currents perpendicular to the Néel order trigger spontaneous oscillations at frequencies between the acoustic and the optical eigenmodes. The direction of the driving current determines the chirality of the excitation. When the current exceeds a threshold, the combined effect of spin pumping and current-induced torques introduces a dynamic feedback that sustains steady-state oscillations with amplitudes controllable via the applied current. The ac voltage output is calculated numerically as a function of the dc current input for different feedback strengths. Our findings open a route towards terahertz antiferromagnetic spin-torque oscillators.

Figure 1

Evolutions of the eigenfrequencies and the eigenmodes of NiO [30] with an increasing STT. In the region ${\omega }_s<{\omega }_{\perp }/2$, $\mathrm{Re}[{\omega }_{+}]$ and $\mathrm{Re}[{\omega }_{-}]$ approach each other with the increasing STT while $\mathrm{Im}[{\omega }_{\pm }]$ remains degenerate. Both ${\mathit{m}}_A$ and ${\mathit{m}}_B$ precess elliptically with opposite chiralities. As ${\omega }_s$ increases, the long axis of the optical (acoustic) precession tilts away from the $z$ axis ($y$ axis). At ${\omega }_s={\omega }_{\perp }/2$, $\mathrm{Re}[{\omega }_{+}]$ and $\mathrm{Re}[{\omega }_{-}]$ become degenerate while $\mathrm{Im}[{\omega }_{+}]$ and $\mathrm{Im}[{\omega }_{-}]$ separate; the elliptical orbit traversed by ${\mathit{m}}_B$ (${\mathit{m}}_A$) in the optical (acoustic) mode shrinks into a line and then opens up into an ellipse again, with its chirality changing sign. Hence, for ${\omega }_s>{\omega }_{\perp }/2$, ${\mathit{m}}_A$, ${\mathit{m}}_B$, and $\mathit{\ell }$ in the optical (acoustic) mode all have the right-handed (left-handed) chirality. At $\omega =0.55{\omega }_{\perp }$, $\mathrm{Im}[{\omega }_{+}]$ vanishes, the optical mode is excited, and the linear response breaks down.

Figure 2

An insulating AF/HM heterostructure. The applied dc current density ${\mathit{J}}_c$ drives the AF via the SHE. The dynamics of the AF pumps spin current back into N, and converts into electric field via the inverse SHE, which is monitored by two voltmeters.

Figure 3

Phase diagram of a SHNO based on the $\mathrm{NiO}(1)/\mathrm{Pt}(25)$ bilayer structure. Phases are characterized by the numerical result of the time-averaged terminal angle $\overline{\theta }\equiv (1/T)\underset{t\to \infty }{\lim }{\int }_t^{t+T}d{t}^{\prime }\arcsin |{\mathit{\ell }}_{\perp }(t^{\prime })|$ as a function of the applied current density $J_c({10}^8\mathrm{A}/{\mathrm{cm}}^2)\in [2.27,5.00]$ and the feedback strength ${\alpha }_{\mathrm{NL}}\in [0,0.03]$. Upper panels: the stable oscillation phase (left) differs from the proliferation phase (right) in that the orbits of ${\mathit{m}}_A$ and ${\mathit{m}}_B$ do not overlap, and the cone angle of the Néel vector $\theta <\pi /2$.

Figure 4

Numerical results of multiple ac outputs associated with steady-state oscillations (at $t\to \infty$) in the range $J_c({10}^8\mathrm{A}/{\mathrm{cm}}^2)\in [2.27,5.00]$ and ${\alpha }_{\mathrm{NL}}\in [0,0.03]$ for a $\mathrm{NiO}(1)/\mathrm{Pt}(25)$ heterostructure. (a) Frequency output. (b) and (c): two perpendicular ac components (in effective values) of the electric field generated by the SHE and the spin pumping.