Terahertz oscillation in a noncollinear antiferromagnet under spin-orbit torques

We perform a theoretic study on equilibria and self-oscillations of a noncollinear antiferromagnet under spin-orbit torques and focus on the latter, which may be detected by the anormal Hall effect. Appealing to the ${120}^{\ensuremath{\circ}}$ rotational symmetry, an analytically tractable single-vector equation is deduced from the complicated coupled Landau-Lifshitz-Gilbert equations. After defining the stable regions of all equilibria, we derive analytic formulas for the lower and upper thresholds of oscillation by Melnikov's method. We further reveal that the oscillation is largely pushed by the exchange interactions in the promise of an average balance between the dampinglike spin-orbit torque and the intrinsic damping. Its precessional conical angle and terahertz frequency can be adjusted by the current. We also analyze the oscillations numerically in the absence of ${120}^{\ensuremath{\circ}}$ rotational symmetry for arbitrary spin polarizations and find similar results. This can be ascribed to the relatively weak anisotropy compared with the strong exchange.